|\^/| 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(c(1.0) + cos(c(x))); > end; exact_soln_y1 := proc(x) return c(1.0) + cos(c(x)) end proc > exact_soln_y2 := proc(x) > return(c(1.0) - sin(c(x))); > end; exact_soln_y2 := proc(x) return c(1.0) - 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 + 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 + 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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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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 - 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_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 - 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_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 - 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_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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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 - 11; 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 - 11; 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 - 11; 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_1, > array_const_0D0, > array_const_1D0, #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_tmp5, > 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 neg FULL $eq_no = 1 > array_tmp1[1] := neg(array_y1[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y2_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp5[1] := array_y2[1] - array_const_1D0[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_tmp5[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 neg FULL $eq_no = 1 > array_tmp1[2] := neg(array_y1[2]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp5[2] := array_y2[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_tmp5[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 neg FULL $eq_no = 1 > array_tmp1[3] := neg(array_y1[3]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp5[3] := array_y2[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_tmp5[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 neg FULL $eq_no = 1 > array_tmp1[4] := neg(array_y1[4]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp5[4] := array_y2[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_tmp5[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 neg FULL $eq_no = 1 > array_tmp1[5] := neg(array_y1[5]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > 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); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp5[5] := array_y2[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_tmp5[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 neg FULL $eq_no = 1 > array_tmp1[kkk] := neg(array_y1[kkk]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > 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_tmp3[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 FULL - NOT FULL sub $eq_no = 2 > array_tmp5[kkk] := array_y2[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_tmp5[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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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] := neg(array_y1[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y2_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y2[2] := temporary; array_y2_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y2_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp5[1] := array_y2[1] - array_const_1D0[1]; if not array_y1_set_initial[2, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[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] := neg(array_y1[2]); array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y2_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y2[3] := temporary; array_y2_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp5[2] := array_y2[2]; if not array_y1_set_initial[2, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[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] := neg(array_y1[3]); array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y2_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y2[4] := temporary; array_y2_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp5[3] := array_y2[3]; if not array_y1_set_initial[2, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[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] := neg(array_y1[4]); array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y2_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y2[5] := temporary; array_y2_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp5[4] := array_y2[4]; if not array_y1_set_initial[2, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[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] := neg(array_y1[5]); array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y2_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 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) end if end if; kkk := 6; array_tmp5[5] := array_y2[5]; if not array_y1_set_initial[2, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[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] := neg(array_y1[kkk]); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y2_set_initial[1, kkk + order_d] then temporary := c(array_tmp3[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; array_tmp5[kkk] := array_y2[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_tmp5[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_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > 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:=16; > 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_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y2_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y2_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y2_higher_work2 := Array(0..(2) ,(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_tmp5[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 <=2) 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 <=2) 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 <=2) 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_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_1D0); > array_const_1D0[1] := c(1.0); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_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] := false; > array_y2_set_initial[1,3] := false; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > 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/mtest3postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; "); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = y2 - 1.0 ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=16;"); > 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,"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,""); > 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(c(1.0) + cos(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(c(1.0) - 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); > 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 := 1; > #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 <= 2) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 2 + 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 := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #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 := 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 , 1 ) = neg ( y1 ) + 1.0 ; "); > omniout_str(INFO,"diff ( y1 , x , 1 ) = y2 - 1.0 ; "); > 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,"2017-11-26T15:18:11-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest3") > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; ") > ; > 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,"mtest3 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest3 maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = y2 - 1.0 ; ") > ; > 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_1, array_const_0D0, array_const_1D0, 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_tmp5, 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 := 16; 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_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y2_higher := Array(0 .. 2, 0 .. 41, []); array_y2_higher_work := Array(0 .. 2, 0 .. 41, []); array_y2_higher_work2 := Array(0 .. 2, 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_tmp5[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 <= 2 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 <= 2 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 <= 2 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_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_1D0); array_const_1D0[1] := c(1.0); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_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] := false; array_y2_set_initial[1, 3] := false; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; 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/mtest3postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; "); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0 ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=16;"); 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, "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, ""); 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(c(1.0) + cos(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(c(1.0) - 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 * 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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); 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 := 1; 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 <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + 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 := 2; 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 := 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 , 1 ) = neg ( y1 ) + 1.0 ; "); omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0 ; ") ; 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, "2017-11-26T15:18:11-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest3"); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; ") ; 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, "mtest3 diffeq.mxt"); logitem_str(html_log_file, "mtest3 maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = y2 - 1.0 ; "); 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=3.7MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/mtest3postcpx.cpx################# diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; ! #BEGIN FIRST INPUT BLOCK Digits:=16; 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); 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(c(1.0) + cos(c(x))); end; exact_soln_y2 := proc(x) return(c(1.0) - 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 x[1] = 0.1 0.1 h = 0.0001 0.005 y2[1] (numeric) = 0.899667000159 -0.0996663334921 y2[1] (closed_form) = 0.899667000159 -0.0996663334921 absolute error = 0 relative error = 0 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 1.99998333334 -0.00999998888889 y1[1] (closed_form) = 1.99998333334 -0.00999998888889 absolute error = 0 relative error = 0 % Correct digits = 14 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=54.4MB, alloc=40.3MB, time=0.72 x[1] = 0.1001 0.105 h = 0.0001 0.003 y2[1] (numeric) = 0.899515696926 -0.104666466122 y2[1] (closed_form) = 0.899515696926 -0.104666466122 absolute error = 1e-16 relative error = 1.104e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.00048412347 -0.0105122476776 y1[1] (closed_form) = 2.00048412347 -0.0105122476776 absolute error = 0 relative error = 0 % Correct digits = 14 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=101.9MB, alloc=40.3MB, time=1.35 x[1] = 0.1002 0.108 h = 0.001 0.001 y2[1] (numeric) = 0.899383628196 -0.107667312081 y2[1] (closed_form) = 0.899383628196 -0.107667312081 absolute error = 1e-16 relative error = 1.104e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.00079256889 -0.0108245151295 y1[1] (closed_form) = 2.00079256889 -0.0108245151295 absolute error = 0 relative error = 0 % Correct digits = 14 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=149.7MB, alloc=40.3MB, time=1.97 x[1] = 0.1012 0.109 h = 0.001 0.003 y2[1] (numeric) = 0.898371903115 -0.108657179181 y2[1] (closed_form) = 0.898371903115 -0.108657179181 absolute error = 1e-16 relative error = 1.105e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.00079960894 -0.0110337996083 y1[1] (closed_form) = 2.00079960894 -0.0110337996083 absolute error = 1e-15 relative error = 4.998e-14 % Correct digits = 15 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 x[1] = 0.1022 0.112 h = 0.0001 0.004 y2[1] (numeric) = 0.897337265253 -0.111648676907 y2[1] (closed_form) = 0.897337265253 -0.111648676907 absolute error = 1.414e-16 relative error = 1.564e-14 % Correct digits = 16 h = 0.0001 0.004 y1[1] (numeric) = 2.00102792236 -0.0114503883919 y1[1] (closed_form) = 2.00102792236 -0.0114503883919 absolute error = 1e-15 relative error = 4.997e-14 % Correct digits = 15 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=197.2MB, alloc=40.3MB, time=2.59 x[1] = 0.1023 0.116 h = 0.003 0.006 y2[1] (numeric) = 0.897190494535 -0.115652505773 y2[1] (closed_form) = 0.897190494535 -0.115652505773 absolute error = 2e-16 relative error = 2.211e-14 % Correct digits = 16 h = 0.003 0.006 y1[1] (numeric) = 2.00147225055 -0.0118726973391 y1[1] (closed_form) = 2.00147225055 -0.0118726973391 absolute error = 1e-15 relative error = 4.996e-14 % Correct digits = 15 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=245.0MB, alloc=40.3MB, time=3.22 x[1] = 0.1053 0.122 h = 0.0001 0.005 y2[1] (numeric) = 0.894111322239 -0.121625440337 y2[1] (closed_form) = 0.894111322239 -0.121625440337 absolute error = 2.236e-16 relative error = 2.478e-14 % Correct digits = 16 h = 0.0001 0.005 y1[1] (numeric) = 2.00187103916 -0.0128547054021 y1[1] (closed_form) = 2.00187103916 -0.0128547054021 absolute error = 1e-15 relative error = 4.995e-14 % Correct digits = 15 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=292.6MB, alloc=40.3MB, time=3.84 x[1] = 0.1054 0.127 h = 0.0001 0.003 y2[1] (numeric) = 0.893945476194 -0.126634997662 y2[1] (closed_form) = 0.893945476194 -0.126634997662 absolute error = 2.236e-16 relative error = 2.477e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.00248109187 -0.0133969752478 y1[1] (closed_form) = 2.00248109187 -0.0133969752478 absolute error = 1.000e-15 relative error = 4.994e-14 % Correct digits = 15 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 x[1] = 0.1055 0.13 h = 0.001 0.001 y2[1] (numeric) = 0.893804521942 -0.129641643138 y2[1] (closed_form) = 0.893804521942 -0.129641643138 absolute error = 2.236e-16 relative error = 2.476e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.00285489407 -0.0137281638158 y1[1] (closed_form) = 2.00285489407 -0.0137281638158 absolute error = 1e-15 relative error = 4.993e-14 % Correct digits = 15 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=340.0MB, alloc=40.3MB, time=4.46 x[1] = 0.1065 0.131 h = 0.001 0.003 y2[1] (numeric) = 0.892787808913 -0.130630663334 y2[1] (closed_form) = 0.892787808913 -0.130630663334 absolute error = 1.414e-16 relative error = 1.567e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.00287832643 -0.0139650037997 y1[1] (closed_form) = 2.00287832643 -0.0139650037997 absolute error = 1e-15 relative error = 4.993e-14 % Correct digits = 15 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=387.7MB, alloc=40.3MB, time=5.08 x[1] = 0.1075 0.134 h = 0.0001 0.004 y2[1] (numeric) = 0.891742210446 -0.133625537144 y2[1] (closed_form) = 0.891742210446 -0.133625537144 absolute error = 1.414e-16 relative error = 1.568e-14 % Correct digits = 16 h = 0.0001 0.004 y1[1] (numeric) = 2.00316697577 -0.014420336423 y1[1] (closed_form) = 2.00316697577 -0.014420336423 absolute error = 1e-15 relative error = 4.992e-14 % Correct digits = 15 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 x[1] = 0.1076 0.138 h = 0.003 0.006 y2[1] (numeric) = 0.891583292474 -0.137637798716 y2[1] (closed_form) = 0.891583292474 -0.137637798716 absolute error = 2.236e-16 relative error = 2.479e-14 % Correct digits = 16 h = 0.003 0.006 y1[1] (numeric) = 2.00369866804 -0.014867247953 y1[1] (closed_form) = 2.00369866804 -0.014867247953 absolute error = 1e-15 relative error = 4.991e-14 % Correct digits = 15 memory used=435.4MB, alloc=40.3MB, time=5.70 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 x[1] = 0.1106 0.144 h = 0.0001 0.005 y2[1] (numeric) = 0.888479002051 -0.143615303875 y2[1] (closed_form) = 0.888479002051 -0.143615303875 absolute error = 2.236e-16 relative error = 2.484e-14 % Correct digits = 16 h = 0.0001 0.005 y1[1] (numeric) = 2.00421252288 -0.015948936748 y1[1] (closed_form) = 2.00421252288 -0.015948936748 absolute error = 1.000e-15 relative error = 4.990e-14 % Correct digits = 15 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=483.0MB, alloc=40.3MB, time=6.32 x[1] = 0.1107 0.149 h = 0.0001 0.003 y2[1] (numeric) = 0.888297369262 -0.148636531188 y2[1] (closed_form) = 0.888297369262 -0.148636531188 absolute error = 2.236e-16 relative error = 2.483e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.00493198983 -0.0165216071589 y1[1] (closed_form) = 2.00493198983 -0.0165216071589 absolute error = 1.000e-15 relative error = 4.988e-14 % Correct digits = 15 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=530.6MB, alloc=40.3MB, time=6.94 x[1] = 0.1108 0.152 h = 0.001 0.001 y2[1] (numeric) = 0.888146764021 -0.151650314108 y2[1] (closed_form) = 0.888146764021 -0.151650314108 absolute error = 2.236e-16 relative error = 2.482e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.005371242 -0.0168719550168 y1[1] (closed_form) = 2.005371242 -0.0168719550168 absolute error = 1.000e-15 relative error = 4.987e-14 % Correct digits = 15 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 x[1] = 0.1118 0.153 h = 0.001 0.003 y2[1] (numeric) = 0.887124368844 -0.152638701201 y2[1] (closed_form) = 0.887124368844 -0.152638701201 absolute error = 2.236e-16 relative error = 2.484e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.00541102212 -0.0171364639514 y1[1] (closed_form) = 2.00541102212 -0.0171364639514 absolute error = 1.000e-15 relative error = 4.987e-14 % Correct digits = 15 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=578.3MB, alloc=40.3MB, time=7.57 x[1] = 0.1128 0.156 h = 0.0001 0.004 y2[1] (numeric) = 0.886066634603 -0.155638072673 y2[1] (closed_form) = 0.886066634603 -0.155638072673 absolute error = 2e-16 relative error = 2.223e-14 % Correct digits = 16 h = 0.0001 0.004 y1[1] (numeric) = 2.00576003279 -0.0176308153291 y1[1] (closed_form) = 2.00576003279 -0.0176308153291 absolute error = 1.000e-15 relative error = 4.986e-14 % Correct digits = 15 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=625.9MB, alloc=40.3MB, time=8.19 x[1] = 0.1129 0.16 h = 0.003 0.006 y2[1] (numeric) = 0.885894561192 -0.159660559171 y2[1] (closed_form) = 0.885894561192 -0.159660559171 absolute error = 2.236e-16 relative error = 2.484e-14 % Correct digits = 16 h = 0.003 0.006 y1[1] (numeric) = 2.00637922732 -0.0181026571991 y1[1] (closed_form) = 2.00637922732 -0.0181026571991 absolute error = 1.000e-15 relative error = 4.984e-14 % Correct digits = 15 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=673.6MB, alloc=40.3MB, time=8.82 x[1] = 0.1159 0.166 h = 0.0001 0.005 y2[1] (numeric) = 0.882762343264 -0.165644636231 y2[1] (closed_form) = 0.882762343264 -0.165644636231 absolute error = 2.236e-16 relative error = 2.490e-14 % Correct digits = 16 h = 0.0001 0.005 y1[1] (numeric) = 2.0070081304 -0.0192846397327 y1[1] (closed_form) = 2.0070081304 -0.0192846397327 absolute error = 1e-17 relative error = 4.982e-16 % Correct digits = 17 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 x[1] = 0.116 0.171 h = 0.0001 0.003 y2[1] (numeric) = 0.882563669882 -0.170679780464 y2[1] (closed_form) = 0.882563669882 -0.170679780464 absolute error = 2.236e-16 relative error = 2.488e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.00783720606 -0.0198881395948 y1[1] (closed_form) = 2.00783720606 -0.0198881395948 absolute error = 1e-15 relative error = 4.980e-14 % Correct digits = 15 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=721.1MB, alloc=40.3MB, time=9.44 x[1] = 0.1161 0.174 h = 0.001 0.001 y2[1] (numeric) = 0.88240264212 -0.173702039755 y2[1] (closed_form) = 0.88240264212 -0.173702039755 absolute error = 2.236e-16 relative error = 2.486e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.00834202675 -0.0202579089155 y1[1] (closed_form) = 2.00834202675 -0.0202579089155 absolute error = 1e-15 relative error = 4.979e-14 % Correct digits = 15 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=768.8MB, alloc=40.3MB, time=10.06 x[1] = 0.1171 0.175 h = 0.001 0.003 y2[1] (numeric) = 0.881373868153 -0.174690005932 y2[1] (closed_form) = 0.881373868153 -0.174690005932 absolute error = 2e-16 relative error = 2.226e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.00839811108 -0.0205502166739 y1[1] (closed_form) = 2.00839811108 -0.0205502166739 absolute error = 1e-15 relative error = 4.979e-14 % Correct digits = 15 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=816.5MB, alloc=40.3MB, time=10.70 x[1] = 0.1181 0.178 h = 0.0001 0.004 y2[1] (numeric) = 0.880302816385 -0.177694995866 y2[1] (closed_form) = 0.880302816385 -0.177694995866 absolute error = 3e-16 relative error = 3.341e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.00880752691 -0.0210838935875 y1[1] (closed_form) = 2.00880752691 -0.0210838935875 absolute error = 1e-15 relative error = 4.978e-14 % Correct digits = 15 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 x[1] = 0.1182 0.182 h = 0.003 0.006 y2[1] (numeric) = 0.880116570968 -0.181729501103 y2[1] (closed_form) = 0.880116570968 -0.181729501103 absolute error = 2e-16 relative error = 2.225e-14 % Correct digits = 16 h = 0.003 0.006 y1[1] (numeric) = 2.00951439597 -0.0215810253281 y1[1] (closed_form) = 2.00951439597 -0.0215810253281 absolute error = 1e-15 relative error = 4.976e-14 % Correct digits = 15 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=864.2MB, alloc=40.3MB, time=11.32 x[1] = 0.1212 0.188 h = 0.0001 0.005 y2[1] (numeric) = 0.876953601894 -0.187722147852 y2[1] (closed_form) = 0.876953601894 -0.187722147852 absolute error = 2e-16 relative error = 2.230e-14 % Correct digits = 16 h = 0.0001 0.005 y1[1] (numeric) = 2.01025835835 -0.0228639871644 y1[1] (closed_form) = 2.01025835835 -0.0228639871644 absolute error = 1e-15 relative error = 4.974e-14 % Correct digits = 15 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=911.9MB, alloc=40.3MB, time=11.95 x[1] = 0.1213 0.193 h = 0.0001 0.003 y2[1] (numeric) = 0.876736623054 -0.192773458308 y2[1] (closed_form) = 0.876736623054 -0.192773458308 absolute error = 3e-16 relative error = 3.342e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.01119727997 -0.0234987849821 y1[1] (closed_form) = 2.01119727997 -0.0234987849821 absolute error = 1e-15 relative error = 4.972e-14 % Correct digits = 15 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=959.5MB, alloc=40.3MB, time=12.57 x[1] = 0.1214 0.196 h = 0.001 0.001 y2[1] (numeric) = 0.87656439451 -0.195805534333 y2[1] (closed_form) = 0.87656439451 -0.195805534333 absolute error = 2e-16 relative error = 2.227e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.01176781311 -0.0238882620851 y1[1] (closed_form) = 2.01176781311 -0.0238882620851 absolute error = 1.000e-15 relative error = 4.971e-14 % Correct digits = 15 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 x[1] = 0.1224 0.197 h = 0.0001 0.004 y2[1] (numeric) = 0.8755285423 -0.196793290103 y2[1] (closed_form) = 0.8755285423 -0.196793290103 absolute error = 2e-16 relative error = 2.229e-14 % Correct digits = 16 h = 0.0001 0.004 y1[1] (numeric) = 2.01184015904 -0.0242085150168 y1[1] (closed_form) = 2.01184015904 -0.0242085150168 absolute error = 1.000e-15 relative error = 4.970e-14 % Correct digits = 15 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=1007.1MB, alloc=40.3MB, time=13.19 x[1] = 0.1225 0.201 h = 0.003 0.006 y2[1] (numeric) = 0.875329449288 -0.200839764217 y2[1] (closed_form) = 0.875329449288 -0.200839764217 absolute error = 3.162e-16 relative error = 3.521e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.01262296704 -0.0247266799437 y1[1] (closed_form) = 2.01262296704 -0.0247266799437 absolute error = 1e-15 relative error = 4.968e-14 % Correct digits = 15 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=1054.8MB, alloc=40.3MB, time=13.82 x[1] = 0.1255 0.207 h = 0.0001 0.005 y2[1] (numeric) = 0.872137871779 -0.206841797121 y2[1] (closed_form) = 0.872137871779 -0.206841797121 absolute error = 3.162e-16 relative error = 3.528e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.01346721491 -0.0260957947093 y1[1] (closed_form) = 2.01346721491 -0.0260957947093 absolute error = 1e-15 relative error = 4.966e-14 % Correct digits = 15 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=1102.6MB, alloc=40.3MB, time=14.44 x[1] = 0.1256 0.212 h = 0.0001 0.003 y2[1] (numeric) = 0.871904343212 -0.211909065234 y2[1] (closed_form) = 0.871904343212 -0.211909065234 absolute error = 2.236e-16 relative error = 2.492e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.01450129208 -0.0267566252526 y1[1] (closed_form) = 2.01450129208 -0.0267566252526 absolute error = 1e-15 relative error = 4.964e-14 % Correct digits = 15 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 x[1] = 0.1257 0.215 h = 0.001 0.001 y2[1] (numeric) = 0.871721983267 -0.214950812089 y2[1] (closed_form) = 0.871721983267 -0.214950812089 absolute error = 2.236e-16 relative error = 2.491e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.01512876276 -0.0271625284212 y1[1] (closed_form) = 2.01512876276 -0.0271625284212 absolute error = 1e-15 relative error = 4.962e-14 % Correct digits = 15 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=1150.2MB, alloc=40.3MB, time=15.06 x[1] = 0.1267 0.216 h = 0.001 0.003 y2[1] (numeric) = 0.870679476696 -0.215938649698 y2[1] (closed_form) = 0.870679476696 -0.215938649698 absolute error = 2.236e-16 relative error = 2.493e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.01521540828 -0.0275067724077 y1[1] (closed_form) = 2.01521540828 -0.0275067724077 absolute error = 0 relative error = 0 % Correct digits = 14 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=1198.0MB, alloc=40.3MB, time=15.69 x[1] = 0.1277 0.219 h = 0.0001 0.004 y2[1] (numeric) = 0.86958057139 -0.218957267869 y2[1] (closed_form) = 0.86958057139 -0.218957267869 absolute error = 2.828e-16 relative error = 3.154e-14 % Correct digits = 16 h = 0.0001 0.004 y1[1] (numeric) = 2.01573788214 -0.0281138296284 y1[1] (closed_form) = 2.01573788214 -0.0281138296284 absolute error = 0 relative error = 0 % Correct digits = 14 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=1245.9MB, alloc=40.3MB, time=16.32 x[1] = 0.1278 0.223 h = 0.003 0.006 y2[1] (numeric) = 0.869365410884 -0.223019117204 y2[1] (closed_form) = 0.869365410884 -0.223019117204 absolute error = 2.828e-16 relative error = 3.151e-14 % Correct digits = 16 h = 0.003 0.006 y1[1] (numeric) = 2.01660878108 -0.0286580356999 y1[1] (closed_form) = 2.01660878108 -0.0286580356999 absolute error = 0 relative error = 0 % Correct digits = 14 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 x[1] = 0.1308 0.229 h = 0.0001 0.005 y2[1] (numeric) = 0.86613780782 -0.229033462834 y2[1] (closed_form) = 0.86613780782 -0.229033462834 absolute error = 2.828e-16 relative error = 3.157e-14 % Correct digits = 16 h = 0.0001 0.005 y1[1] (numeric) = 2.01756819591 -0.0301295987246 y1[1] (closed_form) = 2.01756819591 -0.0301295987246 absolute error = 1e-17 relative error = 4.956e-16 % Correct digits = 17 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=1293.5MB, alloc=40.3MB, time=16.94 x[1] = 0.1309 0.234 h = 0.0001 0.003 y2[1] (numeric) = 0.865883613979 -0.234121106838 y2[1] (closed_form) = 0.865883613979 -0.234121106838 absolute error = 2.828e-16 relative error = 3.153e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.01871268108 -0.0308227013598 y1[1] (closed_form) = 2.01871268108 -0.0308227013598 absolute error = 1e-17 relative error = 4.953e-16 % Correct digits = 17 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=1341.4MB, alloc=40.3MB, time=17.57 x[1] = 0.131 0.237 h = 0.001 0.001 y2[1] (numeric) = 0.86568860092 -0.237175179306 y2[1] (closed_form) = 0.86568860092 -0.237175179306 absolute error = 3.606e-16 relative error = 4.017e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.01940620362 -0.0312489074978 y1[1] (closed_form) = 2.01940620362 -0.0312489074978 absolute error = 1.000e-15 relative error = 4.952e-14 % Correct digits = 15 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=1389.1MB, alloc=40.3MB, time=18.20 x[1] = 0.132 0.238 h = 0.001 0.003 y2[1] (numeric) = 0.864637708305 -0.238163201941 y2[1] (closed_form) = 0.864637708305 -0.238163201941 absolute error = 2.236e-16 relative error = 2.493e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.01950903603 -0.0316214135167 y1[1] (closed_form) = 2.01950903603 -0.0316214135167 absolute error = 2e-17 relative error = 9.902e-16 % Correct digits = 17 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 x[1] = 0.133 0.241 h = 0.0001 0.004 y2[1] (numeric) = 0.863522074576 -0.241190657123 y2[1] (closed_form) = 0.863522074576 -0.241190657123 absolute error = 3.162e-16 relative error = 3.527e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.02009214664 -0.0322688500487 y1[1] (closed_form) = 2.02009214664 -0.0322688500487 absolute error = 2e-17 relative error = 9.899e-16 % Correct digits = 17 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=1436.5MB, alloc=44.3MB, time=18.82 x[1] = 0.1331 0.245 h = 0.003 0.006 y2[1] (numeric) = 0.863289801182 -0.245269683389 y2[1] (closed_form) = 0.863289801182 -0.245269683389 absolute error = 3.162e-16 relative error = 3.524e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.02105140668 -0.0328395484898 y1[1] (closed_form) = 2.02105140668 -0.0328395484898 absolute error = 1.000e-15 relative error = 4.948e-14 % Correct digits = 15 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=1484.4MB, alloc=44.3MB, time=19.45 x[1] = 0.1361 0.251 h = 0.0001 0.005 y2[1] (numeric) = 0.860023298375 -0.251298331088 y2[1] (closed_form) = 0.860023298375 -0.251298331088 absolute error = 2.236e-16 relative error = 2.496e-14 % Correct digits = 16 h = 0.0001 0.005 y1[1] (numeric) = 2.02212608268 -0.0344144544453 y1[1] (closed_form) = 2.02212608268 -0.0344144544453 absolute error = 1.000e-15 relative error = 4.947e-14 % Correct digits = 15 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=1532.1MB, alloc=44.3MB, time=20.08 x[1] = 0.1362 0.256 h = 0.0001 0.003 y2[1] (numeric) = 0.859747136839 -0.256408611272 y2[1] (closed_form) = 0.859747136839 -0.256408611272 absolute error = 2.236e-16 relative error = 2.492e-14 % Correct digits = 16 h = 0.0001 0.003 y1[1] (numeric) = 2.023381336 -0.035140412088 y1[1] (closed_form) = 2.023381336 -0.035140412088 absolute error = 1.000e-15 relative error = 4.944e-14 % Correct digits = 15 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 x[1] = 0.1363 0.259 h = 0.001 0.001 y2[1] (numeric) = 0.859538669491 -0.259476356295 y2[1] (closed_form) = 0.859538669491 -0.259476356295 absolute error = 2.236e-16 relative error = 2.490e-14 % Correct digits = 16 h = 0.001 0.001 y1[1] (numeric) = 2.02414112719 -0.0355872772541 y1[1] (closed_form) = 2.02414112719 -0.0355872772541 absolute error = 4e-17 relative error = 1.976e-15 % Correct digits = 17 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=1579.9MB, alloc=44.3MB, time=20.70 x[1] = 0.1373 0.26 h = 0.001 0.003 y2[1] (numeric) = 0.858478681281 -0.26046476933 y2[1] (closed_form) = 0.858478681281 -0.26046476933 absolute error = 2.236e-16 relative error = 2.492e-14 % Correct digits = 16 h = 0.001 0.003 y1[1] (numeric) = 2.0242601065 -0.0359882391217 y1[1] (closed_form) = 2.0242601065 -0.0359882391217 absolute error = 4e-17 relative error = 1.976e-15 % Correct digits = 17 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=1627.6MB, alloc=44.3MB, time=21.33 x[1] = 0.1383 0.263 h = 0.0001 0.004 y2[1] (numeric) = 0.85734510443 -0.263502181622 y2[1] (closed_form) = 0.85734510443 -0.263502181622 absolute error = 3.162e-16 relative error = 3.526e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.02490396873 -0.0366764861378 y1[1] (closed_form) = 2.02490396873 -0.0366764861378 absolute error = 5e-17 relative error = 2.469e-15 % Correct digits = 17 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 x[1] = 0.1384 0.267 h = 0.003 0.006 y2[1] (numeric) = 0.857094660949 -0.267600190372 y2[1] (closed_form) = 0.857094660949 -0.267600190372 absolute error = 3.606e-16 relative error = 4.016e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.02595189411 -0.0372741608594 y1[1] (closed_form) = 2.02595189411 -0.0372741608594 absolute error = 4e-17 relative error = 1.974e-15 % Correct digits = 17 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=1675.4MB, alloc=44.3MB, time=21.95 x[1] = 0.1414 0.273 h = 0.0001 0.005 y2[1] (numeric) = 0.853786363138 -0.273645126931 y2[1] (closed_form) = 0.853786363138 -0.273645126931 absolute error = 3.606e-16 relative error = 4.022e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.02714195396 -0.0389533784147 y1[1] (closed_form) = 2.02714195396 -0.0389533784147 absolute error = 4e-17 relative error = 1.973e-15 % Correct digits = 17 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=1723.0MB, alloc=44.3MB, time=22.58 x[1] = 0.1415 0.278 h = 0.0001 0.003 y2[1] (numeric) = 0.85348691619 -0.278780308783 y2[1] (closed_form) = 0.85348691619 -0.278780308783 absolute error = 3.606e-16 relative error = 4.016e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.02850837843 -0.0397128147928 y1[1] (closed_form) = 2.02850837843 -0.0397128147928 absolute error = 4e-17 relative error = 1.972e-15 % Correct digits = 17 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=1770.9MB, alloc=44.3MB, time=23.20 x[1] = 0.1416 0.281 h = 0.001 0.001 y2[1] (numeric) = 0.853264184056 -0.281863076396 y2[1] (closed_form) = 0.853264184056 -0.281863076396 absolute error = 3.606e-16 relative error = 4.012e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.02933468047 -0.0401807199198 y1[1] (closed_form) = 2.02933468047 -0.0401807199198 absolute error = 4e-17 relative error = 1.971e-15 % Correct digits = 17 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 x[1] = 0.1426 0.282 h = 0.001 0.003 y2[1] (numeric) = 0.852194386463 -0.282852083264 y2[1] (closed_form) = 0.852194386463 -0.282852083264 absolute error = 3.606e-16 relative error = 4.015e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.0294697674 -0.0406103481919 y1[1] (closed_form) = 2.0294697674 -0.0406103481919 absolute error = 3e-17 relative error = 1.478e-15 % Correct digits = 17 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=1818.7MB, alloc=44.3MB, time=23.82 x[1] = 0.1436 0.285 h = 0.0001 0.004 y2[1] (numeric) = 0.851041641288 -0.285900573122 y2[1] (closed_form) = 0.851041641288 -0.285900573122 absolute error = 3.606e-16 relative error = 4.016e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.0301745143 -0.0413398696397 y1[1] (closed_form) = 2.0301745143 -0.0413398696397 absolute error = 4e-17 relative error = 1.970e-15 % Correct digits = 17 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=1866.4MB, alloc=44.3MB, time=24.44 x[1] = 0.1437 0.289 h = 0.003 0.006 y2[1] (numeric) = 0.85077195781 -0.290019374322 y2[1] (closed_form) = 0.85077195781 -0.290019374322 absolute error = 3.606e-16 relative error = 4.011e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.0313114434 -0.04196503753 y1[1] (closed_form) = 2.0313114434 -0.04196503753 absolute error = 4e-17 relative error = 1.969e-15 % Correct digits = 17 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=1914.2MB, alloc=44.3MB, time=25.07 x[1] = 0.1467 0.295 h = 0.0001 0.005 y2[1] (numeric) = 0.847418946879 -0.296082584212 y2[1] (closed_form) = 0.847418946879 -0.296082584212 absolute error = 4.243e-16 relative error = 4.726e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.03261703805 -0.0437496098217 y1[1] (closed_form) = 2.03261703805 -0.0437496098217 absolute error = 4e-17 relative error = 1.967e-15 % Correct digits = 17 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 x[1] = 0.1468 0.3 h = 0.0001 0.003 y2[1] (numeric) = 0.847094880379 -0.301244939142 y2[1] (closed_form) = 0.847094880379 -0.301244939142 absolute error = 4.472e-16 relative error = 4.974e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.03409507953 -0.0445431898539 y1[1] (closed_form) = 2.03409507953 -0.0445431898539 absolute error = 5e-17 relative error = 2.458e-15 % Correct digits = 17 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=1961.7MB, alloc=44.3MB, time=25.68 x[1] = 0.1469 0.303 h = 0.001 0.001 y2[1] (numeric) = 0.846857062954 -0.304344082905 y2[1] (closed_form) = 0.846857062954 -0.304344082905 absolute error = 4.472e-16 relative error = 4.970e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.03498816002 -0.0450325409788 y1[1] (closed_form) = 2.03498816002 -0.0450325409788 absolute error = 5e-17 relative error = 2.456e-15 % Correct digits = 17 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=2009.5MB, alloc=44.3MB, time=26.31 x[1] = 0.1479 0.304 h = 0.0001 0.004 y2[1] (numeric) = 0.845776737579 -0.305333885021 y2[1] (closed_form) = 0.845776737579 -0.305333885021 absolute error = 4.472e-16 relative error = 4.973e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.03513931598 -0.0454910630373 y1[1] (closed_form) = 2.03513931598 -0.0454910630373 absolute error = 5e-17 relative error = 2.456e-15 % Correct digits = 17 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=2057.4MB, alloc=44.3MB, time=26.94 x[1] = 0.148 0.308 h = 0.003 0.006 y2[1] (numeric) = 0.845489902933 -0.309472283621 y2[1] (closed_form) = 0.845489902933 -0.309472283621 absolute error = 4.472e-16 relative error = 4.967e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.03635349007 -0.04613926912 y1[1] (closed_form) = 2.03635349007 -0.04613926912 absolute error = 6e-17 relative error = 2.946e-15 % Correct digits = 17 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 x[1] = 0.151 0.314 h = 0.0001 0.005 y2[1] (numeric) = 0.842096298724 -0.315553390472 y2[1] (closed_form) = 0.842096298724 -0.315553390472 absolute error = 4.243e-16 relative error = 4.718e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.03775994886 -0.0480140405886 y1[1] (closed_form) = 2.03775994886 -0.0480140405886 absolute error = 6e-17 relative error = 2.944e-15 % Correct digits = 17 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=2105.0MB, alloc=44.3MB, time=27.56 x[1] = 0.1511 0.319 h = 0.0001 0.003 y2[1] (numeric) = 0.841750319442 -0.320741274242 y2[1] (closed_form) = 0.841750319442 -0.320741274242 absolute error = 4.243e-16 relative error = 4.710e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.03933487464 -0.0488362369329 y1[1] (closed_form) = 2.03933487464 -0.0488362369329 absolute error = 5e-17 relative error = 2.451e-15 % Correct digits = 17 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=2152.8MB, alloc=44.3MB, time=28.19 x[1] = 0.1512 0.322 h = 0.001 0.001 y2[1] (numeric) = 0.841499069002 -0.32385579414 y2[1] (closed_form) = 0.841499069002 -0.32385579414 absolute error = 4.243e-16 relative error = 4.705e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.04028593203 -0.049343592276 y1[1] (closed_form) = 2.04028593203 -0.049343592276 absolute error = 1.002e-15 relative error = 4.909e-14 % Correct digits = 15 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=2200.6MB, alloc=44.3MB, time=28.81 x[1] = 0.1522 0.323 h = 0.001 0.003 y2[1] (numeric) = 0.840409115291 -0.324846577615 y2[1] (closed_form) = 0.840409115291 -0.324846577615 absolute error = 5.000e-16 relative error = 5.549e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.04045123738 -0.0498269893422 y1[1] (closed_form) = 2.04045123738 -0.0498269893422 absolute error = 1.002e-15 relative error = 4.908e-14 % Correct digits = 15 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 x[1] = 0.1532 0.326 h = 0.0001 0.004 y2[1] (numeric) = 0.839217565523 -0.327918927857 y2[1] (closed_form) = 0.839217565523 -0.327918927857 absolute error = 5.000e-16 relative error = 5.549e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.04127019884 -0.0506339311263 y1[1] (closed_form) = 2.04127019884 -0.0506339311263 absolute error = 1.002e-15 relative error = 4.906e-14 % Correct digits = 15 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=2248.2MB, alloc=44.3MB, time=29.43 x[1] = 0.1533 0.33 h = 0.003 0.006 y2[1] (numeric) = 0.838909484782 -0.332081513707 y2[1] (closed_form) = 0.838909484782 -0.332081513707 absolute error = 4.243e-16 relative error = 4.702e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.04257410438 -0.0513106760591 y1[1] (closed_form) = 2.04257410438 -0.0513106760591 absolute error = 1.002e-15 relative error = 4.906e-14 % Correct digits = 15 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=2296.0MB, alloc=44.3MB, time=30.05 x[1] = 0.1563 0.336 h = 0.0001 0.005 y2[1] (numeric) = 0.83546569413 -0.338184616598 y2[1] (closed_form) = 0.83546569413 -0.338184616598 absolute error = 4.243e-16 relative error = 4.707e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.04409646806 -0.0532929406906 y1[1] (closed_form) = 2.04409646806 -0.0532929406906 absolute error = 7e-17 relative error = 3.423e-15 % Correct digits = 16 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=2343.6MB, alloc=44.3MB, time=30.68 x[1] = 0.1564 0.341 h = 0.0001 0.003 y2[1] (numeric) = 0.835092592413 -0.343403934662 y2[1] (closed_form) = 0.835092592413 -0.343403934662 absolute error = 4.243e-16 relative error = 4.699e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.04578396391 -0.0541506224751 y1[1] (closed_form) = 2.04578396391 -0.0541506224751 absolute error = 7e-17 relative error = 3.420e-15 % Correct digits = 16 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 x[1] = 0.1565 0.344 h = 0.001 0.001 y2[1] (numeric) = 0.834824717155 -0.346537370287 y2[1] (closed_form) = 0.834824717155 -0.346537370287 absolute error = 5.000e-16 relative error = 5.532e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.046802371 -0.0546802431283 y1[1] (closed_form) = 2.046802371 -0.0546802431283 absolute error = 1.002e-15 relative error = 4.896e-14 % Correct digits = 15 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=2391.4MB, alloc=44.3MB, time=31.30 x[1] = 0.1575 0.345 h = 0.001 0.003 y2[1] (numeric) = 0.833722887673 -0.347529326872 y2[1] (closed_form) = 0.833722887673 -0.347529326872 absolute error = 5.000e-16 relative error = 5.536e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.04698367824 -0.0551930026442 y1[1] (closed_form) = 2.04698367824 -0.0551930026442 absolute error = 1.002e-15 relative error = 4.895e-14 % Correct digits = 15 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=2439.2MB, alloc=44.3MB, time=31.92 x[1] = 0.1585 0.348 h = 0.0001 0.004 y2[1] (numeric) = 0.832508612586 -0.350615979092 y2[1] (closed_form) = 0.832508612586 -0.350615979092 absolute error = 5.000e-16 relative error = 5.535e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.04786401178 -0.0560427270402 y1[1] (closed_form) = 2.04786401178 -0.0560427270402 absolute error = 1.002e-15 relative error = 4.893e-14 % Correct digits = 15 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=2487.0MB, alloc=44.3MB, time=32.54 x[1] = 0.1586 0.352 h = 0.003 0.006 y2[1] (numeric) = 0.8321781745 -0.35480457816 y2[1] (closed_form) = 0.8321781745 -0.35480457816 absolute error = 5.000e-16 relative error = 5.527e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.04925808543 -0.0567486234603 y1[1] (closed_form) = 2.04925808543 -0.0567486234603 absolute error = 2.002e-15 relative error = 9.764e-14 % Correct digits = 15 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 x[1] = 0.1616 0.358 h = 0.0001 0.005 y2[1] (numeric) = 0.828681203952 -0.360931656483 y2[1] (closed_form) = 0.828681203952 -0.360931656483 absolute error = 5.000e-16 relative error = 5.532e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.05089658578 -0.0588396400566 y1[1] (closed_form) = 2.05089658578 -0.0588396400566 absolute error = 1.003e-15 relative error = 4.889e-14 % Correct digits = 15 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=2534.6MB, alloc=44.3MB, time=33.16 x[1] = 0.1617 0.363 h = 0.0001 0.003 y2[1] (numeric) = 0.828279592456 -0.366184701432 y2[1] (closed_form) = 0.828279592456 -0.366184701432 absolute error = 5.000e-16 relative error = 5.521e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.05269722104 -0.0597335918718 y1[1] (closed_form) = 2.05269722104 -0.0597335918718 absolute error = 1.003e-15 relative error = 4.885e-14 % Correct digits = 15 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=2582.5MB, alloc=44.3MB, time=33.79 x[1] = 0.1618 0.366 h = 0.001 0.001 y2[1] (numeric) = 0.827994239477 -0.369338418916 y2[1] (closed_form) = 0.827994239477 -0.369338418916 absolute error = 4.243e-16 relative error = 4.680e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.05378331863 -0.0602859568118 y1[1] (closed_form) = 2.05378331863 -0.0602859568118 absolute error = 1.003e-15 relative error = 4.883e-14 % Correct digits = 15 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 x[1] = 0.1628 0.367 h = 0.001 0.003 y2[1] (numeric) = 0.826879800532 -0.370331743901 y2[1] (closed_form) = 0.826879800532 -0.370331743901 absolute error = 5.000e-16 relative error = 5.519e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.05398059082 -0.0608283548403 y1[1] (closed_form) = 2.05398059082 -0.0608283548403 absolute error = 1.003e-15 relative error = 4.882e-14 % Correct digits = 15 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=2630.2MB, alloc=44.3MB, time=34.40 x[1] = 0.1638 0.37 h = 0.0001 0.004 y2[1] (numeric) = 0.825641526649 -0.373433822183 y2[1] (closed_form) = 0.825641526649 -0.373433822183 absolute error = 5.000e-16 relative error = 5.518e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.05492249965 -0.0617214545662 y1[1] (closed_form) = 2.05492249965 -0.0617214545662 absolute error = 2.002e-15 relative error = 9.736e-14 % Correct digits = 15 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=2678.0MB, alloc=44.3MB, time=35.02 x[1] = 0.1639 0.374 h = 0.003 0.006 y2[1] (numeric) = 0.825287603709 -0.377650267082 y2[1] (closed_form) = 0.825287603709 -0.377650267082 absolute error = 5.000e-16 relative error = 5.509e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.05640721236 -0.0624571494307 y1[1] (closed_form) = 2.05640721236 -0.0624571494307 absolute error = 1.002e-15 relative error = 4.873e-14 % Correct digits = 15 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=2725.9MB, alloc=44.3MB, time=35.65 x[1] = 0.1669 0.38 h = 0.0001 0.005 y2[1] (numeric) = 0.821734429972 -0.383803298756 y2[1] (closed_form) = 0.821734429972 -0.383803298756 absolute error = 4.243e-16 relative error = 4.678e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.05816210876 -0.0646582534612 y1[1] (closed_form) = 2.05816210876 -0.0646582534612 absolute error = 1.003e-15 relative error = 4.872e-14 % Correct digits = 15 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 x[1] = 0.167 0.385 h = 0.0001 0.003 y2[1] (numeric) = 0.82130290049 -0.389092371911 y2[1] (closed_form) = 0.82130290049 -0.389092371911 absolute error = 4.243e-16 relative error = 4.668e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.0600764959 -0.0655893028202 y1[1] (closed_form) = 2.0600764959 -0.0655893028202 absolute error = 8e-17 relative error = 3.881e-15 % Correct digits = 16 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=2773.5MB, alloc=44.3MB, time=36.27 x[1] = 0.1671 0.388 h = 0.001 0.001 y2[1] (numeric) = 0.820999204189 -0.392267742556 y2[1] (closed_form) = 0.820999204189 -0.392267742556 absolute error = 4.243e-16 relative error = 4.663e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.06123065034 -0.0661649171799 y1[1] (closed_form) = 2.06123065034 -0.0661649171799 absolute error = 1.003e-15 relative error = 4.864e-14 % Correct digits = 15 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=2821.4MB, alloc=44.3MB, time=36.89 x[1] = 0.1681 0.389 h = 0.001 0.003 y2[1] (numeric) = 0.819871416022 -0.393262628912 y2[1] (closed_form) = 0.819871416022 -0.393262628912 absolute error = 4.472e-16 relative error = 4.918e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.06144385093 -0.06673724702 y1[1] (closed_form) = 2.06144385093 -0.06673724702 absolute error = 1.003e-15 relative error = 4.864e-14 % Correct digits = 15 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=2869.2MB, alloc=44.3MB, time=37.51 x[1] = 0.1691 0.392 h = 0.0001 0.004 y2[1] (numeric) = 0.818607855327 -0.396381258778 y2[1] (closed_form) = 0.818607855327 -0.396381258778 absolute error = 3.606e-16 relative error = 3.964e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.06244755619 -0.0676743489303 y1[1] (closed_form) = 2.06244755619 -0.0676743489303 absolute error = 1.003e-15 relative error = 4.861e-14 % Correct digits = 15 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 x[1] = 0.1692 0.396 h = 0.003 0.006 y2[1] (numeric) = 0.81822930282 -0.400627389341 y2[1] (closed_form) = 0.81822930282 -0.400627389341 absolute error = 4.472e-16 relative error = 4.909e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.0640234133 -0.0684405239204 y1[1] (closed_form) = 2.0640234133 -0.0684405239204 absolute error = 9e-17 relative error = 4.358e-15 % Correct digits = 16 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=2916.9MB, alloc=44.3MB, time=38.13 x[1] = 0.1722 0.402 h = 0.0001 0.005 y2[1] (numeric) = 0.814616870926 -0.40680835101 y2[1] (closed_form) = 0.814616870926 -0.40680835101 absolute error = 4.472e-16 relative error = 4.911e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.06589499251 -0.0707531281916 y1[1] (closed_form) = 2.06589499251 -0.0707531281916 absolute error = 1.004e-15 relative error = 4.857e-14 % Correct digits = 15 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=2964.7MB, alloc=44.3MB, time=38.76 x[1] = 0.1723 0.407 h = 0.0001 0.003 y2[1] (numeric) = 0.814153993209 -0.41213576314 y2[1] (closed_form) = 0.814153993209 -0.41213576314 absolute error = 4.472e-16 relative error = 4.901e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.06792378719 -0.0717221460499 y1[1] (closed_form) = 2.06792378719 -0.0717221460499 absolute error = 1.005e-15 relative error = 4.857e-14 % Correct digits = 15 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=3012.6MB, alloc=44.3MB, time=39.38 x[1] = 0.1724 0.41 h = 0.001 0.001 y2[1] (numeric) = 0.813831074571 -0.415334163842 y2[1] (closed_form) = 0.813831074571 -0.415334163842 absolute error = 4.472e-16 relative error = 4.895e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.06914639045 -0.0723215414344 y1[1] (closed_form) = 2.06914639045 -0.0723215414344 absolute error = 1.0e-16 relative error = 4.830e-15 % Correct digits = 16 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 x[1] = 0.1734 0.411 h = 0.0001 0.004 y2[1] (numeric) = 0.812689190973 -0.416330802141 y2[1] (closed_form) = 0.812689190973 -0.416330802141 absolute error = 4.472e-16 relative error = 4.898e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.06937548317 -0.0729241137464 y1[1] (closed_form) = 2.06937548317 -0.0729241137464 absolute error = 1.0e-16 relative error = 4.829e-15 % Correct digits = 16 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=3060.3MB, alloc=44.3MB, time=40.00 x[1] = 0.1735 0.415 h = 0.003 0.006 y2[1] (numeric) = 0.812288891253 -0.420604276634 y2[1] (closed_form) = 0.812288891253 -0.420604276634 absolute error = 4.123e-16 relative error = 4.507e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.07103060008 -0.0737160031704 y1[1] (closed_form) = 2.07103060008 -0.0737160031704 absolute error = 1.1e-16 relative error = 5.308e-15 % Correct digits = 16 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=3108.0MB, alloc=44.3MB, time=40.62 x[1] = 0.1765 0.421 h = 0.0001 0.005 y2[1] (numeric) = 0.808623344747 -0.426811617548 y2[1] (closed_form) = 0.808623344747 -0.426811617548 absolute error = 4.123e-16 relative error = 4.509e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.0730042189 -0.076124378964 y1[1] (closed_form) = 2.0730042189 -0.076124378964 absolute error = 1.1e-16 relative error = 5.303e-15 % Correct digits = 16 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=3155.6MB, alloc=44.3MB, time=41.24 x[1] = 0.1766 0.426 h = 0.0001 0.003 y2[1] (numeric) = 0.808132814843 -0.43217428577 y2[1] (closed_form) = 0.808132814843 -0.43217428577 absolute error = 5.099e-16 relative error = 5.564e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.07513251711 -0.0771254355981 y1[1] (closed_form) = 2.07513251711 -0.0771254355981 absolute error = 1.1e-16 relative error = 5.297e-15 % Correct digits = 16 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 x[1] = 0.1767 0.429 h = 0.001 0.001 y2[1] (numeric) = 0.807792932359 -0.43539386063 y2[1] (closed_form) = 0.807792932359 -0.43539386063 absolute error = 5.099e-16 relative error = 5.557e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.07641466469 -0.0777449248564 y1[1] (closed_form) = 2.07641466469 -0.0777449248564 absolute error = 1.006e-15 relative error = 4.842e-14 % Correct digits = 15 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=3203.2MB, alloc=44.3MB, time=41.86 x[1] = 0.1777 0.43 h = 0.001 0.003 y2[1] (numeric) = 0.806638337042 -0.436392337778 y2[1] (closed_form) = 0.806638337042 -0.436392337778 absolute error = 5.099e-16 relative error = 5.560e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.07665777353 -0.0783736022804 y1[1] (closed_form) = 2.07665777353 -0.0783736022804 absolute error = 1.006e-15 relative error = 4.841e-14 % Correct digits = 15 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=3251.0MB, alloc=44.3MB, time=42.48 x[1] = 0.1787 0.433 h = 0.0001 0.004 y2[1] (numeric) = 0.805324470936 -0.439545105871 y2[1] (closed_form) = 0.805324470936 -0.439545105871 absolute error = 5.099e-16 relative error = 5.558e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.07777766086 -0.0793936255503 y1[1] (closed_form) = 2.07777766086 -0.0793936255503 absolute error = 1.1e-16 relative error = 5.290e-15 % Correct digits = 16 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=3298.7MB, alloc=44.3MB, time=43.11 x[1] = 0.1788 0.437 h = 0.003 0.006 y2[1] (numeric) = 0.804897384709 -0.44385172486 y2[1] (closed_form) = 0.804897384709 -0.44385172486 absolute error = 5.099e-16 relative error = 5.547e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.07952496334 -0.0802173504665 y1[1] (closed_form) = 2.07952496334 -0.0802173504665 absolute error = 1.2e-16 relative error = 5.766e-15 % Correct digits = 16 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 x[1] = 0.1818 0.443 h = 0.0001 0.005 y2[1] (numeric) = 0.80116682831 -0.450090708459 y2[1] (closed_form) = 0.80116682831 -0.450090708459 absolute error = 5.099e-16 relative error = 5.549e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.08161588983 -0.0827400595285 y1[1] (closed_form) = 2.08161588983 -0.0827400595285 absolute error = 1.008e-15 relative error = 4.841e-14 % Correct digits = 15 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=3346.3MB, alloc=44.3MB, time=43.73 x[1] = 0.1819 0.448 h = 0.0001 0.003 y2[1] (numeric) = 0.800642253877 -0.455496060783 y2[1] (closed_form) = 0.800642253877 -0.455496060783 absolute error = 5.099e-16 relative error = 5.536e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.08385994262 -0.0837808138071 y1[1] (closed_form) = 2.08385994262 -0.0837808138071 absolute error = 1.3e-16 relative error = 6.233e-15 % Correct digits = 16 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=3394.1MB, alloc=44.3MB, time=44.35 x[1] = 0.182 0.451 h = 0.001 0.001 y2[1] (numeric) = 0.800281491816 -0.458741255002 y2[1] (closed_form) = 0.800281491816 -0.458741255002 absolute error = 5e-16 relative error = 5.420e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.0852113438 -0.0844251395041 y1[1] (closed_form) = 2.0852113438 -0.0844251395041 absolute error = 1.3e-16 relative error = 6.229e-15 % Correct digits = 16 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=3442.0MB, alloc=44.3MB, time=44.98 x[1] = 0.183 0.452 h = 0.001 0.003 y2[1] (numeric) = 0.799111396258 -0.459741841098 y2[1] (closed_form) = 0.799111396258 -0.459741841098 absolute error = 5e-16 relative error = 5.423e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.0854702819 -0.085084684565 y1[1] (closed_form) = 2.0854702819 -0.085084684565 absolute error = 1.3e-16 relative error = 6.228e-15 % Correct digits = 16 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 x[1] = 0.184 0.455 h = 0.0001 0.004 y2[1] (numeric) = 0.797768484181 -0.462914406448 y2[1] (closed_form) = 0.797768484181 -0.462914406448 absolute error = 5e-16 relative error = 5.421e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.08665270596 -0.0861506915662 y1[1] (closed_form) = 2.08665270596 -0.0861506915662 absolute error = 1.3e-16 relative error = 6.225e-15 % Correct digits = 16 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=3489.6MB, alloc=44.3MB, time=45.60 x[1] = 0.1841 0.459 h = 0.003 0.006 y2[1] (numeric) = 0.797313412348 -0.467256033816 y2[1] (closed_form) = 0.797313412348 -0.467256033816 absolute error = 5e-16 relative error = 5.410e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.08849279854 -0.0870070350314 y1[1] (closed_form) = 2.08849279854 -0.0870070350314 absolute error = 1.4e-16 relative error = 6.698e-15 % Correct digits = 16 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=3537.3MB, alloc=44.3MB, time=46.22 x[1] = 0.1871 0.465 h = 0.0001 0.005 y2[1] (numeric) = 0.793514690168 -0.473528634562 y2[1] (closed_form) = 0.793514690168 -0.473528634562 absolute error = 5.099e-16 relative error = 5.518e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.09070139764 -0.0896457151636 y1[1] (closed_form) = 2.09070139764 -0.0896457151636 absolute error = 1.4e-16 relative error = 6.690e-15 % Correct digits = 16 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=3585.0MB, alloc=44.3MB, time=46.84 x[1] = 0.1872 0.47 h = 0.0001 0.003 y2[1] (numeric) = 0.79295457142 -0.478979013072 y2[1] (closed_form) = 0.79295457142 -0.478979013072 absolute error = 5.099e-16 relative error = 5.504e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.0930619854 -0.0907271649432 y1[1] (closed_form) = 2.0930619854 -0.0907271649432 absolute error = 1.4e-16 relative error = 6.682e-15 % Correct digits = 16 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 x[1] = 0.1873 0.473 h = 0.001 0.001 y2[1] (numeric) = 0.792572008464 -0.482251222072 y2[1] (closed_form) = 0.792572008464 -0.482251222072 absolute error = 5.385e-16 relative error = 5.804e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.09448310605 -0.0913969360123 y1[1] (closed_form) = 2.09448310605 -0.0913969360123 absolute error = 1.5e-16 relative error = 7.155e-15 % Correct digits = 16 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=3632.7MB, alloc=44.3MB, time=47.46 x[1] = 0.1883 0.474 h = 0.001 0.003 y2[1] (numeric) = 0.791385645836 -0.483254100418 y2[1] (closed_form) = 0.791385645836 -0.483254100418 absolute error = 5.099e-16 relative error = 5.499e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.09475783765 -0.0920877098006 y1[1] (closed_form) = 2.09475783765 -0.0920877098006 absolute error = 1.5e-16 relative error = 7.154e-15 % Correct digits = 16 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=3680.4MB, alloc=44.3MB, time=48.08 x[1] = 0.1893 0.477 h = 0.0001 0.004 y2[1] (numeric) = 0.790012335627 -0.48644759628 y2[1] (closed_form) = 0.790012335627 -0.48644759628 absolute error = 6.083e-16 relative error = 6.556e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.09600308892 -0.0932004623123 y1[1] (closed_form) = 2.09600308892 -0.0932004623123 absolute error = 1.011e-15 relative error = 4.820e-14 % Correct digits = 15 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 x[1] = 0.1894 0.481 h = 0.003 0.006 y2[1] (numeric) = 0.789528058167 -0.490826105342 y2[1] (closed_form) = 0.789528058167 -0.490826105342 absolute error = 5.099e-16 relative error = 5.485e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.09793661082 -0.0940902438952 y1[1] (closed_form) = 2.09793661082 -0.0940902438952 absolute error = 1.013e-15 relative error = 4.822e-14 % Correct digits = 15 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=3728.2MB, alloc=44.3MB, time=48.70 x[1] = 0.1924 0.487 h = 0.0001 0.005 y2[1] (numeric) = 0.7856579754 -0.497134297128 y2[1] (closed_form) = 0.7856579754 -0.497134297128 absolute error = 5.099e-16 relative error = 5.484e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.10026327411 -0.0968466132164 y1[1] (closed_form) = 2.10026327411 -0.0968466132164 absolute error = 1.013e-15 relative error = 4.817e-14 % Correct digits = 15 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=3775.8MB, alloc=44.3MB, time=49.33 x[1] = 0.1925 0.492 h = 0.0001 0.003 y2[1] (numeric) = 0.785060785839 -0.502632056145 y2[1] (closed_form) = 0.785060785839 -0.502632056145 absolute error = 5.099e-16 relative error = 5.470e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.10274122087 -0.0979698020854 y1[1] (closed_form) = 2.10274122087 -0.0979698020854 absolute error = 1.013e-15 relative error = 4.811e-14 % Correct digits = 15 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=3823.7MB, alloc=44.3MB, time=49.96 x[1] = 0.1926 0.495 h = 0.001 0.001 y2[1] (numeric) = 0.784655484433 -0.50593268258 y2[1] (closed_form) = 0.784655484433 -0.50593268258 absolute error = 5.385e-16 relative error = 5.768e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.10423255271 -0.0986656553211 y1[1] (closed_form) = 2.10423255271 -0.0986656553211 absolute error = 2.006e-15 relative error = 9.525e-14 % Correct digits = 15 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 x[1] = 0.1936 0.496 h = 0.001 0.003 y2[1] (numeric) = 0.783452079957 -0.506938033732 y2[1] (closed_form) = 0.783452079957 -0.506938033732 absolute error = 5.385e-16 relative error = 5.771e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.10452304197 -0.0993880368486 y1[1] (closed_form) = 2.10452304197 -0.0993880368486 absolute error = 1.013e-15 relative error = 4.807e-14 % Correct digits = 15 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=3871.4MB, alloc=44.3MB, time=50.58 x[1] = 0.1946 0.499 h = 0.0001 0.004 y2[1] (numeric) = 0.782047000712 -0.510153595812 y2[1] (closed_form) = 0.782047000712 -0.510153595812 absolute error = 5.831e-16 relative error = 6.245e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.10583142866 -0.100548332615 y1[1] (closed_form) = 2.10583142866 -0.100548332615 absolute error = 1.020e-15 relative error = 4.837e-14 % Correct digits = 15 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=3919.2MB, alloc=44.3MB, time=51.20 x[1] = 0.1947 0.503 h = 0.003 0.006 y2[1] (numeric) = 0.781532275685 -0.514570869889 y2[1] (closed_form) = 0.781532275685 -0.514570869889 absolute error = 5.831e-16 relative error = 6.231e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.10785905392 -0.101472408919 y1[1] (closed_form) = 2.10785905392 -0.101472408919 absolute error = 1.020e-15 relative error = 4.833e-14 % Correct digits = 15 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=3967.1MB, alloc=44.3MB, time=51.82 x[1] = 0.1977 0.509 h = 0.0001 0.005 y2[1] (numeric) = 0.777587596691 -0.520916626191 y2[1] (closed_form) = 0.777587596691 -0.520916626191 absolute error = 5.000e-16 relative error = 5.342e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.11030419934 -0.10434826674 y1[1] (closed_form) = 2.11030419934 -0.10434826674 absolute error = 1.044e-15 relative error = 4.941e-14 % Correct digits = 15 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 x[1] = 0.1978 0.514 h = 0.0001 0.003 y2[1] (numeric) = 0.77695178187 -0.526464132994 y2[1] (closed_form) = 0.77695178187 -0.526464132994 absolute error = 5.000e-16 relative error = 5.328e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.1129003729 -0.105514284687 y1[1] (closed_form) = 2.1129003729 -0.105514284687 absolute error = 2.010e-15 relative error = 9.501e-14 % Correct digits = 15 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=4014.7MB, alloc=44.3MB, time=52.44 x[1] = 0.1979 0.517 h = 0.001 0.001 y2[1] (numeric) = 0.776522787463 -0.529794587172 y2[1] (closed_form) = 0.776522787463 -0.529794587172 absolute error = 5.000e-16 relative error = 5.319e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.11446243357 -0.106236885149 y1[1] (closed_form) = 2.11446243357 -0.106236885149 absolute error = 2.010e-15 relative error = 9.494e-14 % Correct digits = 15 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=4062.6MB, alloc=44.3MB, time=53.07 x[1] = 0.1989 0.518 h = 0.0001 0.004 y2[1] (numeric) = 0.775301558014 -0.530802588836 y2[1] (closed_form) = 0.775301558014 -0.530802588836 absolute error = 5.000e-16 relative error = 5.321e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.11476864446 -0.106991271513 y1[1] (closed_form) = 2.11476864446 -0.106991271513 absolute error = 2.010e-15 relative error = 9.492e-14 % Correct digits = 15 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=4110.4MB, alloc=44.3MB, time=53.69 x[1] = 0.199 0.522 h = 0.003 0.006 y2[1] (numeric) = 0.774760105245 -0.535255129962 y2[1] (closed_form) = 0.774760105245 -0.535255129962 absolute error = 5.000e-16 relative error = 5.310e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.11687826023 -0.107944449662 y1[1] (closed_form) = 2.11687826023 -0.107944449662 absolute error = 2.022e-15 relative error = 9.541e-14 % Correct digits = 15 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 x[1] = 0.202 0.528 h = 0.0001 0.005 y2[1] (numeric) = 0.77074907214 -0.541635742479 y2[1] (closed_form) = 0.77074907214 -0.541635742479 absolute error = 5.000e-16 relative error = 5.308e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.11942719981 -0.110923244089 y1[1] (closed_form) = 2.11942719981 -0.110923244089 absolute error = 2.022e-15 relative error = 9.529e-14 % Correct digits = 15 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=4158.0MB, alloc=44.3MB, time=54.31 x[1] = 0.2021 0.533 h = 0.0001 0.003 y2[1] (numeric) = 0.770079374177 -0.547228462435 y2[1] (closed_form) = 0.770079374177 -0.547228462435 absolute error = 5.000e-16 relative error = 5.293e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.12212639623 -0.112125613455 y1[1] (closed_form) = 2.12212639623 -0.112125613455 absolute error = 3.015e-15 relative error = 1.419e-13 % Correct digits = 15 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=4205.7MB, alloc=44.3MB, time=54.93 x[1] = 0.2022 0.536 h = 0.001 0.001 y2[1] (numeric) = 0.769629586027 -0.550586024862 y2[1] (closed_form) = 0.769629586027 -0.550586024862 absolute error = 5.000e-16 relative error = 5.284e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.12375010223 -0.112870940099 y1[1] (closed_form) = 2.12375010223 -0.112870940099 absolute error = 2.010e-15 relative error = 9.451e-14 % Correct digits = 15 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=4253.6MB, alloc=44.3MB, time=55.55 x[1] = 0.2032 0.537 h = 0.001 0.003 y2[1] (numeric) = 0.768392414061 -0.551596673241 y2[1] (closed_form) = 0.768392414061 -0.551596673241 absolute error = 4.243e-16 relative error = 4.485e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.12407020471 -0.113653020395 y1[1] (closed_form) = 2.12407020471 -0.113653020395 absolute error = 2.010e-15 relative error = 9.449e-14 % Correct digits = 15 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 x[1] = 0.2042 0.54 h = 0.0001 0.004 y2[1] (numeric) = 0.766924798361 -0.554856745278 y2[1] (closed_form) = 0.766924798361 -0.554856745278 absolute error = 4.243e-16 relative error = 4.482e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.12549754312 -0.114903269739 y1[1] (closed_form) = 2.12549754312 -0.114903269739 absolute error = 1.020e-15 relative error = 4.791e-14 % Correct digits = 15 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=4301.1MB, alloc=44.3MB, time=56.17 x[1] = 0.2043 0.544 h = 0.003 0.006 y2[1] (numeric) = 0.766350548022 -0.55935159987 y2[1] (closed_form) = 0.766350548022 -0.55935159987 absolute error = 5.000e-16 relative error = 5.270e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.1277026207 -0.115892427998 y1[1] (closed_form) = 2.1277026207 -0.115892427998 absolute error = 1.044e-15 relative error = 4.900e-14 % Correct digits = 15 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=4348.9MB, alloc=44.3MB, time=56.80 x[1] = 0.2073 0.55 h = 0.0001 0.005 y2[1] (numeric) = 0.762258806091 -0.565773488247 y2[1] (closed_form) = 0.762258806091 -0.565773488247 absolute error = 4.243e-16 relative error = 4.469e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.1303709133 -0.118994272584 y1[1] (closed_form) = 2.1303709133 -0.118994272584 absolute error = 1.044e-15 relative error = 4.893e-14 % Correct digits = 15 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=4396.7MB, alloc=44.3MB, time=57.42 x[1] = 0.2074 0.555 h = 0.0001 0.003 y2[1] (numeric) = 0.761547540278 -0.571420417242 y2[1] (closed_form) = 0.761547540278 -0.571420417242 absolute error = 4.243e-16 relative error = 4.456e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.13319008261 -0.120241613581 y1[1] (closed_form) = 2.13319008261 -0.120241613581 absolute error = 1.044e-15 relative error = 4.886e-14 % Correct digits = 15 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 x[1] = 0.2075 0.558 h = 0.001 0.001 y2[1] (numeric) = 0.761072252109 -0.574810465358 y2[1] (closed_form) = 0.761072252109 -0.574810465358 absolute error = 5.000e-16 relative error = 5.242e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.13488555869 -0.121014994772 y1[1] (closed_form) = 2.13488555869 -0.121014994772 absolute error = 3e-16 relative error = 1.403e-14 % Correct digits = 16 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=4444.4MB, alloc=44.3MB, time=58.04 x[1] = 0.2085 0.559 h = 0.001 0.003 y2[1] (numeric) = 0.759815776407 -0.575824096575 y2[1] (closed_form) = 0.759815776407 -0.575824096575 absolute error = 4.243e-16 relative error = 4.450e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.13522132013 -0.121829867983 y1[1] (closed_form) = 2.13522132013 -0.121829867983 absolute error = 1.044e-15 relative error = 4.882e-14 % Correct digits = 15 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=4492.3MB, alloc=44.3MB, time=58.66 x[1] = 0.2095 0.562 h = 0.0001 0.004 y2[1] (numeric) = 0.758312371986 -0.579109516289 y2[1] (closed_form) = 0.758312371986 -0.579109516289 absolute error = 4.243e-16 relative error = 4.447e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.13671278427 -0.123130140954 y1[1] (closed_form) = 2.13671278427 -0.123130140954 absolute error = 1.044e-15 relative error = 4.878e-14 % Correct digits = 15 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=4540.2MB, alloc=44.3MB, time=59.29 x[1] = 0.2096 0.566 h = 0.003 0.006 y2[1] (numeric) = 0.757704013984 -0.583648599727 y2[1] (closed_form) = 0.757704013984 -0.583648599727 absolute error = 5.000e-16 relative error = 5.228e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.13901409833 -0.124156244567 y1[1] (closed_form) = 2.13901409833 -0.124156244567 absolute error = 2.022e-15 relative error = 9.439e-14 % Correct digits = 15 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 x[1] = 0.2126 0.572 h = 0.0001 0.005 y2[1] (numeric) = 0.753528200011 -0.590113737583 y2[1] (closed_form) = 0.753528200011 -0.590113737583 absolute error = 5.000e-16 relative error = 5.224e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.14180223707 -0.127383175806 y1[1] (closed_form) = 2.14180223707 -0.127383175806 absolute error = 2.022e-15 relative error = 9.426e-14 % Correct digits = 15 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=4587.7MB, alloc=44.3MB, time=59.91 x[1] = 0.2127 0.577 h = 0.0001 0.003 y2[1] (numeric) = 0.752773725101 -0.595817284301 y2[1] (closed_form) = 0.752773725101 -0.595817284301 absolute error = 5.000e-16 relative error = 5.208e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.1447423737 -0.128676714606 y1[1] (closed_form) = 2.1447423737 -0.128676714606 absolute error = 2.040e-15 relative error = 9.493e-14 % Correct digits = 15 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=4635.6MB, alloc=44.3MB, time=60.53 x[1] = 0.2128 0.58 h = 0.001 0.001 y2[1] (numeric) = 0.752271929599 -0.59924125286 y2[1] (closed_form) = 0.752271929599 -0.59924125286 absolute error = 4.472e-16 relative error = 4.650e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.14651021251 -0.129478898361 y1[1] (closed_form) = 2.14651021251 -0.129478898361 absolute error = 2.040e-15 relative error = 9.485e-14 % Correct digits = 15 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 x[1] = 0.2138 0.581 h = 0.001 0.003 y2[1] (numeric) = 0.750995340908 -0.60025803602 y2[1] (closed_form) = 0.750995340908 -0.60025803602 absolute error = 4.472e-16 relative error = 4.652e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.14686159593 -0.130327014312 y1[1] (closed_form) = 2.14686159593 -0.130327014312 absolute error = 3.027e-15 relative error = 1.407e-13 % Correct digits = 15 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=4683.4MB, alloc=44.3MB, time=61.15 x[1] = 0.2148 0.584 h = 0.0001 0.004 y2[1] (numeric) = 0.749454696113 -0.603569950688 y2[1] (closed_form) = 0.749454696113 -0.603569950688 absolute error = 5.000e-16 relative error = 5.196e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.14841756257 -0.131678251571 y1[1] (closed_form) = 2.14841756257 -0.131678251571 absolute error = 2.040e-15 relative error = 9.476e-14 % Correct digits = 15 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=4731.1MB, alloc=44.3MB, time=61.78 x[1] = 0.2149 0.588 h = 0.003 0.006 y2[1] (numeric) = 0.748810894489 -0.608155190564 y2[1] (closed_form) = 0.748810894489 -0.608155190564 absolute error = 5.000e-16 relative error = 5.183e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.150815923 -0.132742305069 y1[1] (closed_form) = 2.150815923 -0.132742305069 absolute error = 3.041e-15 relative error = 1.411e-13 % Correct digits = 15 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=4778.9MB, alloc=44.3MB, time=62.40 x[1] = 0.2179 0.594 h = 0.0001 0.005 y2[1] (numeric) = 0.74454759684 -0.61466555163 y2[1] (closed_form) = 0.74454759684 -0.61466555163 absolute error = 4.472e-16 relative error = 4.632e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.15372442649 -0.136096444436 y1[1] (closed_form) = 2.15372442649 -0.136096444436 absolute error = 3.041e-15 relative error = 1.409e-13 % Correct digits = 15 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 x[1] = 0.218 0.599 h = 0.0001 0.003 y2[1] (numeric) = 0.743748238683 -0.62042814049 y2[1] (closed_form) = 0.743748238683 -0.62042814049 absolute error = 4.472e-16 relative error = 4.617e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.15678656924 -0.137437456484 y1[1] (closed_form) = 2.15678656924 -0.137437456484 absolute error = 3.041e-15 relative error = 1.407e-13 % Correct digits = 15 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=4826.5MB, alloc=44.3MB, time=63.02 x[1] = 0.2181 0.602 h = 0.001 0.001 y2[1] (numeric) = 0.743218908538 -0.623887473529 y2[1] (closed_form) = 0.743218908538 -0.623887473529 absolute error = 3.162e-16 relative error = 3.259e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.15862738968 -0.138269220829 y1[1] (closed_form) = 2.15862738968 -0.138269220829 absolute error = 3.041e-15 relative error = 1.406e-13 % Correct digits = 15 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=4874.3MB, alloc=44.3MB, time=63.64 x[1] = 0.2191 0.603 h = 0.001 0.003 y2[1] (numeric) = 0.7419213877 -0.624907574485 y2[1] (closed_form) = 0.7419213877 -0.624907574485 absolute error = 4.472e-16 relative error = 4.610e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.1589943575 -0.139151048143 y1[1] (closed_form) = 2.1589943575 -0.139151048143 absolute error = 3.041e-15 relative error = 1.406e-13 % Correct digits = 15 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=4922.2MB, alloc=44.3MB, time=64.26 x[1] = 0.2201 0.606 h = 0.0001 0.004 y2[1] (numeric) = 0.740342027719 -0.628247134777 y2[1] (closed_form) = 0.740342027719 -0.628247134777 absolute error = 3.606e-16 relative error = 3.713e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.16061522089 -0.140554228629 y1[1] (closed_form) = 2.16061522089 -0.140554228629 absolute error = 3.041e-15 relative error = 1.405e-13 % Correct digits = 15 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 x[1] = 0.2202 0.61 h = 0.003 0.006 y2[1] (numeric) = 0.73966141959 -0.632880471461 y2[1] (closed_form) = 0.73966141959 -0.632880471461 absolute error = 4.123e-16 relative error = 4.235e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.16311147303 -0.141657276478 y1[1] (closed_form) = 2.16311147303 -0.141657276478 absolute error = 3.041e-15 relative error = 1.403e-13 % Correct digits = 15 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=4969.8MB, alloc=44.3MB, time=64.88 x[1] = 0.2232 0.616 h = 0.0001 0.005 y2[1] (numeric) = 0.735307176198 -0.639438029682 y2[1] (closed_form) = 0.735307176198 -0.639438029682 absolute error = 4.123e-16 relative error = 4.231e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.16614088506 -0.145140831516 y1[1] (closed_form) = 2.16614088506 -0.145140831516 absolute error = 3.041e-15 relative error = 1.401e-13 % Correct digits = 15 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=5017.6MB, alloc=44.3MB, time=65.50 x[1] = 0.2233 0.621 h = 0.0001 0.003 y2[1] (numeric) = 0.73446122641 -0.645262101556 y2[1] (closed_form) = 0.73446122641 -0.645262101556 absolute error = 4.123e-16 relative error = 4.217e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.16932611729 -0.146530642357 y1[1] (closed_form) = 2.16932611729 -0.146530642357 absolute error = 3.059e-15 relative error = 1.407e-13 % Correct digits = 15 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=5065.6MB, alloc=44.3MB, time=66.13 x[1] = 0.2234 0.624 h = 0.001 0.001 y2[1] (numeric) = 0.733903313512 -0.648758252816 y2[1] (closed_form) = 0.733903313512 -0.648758252816 absolute error = 4.123e-16 relative error = 4.209e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.17124056466 -0.147392795823 y1[1] (closed_form) = 2.17124056466 -0.147392795823 absolute error = 3.059e-15 relative error = 1.406e-13 % Correct digits = 15 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 x[1] = 0.2244 0.625 h = 0.0001 0.004 y2[1] (numeric) = 0.732584031052 -0.649781834048 y2[1] (closed_form) = 0.732584031052 -0.649781834048 absolute error = 4e-16 relative error = 4.085e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.17162307852 -0.14830882213 y1[1] (closed_form) = 2.17162307852 -0.14830882213 absolute error = 3.059e-15 relative error = 1.406e-13 % Correct digits = 15 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=5113.2MB, alloc=44.3MB, time=66.75 x[1] = 0.2245 0.629 h = 0.003 0.006 y2[1] (numeric) = 0.731871233032 -0.654458595881 y2[1] (closed_form) = 0.731871233032 -0.654458595881 absolute error = 5e-16 relative error = 5.093e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.17420477878 -0.149445121938 y1[1] (closed_form) = 2.17420477878 -0.149445121938 absolute error = 3.059e-15 relative error = 1.404e-13 % Correct digits = 15 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=5160.9MB, alloc=44.3MB, time=67.37 x[1] = 0.2275 0.635 h = 0.0001 0.005 y2[1] (numeric) = 0.727436488457 -0.661059501194 y2[1] (closed_form) = 0.727436488457 -0.661059501194 absolute error = 4e-16 relative error = 4.069e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.17734029839 -0.153040458423 y1[1] (closed_form) = 2.17734029839 -0.153040458423 absolute error = 3.059e-15 relative error = 1.402e-13 % Correct digits = 15 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=5208.6MB, alloc=44.3MB, time=67.99 x[1] = 0.2276 0.64 h = 0.0001 0.003 y2[1] (numeric) = 0.726549811259 -0.666939046621 y2[1] (closed_form) = 0.726549811259 -0.666939046621 absolute error = 5.099e-16 relative error = 5.170e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.18063298733 -0.154471889345 y1[1] (closed_form) = 2.18063298733 -0.154471889345 absolute error = 3.059e-15 relative error = 1.399e-13 % Correct digits = 15 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 x[1] = 0.2277 0.643 h = 0.001 0.001 y2[1] (numeric) = 0.725966901827 -0.670468419478 y2[1] (closed_form) = 0.725966901827 -0.670468419478 absolute error = 4.123e-16 relative error = 4.172e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.18261172293 -0.155359983885 y1[1] (closed_form) = 2.18261172293 -0.155359983885 absolute error = 3.059e-15 relative error = 1.398e-13 % Correct digits = 15 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=5256.3MB, alloc=44.3MB, time=68.61 x[1] = 0.2287 0.644 h = 0.001 0.003 y2[1] (numeric) = 0.724628259309 -0.671495396738 y2[1] (closed_form) = 0.724628259309 -0.671495396738 absolute error = 4.123e-16 relative error = 4.174e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.18300800258 -0.156305668146 y1[1] (closed_form) = 2.18300800258 -0.156305668146 absolute error = 3.059e-15 relative error = 1.398e-13 % Correct digits = 15 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=5304.1MB, alloc=44.3MB, time=69.23 x[1] = 0.2297 0.647 h = 0.0001 0.004 y2[1] (numeric) = 0.722973212731 -0.674889977815 y2[1] (closed_form) = 0.722973212731 -0.674889977815 absolute error = 3.162e-16 relative error = 3.197e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.18475138096 -0.157807456753 y1[1] (closed_form) = 2.18475138096 -0.157807456753 absolute error = 3.059e-15 relative error = 1.397e-13 % Correct digits = 15 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=5351.9MB, alloc=44.3MB, time=69.86 x[1] = 0.2298 0.651 h = 0.003 0.006 y2[1] (numeric) = 0.722221020349 -0.679618500022 y2[1] (closed_form) = 0.722221020349 -0.679618500022 absolute error = 3.162e-16 relative error = 3.189e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.18743265414 -0.158984791963 y1[1] (closed_form) = 2.18743265414 -0.158984791963 absolute error = 4.061e-15 relative error = 1.852e-13 % Correct digits = 15 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 x[1] = 0.2328 0.657 h = 0.0001 0.005 y2[1] (numeric) = 0.717688770229 -0.686270319178 y2[1] (closed_form) = 0.717688770229 -0.686270319178 absolute error = 3.162e-16 relative error = 3.185e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.19069018914 -0.162713877657 y1[1] (closed_form) = 2.19069018914 -0.162713877657 absolute error = 4.045e-15 relative error = 1.841e-13 % Correct digits = 15 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=5399.4MB, alloc=44.3MB, time=70.48 x[1] = 0.2329 0.662 h = 0.0001 0.003 y2[1] (numeric) = 0.716752256325 -0.692215957118 y2[1] (closed_form) = 0.716752256325 -0.692215957118 absolute error = 3.162e-16 relative error = 3.174e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.19410811989 -0.164196696031 y1[1] (closed_form) = 2.19410811989 -0.164196696031 absolute error = 4.061e-15 relative error = 1.846e-13 % Correct digits = 15 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=5447.3MB, alloc=44.3MB, time=71.10 x[1] = 0.233 0.665 h = 0.001 0.001 y2[1] (numeric) = 0.716138773286 -0.695784893628 y2[1] (closed_form) = 0.716138773286 -0.695784893628 absolute error = 3.162e-16 relative error = 3.167e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.19616176422 -0.165116758738 y1[1] (closed_form) = 2.19616176422 -0.165116758738 absolute error = 4.045e-15 relative error = 1.837e-13 % Correct digits = 15 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=5495.3MB, alloc=44.3MB, time=71.72 x[1] = 0.234 0.666 h = 0.001 0.003 y2[1] (numeric) = 0.714776798635 -0.696815654319 y2[1] (closed_form) = 0.714776798635 -0.696815654319 absolute error = 3.162e-16 relative error = 3.168e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.19657352245 -0.166097601157 y1[1] (closed_form) = 2.19657352245 -0.166097601157 absolute error = 5.036e-15 relative error = 2.286e-13 % Correct digits = 15 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 x[1] = 0.235 0.669 h = 0.0001 0.004 y2[1] (numeric) = 0.713078695283 -0.700241211747 y2[1] (closed_form) = 0.713078695283 -0.700241211747 absolute error = 2.236e-16 relative error = 2.237e-14 % Correct digits = 16 h = 0.0001 0.004 y1[1] (numeric) = 2.19838303506 -0.167654344407 y1[1] (closed_form) = 2.19838303506 -0.167654344407 absolute error = 4.045e-15 relative error = 1.835e-13 % Correct digits = 15 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=5543.0MB, alloc=44.3MB, time=72.34 x[1] = 0.2351 0.673 h = 0.003 0.006 y2[1] (numeric) = 0.712285662822 -0.705023474745 y2[1] (closed_form) = 0.712285662822 -0.705023474745 absolute error = 2.828e-16 relative error = 2.822e-14 % Correct digits = 16 h = 0.003 0.006 y1[1] (numeric) = 2.20116482903 -0.168873877114 y1[1] (closed_form) = 2.20116482903 -0.168873877114 absolute error = 5.036e-15 relative error = 2.281e-13 % Correct digits = 15 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=5590.8MB, alloc=44.3MB, time=72.96 x[1] = 0.2381 0.679 h = 0.0001 0.005 y2[1] (numeric) = 0.707652289478 -0.711728183458 y2[1] (closed_form) = 0.707652289478 -0.711728183458 absolute error = 3.606e-16 relative error = 3.592e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.20454499492 -0.172739171907 y1[1] (closed_form) = 2.20454499492 -0.172739171907 absolute error = 4.045e-15 relative error = 1.829e-13 % Correct digits = 15 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 x[1] = 0.2382 0.684 h = 0.0001 0.003 y2[1] (numeric) = 0.706664125261 -0.717742406252 y2[1] (closed_form) = 0.706664125261 -0.717742406252 absolute error = 3.606e-16 relative error = 3.580e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.20808937996 -0.174274850906 y1[1] (closed_form) = 2.20808937996 -0.174274850906 absolute error = 5.036e-15 relative error = 2.274e-13 % Correct digits = 15 memory used=5638.5MB, alloc=44.3MB, time=73.58 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 x[1] = 0.2383 0.687 h = 0.001 0.001 y2[1] (numeric) = 0.706018956577 -0.7213523905 y2[1] (closed_form) = 0.706018956577 -0.7213523905 absolute error = 4.243e-16 relative error = 4.203e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.21021865477 -0.175227780203 y1[1] (closed_form) = 2.21021865477 -0.175227780203 absolute error = 4.061e-15 relative error = 1.832e-13 % Correct digits = 15 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=5686.2MB, alloc=44.3MB, time=74.20 x[1] = 0.2393 0.688 h = 0.001 0.003 y2[1] (numeric) = 0.704632788445 -0.722387086932 y2[1] (closed_form) = 0.704632788445 -0.722387086932 absolute error = 3.606e-16 relative error = 3.573e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.21064585055 -0.176244323998 y1[1] (closed_form) = 2.21064585055 -0.176244323998 absolute error = 4.045e-15 relative error = 1.824e-13 % Correct digits = 15 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=5734.0MB, alloc=44.3MB, time=74.82 x[1] = 0.2403 0.691 h = 0.0001 0.004 y2[1] (numeric) = 0.702890055214 -0.725844786474 y2[1] (closed_form) = 0.702890055214 -0.725844786474 absolute error = 3.606e-16 relative error = 3.568e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.21252195933 -0.177857153656 y1[1] (closed_form) = 2.21252195933 -0.177857153656 absolute error = 4.045e-15 relative error = 1.822e-13 % Correct digits = 15 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 x[1] = 0.2404 0.695 h = 0.003 0.006 y2[1] (numeric) = 0.702054705804 -0.730682785655 y2[1] (closed_form) = 0.702054705804 -0.730682785655 absolute error = 3.606e-16 relative error = 3.558e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.21540525796 -0.179120088638 y1[1] (closed_form) = 2.21540525796 -0.179120088638 absolute error = 4.045e-15 relative error = 1.820e-13 % Correct digits = 15 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=5781.7MB, alloc=44.3MB, time=75.44 x[1] = 0.2434 0.701 h = 0.0001 0.005 y2[1] (numeric) = 0.69731653312 -0.73744236017 y2[1] (closed_form) = 0.69731653312 -0.73744236017 absolute error = 4.243e-16 relative error = 4.180e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.21890869438 -0.18312414312 y1[1] (closed_form) = 2.21890869438 -0.18312414312 absolute error = 5.036e-15 relative error = 2.262e-13 % Correct digits = 15 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=5829.4MB, alloc=44.3MB, time=76.07 x[1] = 0.2435 0.706 h = 0.0001 0.003 y2[1] (numeric) = 0.69627486544 -0.743527679381 y2[1] (closed_form) = 0.69627486544 -0.743527679381 absolute error = 4.243e-16 relative error = 4.165e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.22258079154 -0.184714209508 y1[1] (closed_form) = 2.22258079154 -0.184714209508 absolute error = 5.036e-15 relative error = 2.258e-13 % Correct digits = 15 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=5877.3MB, alloc=44.3MB, time=76.69 x[1] = 0.2436 0.709 h = 0.001 0.001 y2[1] (numeric) = 0.69559687505 -0.747180206777 y2[1] (closed_form) = 0.69559687505 -0.747180206777 absolute error = 3.606e-16 relative error = 3.532e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.22478644535 -0.185700936442 y1[1] (closed_form) = 2.22478644535 -0.185700936442 absolute error = 4.045e-15 relative error = 1.812e-13 % Correct digits = 15 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 x[1] = 0.2446 0.71 h = 0.001 0.003 y2[1] (numeric) = 0.694185640142 -0.748218987413 y2[1] (closed_form) = 0.694185640142 -0.748218987413 absolute error = 3.606e-16 relative error = 3.533e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.22522903638 -0.186753744708 y1[1] (closed_form) = 2.22522903638 -0.186753744708 absolute error = 5.036e-15 relative error = 2.255e-13 % Correct digits = 15 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=5924.9MB, alloc=44.3MB, time=77.31 x[1] = 0.2456 0.713 h = 0.0001 0.004 y2[1] (numeric) = 0.692396676084 -0.751709999076 y2[1] (closed_form) = 0.692396676084 -0.751709999076 absolute error = 3.606e-16 relative error = 3.528e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.22717222056 -0.188423833642 y1[1] (closed_form) = 2.22717222056 -0.188423833642 absolute error = 5.025e-15 relative error = 2.248e-13 % Correct digits = 15 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=5972.7MB, alloc=44.3MB, time=77.94 x[1] = 0.2457 0.717 h = 0.003 0.006 y2[1] (numeric) = 0.691517500563 -0.756605745377 y2[1] (closed_form) = 0.691517500563 -0.756605745377 absolute error = 3.606e-16 relative error = 3.518e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.23015804386 -0.189731419135 y1[1] (closed_form) = 2.23015804386 -0.189731419135 absolute error = 5.025e-15 relative error = 2.245e-13 % Correct digits = 15 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=6020.5MB, alloc=44.3MB, time=78.56 x[1] = 0.2487 0.723 h = 0.0001 0.005 y2[1] (numeric) = 0.686670791845 -0.763422162512 y2[1] (closed_form) = 0.686670791845 -0.763422162512 absolute error = 4.243e-16 relative error = 4.132e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.2337854143 -0.19387687591 y1[1] (closed_form) = 2.2337854143 -0.19387687591 absolute error = 5.036e-15 relative error = 2.246e-13 % Correct digits = 15 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 x[1] = 0.2488 0.728 h = 0.0001 0.003 y2[1] (numeric) = 0.685573726578 -0.769581109641 y2[1] (closed_form) = 0.685573726578 -0.769581109641 absolute error = 3.606e-16 relative error = 3.498e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.23758652693 -0.195522911033 y1[1] (closed_form) = 2.23758652693 -0.195522911033 absolute error = 5.036e-15 relative error = 2.242e-13 % Correct digits = 15 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=6068.1MB, alloc=44.3MB, time=79.18 x[1] = 0.2489 0.731 h = 0.001 0.001 y2[1] (numeric) = 0.684861753537 -0.773277687335 y2[1] (closed_form) = 0.684861753537 -0.773277687335 absolute error = 3.606e-16 relative error = 3.491e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.23986933524 -0.196544399873 y1[1] (closed_form) = 2.23986933524 -0.196544399873 absolute error = 6.030e-15 relative error = 2.682e-13 % Correct digits = 15 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=6116.0MB, alloc=44.3MB, time=79.80 x[1] = 0.2499 0.732 h = 0.0001 0.004 y2[1] (numeric) = 0.683424566177 -0.774320696654 y2[1] (closed_form) = 0.683424566177 -0.774320696654 absolute error = 4.243e-16 relative error = 4.108e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.24032727777 -0.197634055829 y1[1] (closed_form) = 2.24032727777 -0.197634055829 absolute error = 6.030e-15 relative error = 2.681e-13 % Correct digits = 15 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=6163.9MB, alloc=44.3MB, time=80.42 x[1] = 0.25 0.736 h = 0.003 0.006 y2[1] (numeric) = 0.682507153376 -0.779268319478 y2[1] (closed_form) = 0.682507153376 -0.779268319478 absolute error = 4.243e-16 relative error = 4.096e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.24340274838 -0.198979869842 y1[1] (closed_form) = 2.24340274838 -0.198979869842 absolute error = 6.030e-15 relative error = 2.677e-13 % Correct digits = 15 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 x[1] = 0.253 0.742 h = 0.0001 0.005 y2[1] (numeric) = 0.677564689534 -0.786136602907 y2[1] (closed_form) = 0.677564689534 -0.786136602907 absolute error = 4.243e-16 relative error = 4.088e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.24713907531 -0.203247740885 y1[1] (closed_form) = 2.24713907531 -0.203247740885 absolute error = 6.030e-15 relative error = 2.672e-13 % Correct digits = 15 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=6211.5MB, alloc=44.3MB, time=81.04 x[1] = 0.2531 0.747 h = 0.0001 0.003 y2[1] (numeric) = 0.676419309226 -0.792361660785 y2[1] (closed_form) = 0.676419309226 -0.792361660785 absolute error = 4.243e-16 relative error = 4.072e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.25105301216 -0.204941701948 y1[1] (closed_form) = 2.25105301216 -0.204941701948 absolute error = 7.026e-15 relative error = 3.108e-13 % Correct digits = 15 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=6259.2MB, alloc=44.3MB, time=81.66 x[1] = 0.2532 0.75 h = 0.001 0.001 y2[1] (numeric) = 0.675677685132 -0.796097795764 y2[1] (closed_form) = 0.675677685132 -0.796097795764 absolute error = 4.243e-16 relative error = 4.063e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.25340330449 -0.205992978524 y1[1] (closed_form) = 2.25340330449 -0.205992978524 absolute error = 7.018e-15 relative error = 3.101e-13 % Correct digits = 15 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=6307.2MB, alloc=44.3MB, time=82.29 x[1] = 0.2542 0.751 h = 0.001 0.003 y2[1] (numeric) = 0.674217492402 -0.797144881281 y2[1] (closed_form) = 0.674217492402 -0.797144881281 absolute error = 4.243e-16 relative error = 4.064e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.2538748736 -0.207114652195 y1[1] (closed_form) = 2.2538748736 -0.207114652195 absolute error = 7.026e-15 relative error = 3.104e-13 % Correct digits = 15 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 x[1] = 0.2552 0.754 h = 0.0001 0.004 y2[1] (numeric) = 0.672338572949 -0.800701605346 y2[1] (closed_form) = 0.672338572949 -0.800701605346 absolute error = 5.000e-16 relative error = 4.782e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.25594492087 -0.208893739119 y1[1] (closed_form) = 2.25594492087 -0.208893739119 absolute error = 7.026e-15 relative error = 3.101e-13 % Correct digits = 15 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=6354.6MB, alloc=44.3MB, time=82.90 x[1] = 0.2553 0.758 h = 0.0001 0.004 y2[1] (numeric) = 0.671374460334 -0.805710779413 y2[1] (closed_form) = 0.671374460334 -0.805710779413 absolute error = 5.000e-16 relative error = 4.768e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.25912492715 -0.210286631604 y1[1] (closed_form) = 2.25912492715 -0.210286631604 absolute error = 8.022e-15 relative error = 3.536e-13 % Correct digits = 14 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=6402.5MB, alloc=44.3MB, time=83.53 x[1] = 0.2554 0.762 h = 0.003 0.006 y2[1] (numeric) = 0.670404448419 -0.810732573911 y2[1] (closed_form) = 0.670404448419 -0.810732573911 absolute error = 5.831e-16 relative error = 5.543e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.26232489863 -0.211683893879 y1[1] (closed_form) = 2.26232489863 -0.211683893879 absolute error = 8.022e-15 relative error = 3.531e-13 % Correct digits = 14 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=6450.3MB, alloc=44.3MB, time=84.16 x[1] = 0.2584 0.768 h = 0.0001 0.005 y2[1] (numeric) = 0.665328263185 -0.817676484628 y2[1] (closed_form) = 0.665328263185 -0.817676484628 absolute error = 6.708e-16 relative error = 6.364e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.26621372943 -0.216119287686 y1[1] (closed_form) = 2.26621372943 -0.216119287686 absolute error = 8.022e-15 relative error = 3.524e-13 % Correct digits = 14 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 x[1] = 0.2585 0.773 h = 0.0001 0.003 y2[1] (numeric) = 0.664116448722 -0.823996016976 y2[1] (closed_form) = 0.664116448722 -0.823996016976 absolute error = 6.708e-16 relative error = 6.339e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.27028437459 -0.21787775553 y1[1] (closed_form) = 2.27028437459 -0.21787775553 absolute error = 8.022e-15 relative error = 3.518e-13 % Correct digits = 14 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=6498.0MB, alloc=44.3MB, time=84.77 x[1] = 0.2586 0.776 h = 0.001 0.001 y2[1] (numeric) = 0.663334028473 -0.827788691023 y2[1] (closed_form) = 0.663334028473 -0.827788691023 absolute error = 6.708e-16 relative error = 6.324e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.2727284224 -0.21896916811 y1[1] (closed_form) = 2.2727284224 -0.21896916811 absolute error = 7.035e-15 relative error = 3.081e-13 % Correct digits = 15 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=6545.9MB, alloc=44.3MB, time=85.40 x[1] = 0.2596 0.777 h = 0.001 0.003 y2[1] (numeric) = 0.661841502742 -0.828842113114 y2[1] (closed_form) = 0.661841502742 -0.828842113114 absolute error = 6.708e-16 relative error = 6.325e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.27321932576 -0.220134895664 y1[1] (closed_form) = 2.27321932576 -0.220134895664 absolute error = 7.035e-15 relative error = 3.080e-13 % Correct digits = 15 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 x[1] = 0.2606 0.78 h = 0.0001 0.004 y2[1] (numeric) = 0.659904033388 -0.832443939954 y2[1] (closed_form) = 0.659904033388 -0.832443939954 absolute error = 7.616e-16 relative error = 7.169e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.2753721271 -0.221982918078 y1[1] (closed_form) = 2.2753721271 -0.221982918078 memory used=6593.9MB, alloc=44.3MB, time=86.02 absolute error = 7.035e-15 relative error = 3.077e-13 % Correct digits = 15 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 x[1] = 0.2607 0.784 h = 0.003 0.006 y2[1] (numeric) = 0.65888550907 -0.837529762931 y2[1] (closed_form) = 0.65888550907 -0.837529762931 absolute error = 7.616e-16 relative error = 7.147e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.27867800967 -0.223428835531 y1[1] (closed_form) = 2.27867800967 -0.223428835531 absolute error = 7.035e-15 relative error = 3.073e-13 % Correct digits = 15 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=6641.6MB, alloc=44.3MB, time=86.64 x[1] = 0.2637 0.79 h = 0.0001 0.005 y2[1] (numeric) = 0.653689156081 -0.844536711474 y2[1] (closed_form) = 0.653689156081 -0.844536711474 absolute error = 8.544e-16 relative error = 8.000e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.28269307582 -0.228014188885 y1[1] (closed_form) = 2.28269307582 -0.228014188885 absolute error = 7.035e-15 relative error = 3.067e-13 % Correct digits = 15 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=6689.4MB, alloc=44.3MB, time=87.26 x[1] = 0.2638 0.795 h = 0.0001 0.003 y2[1] (numeric) = 0.652416060048 -0.850937781192 y2[1] (closed_form) = 0.652416060048 -0.850937781192 absolute error = 8.544e-16 relative error = 7.968e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.2868970587 -0.22983369543 y1[1] (closed_form) = 2.2868970587 -0.22983369543 absolute error = 7.035e-15 relative error = 3.061e-13 % Correct digits = 15 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 x[1] = 0.2639 0.798 h = 0.001 0.001 y2[1] (numeric) = 0.651596049974 -0.85477921536 y2[1] (closed_form) = 0.651596049974 -0.85477921536 absolute error = 8.544e-16 relative error = 7.949e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.28942083297 -0.230962962143 y1[1] (closed_form) = 2.28942083297 -0.230962962143 absolute error = 7.026e-15 relative error = 3.053e-13 % Correct digits = 15 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=6737.2MB, alloc=44.3MB, time=87.88 x[1] = 0.2649 0.799 h = 0.001 0.003 y2[1] (numeric) = 0.650074811047 -0.85583732432 y2[1] (closed_form) = 0.650074811047 -0.85583732432 absolute error = 8.246e-16 relative error = 7.673e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.28992697687 -0.232167434898 y1[1] (closed_form) = 2.28992697687 -0.232167434898 absolute error = 8.031e-15 relative error = 3.489e-13 % Correct digits = 14 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=6785.0MB, alloc=44.3MB, time=88.50 x[1] = 0.2659 0.802 h = 0.0001 0.004 y2[1] (numeric) = 0.648084408263 -0.859477314253 y2[1] (closed_form) = 0.648084408263 -0.859477314253 absolute error = 8.246e-16 relative error = 7.661e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.29214902791 -0.234077851003 y1[1] (closed_form) = 2.29214902791 -0.234077851003 absolute error = 8.022e-15 relative error = 3.482e-13 % Correct digits = 14 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=6832.9MB, alloc=44.3MB, time=89.13 x[1] = 0.266 0.806 h = 0.003 0.006 y2[1] (numeric) = 0.647015721069 -0.864629246913 y2[1] (closed_form) = 0.647015721069 -0.864629246913 absolute error = 8.544e-16 relative error = 7.912e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.29556199159 -0.235573853852 y1[1] (closed_form) = 2.29556199159 -0.235573853852 absolute error = 8.031e-15 relative error = 3.480e-13 % Correct digits = 14 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 x[1] = 0.269 0.812 h = 0.0001 0.005 y2[1] (numeric) = 0.641695197045 -0.871701216028 y2[1] (closed_form) = 0.641695197045 -0.871701216028 absolute error = 9.220e-16 relative error = 8.518e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.29970405426 -0.240312193705 y1[1] (closed_form) = 2.29970405426 -0.240312193705 absolute error = 8.022e-15 relative error = 3.470e-13 % Correct digits = 14 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=6880.5MB, alloc=44.3MB, time=89.75 x[1] = 0.2691 0.817 h = 0.0001 0.003 y2[1] (numeric) = 0.640358746166 -0.878186444601 y2[1] (closed_form) = 0.640358746166 -0.878186444601 absolute error = 9.220e-16 relative error = 8.483e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.30404286723 -0.242194548948 y1[1] (closed_form) = 2.30404286723 -0.242194548948 absolute error = 9.027e-15 relative error = 3.897e-13 % Correct digits = 14 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=6928.3MB, alloc=44.3MB, time=90.37 x[1] = 0.2692 0.82 h = 0.001 0.001 y2[1] (numeric) = 0.639499876514 -0.882078199046 y2[1] (closed_form) = 0.639499876514 -0.882078199046 absolute error = 1.020e-15 relative error = 9.360e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.30664725523 -0.243362773241 y1[1] (closed_form) = 2.30664725523 -0.243362773241 absolute error = 9.020e-15 relative error = 3.889e-13 % Correct digits = 14 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=6976.2MB, alloc=44.3MB, time=91.00 x[1] = 0.2702 0.821 h = 0.001 0.003 y2[1] (numeric) = 0.637948984053 -0.883141122511 y2[1] (closed_form) = 0.637948984053 -0.883141122511 absolute error = 1.020e-15 relative error = 9.361e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.30716858953 -0.244606658384 y1[1] (closed_form) = 2.30716858953 -0.244606658384 absolute error = 9.020e-15 relative error = 3.888e-13 % Correct digits = 14 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 x[1] = 0.2712 0.824 h = 0.0001 0.004 y2[1] (numeric) = 0.635903891459 -0.886820470894 y2[1] (closed_form) = 0.635903891459 -0.886820470894 absolute error = 1.020e-15 relative error = 9.345e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.30946045781 -0.246580857406 y1[1] (closed_form) = 2.30946045781 -0.246580857406 absolute error = 9.027e-15 relative error = 3.887e-13 % Correct digits = 14 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=7023.9MB, alloc=44.3MB, time=91.62 x[1] = 0.2713 0.828 h = 0.003 0.006 y2[1] (numeric) = 0.63478335263 -0.892040612884 y2[1] (closed_form) = 0.63478335263 -0.892040612884 absolute error = 1.020e-15 relative error = 9.315e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.31298170976 -0.248128423675 y1[1] (closed_form) = 2.31298170976 -0.248128423675 absolute error = 9.027e-15 relative error = 3.881e-13 % Correct digits = 14 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=7071.7MB, alloc=44.3MB, time=92.23 x[1] = 0.2743 0.834 h = 0.0001 0.005 y2[1] (numeric) = 0.629334582513 -0.899179586003 y2[1] (closed_form) = 0.629334582513 -0.899179586003 absolute error = 1.118e-15 relative error = 1.019e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.31725155233 -0.253022876346 y1[1] (closed_form) = 2.31725155233 -0.253022876346 absolute error = 8.022e-15 relative error = 3.442e-13 % Correct digits = 14 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=7119.4MB, alloc=44.3MB, time=92.86 x[1] = 0.2744 0.839 h = 0.0001 0.003 y2[1] (numeric) = 0.627932654999 -0.90575161851 y2[1] (closed_form) = 0.627932654999 -0.90575161851 absolute error = 1.105e-15 relative error = 1.002e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.32172673455 -0.254969950384 y1[1] (closed_form) = 2.32172673455 -0.254969950384 absolute error = 8.022e-15 relative error = 3.435e-13 % Correct digits = 14 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 x[1] = 0.2745 0.842 h = 0.001 0.001 y2[1] (numeric) = 0.627033626567 -0.909695267268 y2[1] (closed_form) = 0.627033626567 -0.909695267268 absolute error = 1.118e-15 relative error = 1.012e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.32441265124 -0.256178272267 y1[1] (closed_form) = 2.32441265124 -0.256178272267 absolute error = 8.022e-15 relative error = 3.431e-13 % Correct digits = 14 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=7167.2MB, alloc=44.3MB, time=93.48 x[1] = 0.2755 0.843 h = 0.001 0.003 y2[1] (numeric) = 0.625452125592 -0.910763128154 y2[1] (closed_form) = 0.625452125592 -0.910763128154 absolute error = 1.105e-15 relative error = 9.997e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.32494912353 -0.257462258499 y1[1] (closed_form) = 2.32494912353 -0.257462258499 absolute error = 9.020e-15 relative error = 3.856e-13 % Correct digits = 14 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=7215.0MB, alloc=44.3MB, time=94.10 x[1] = 0.2765 0.846 h = 0.0001 0.004 y2[1] (numeric) = 0.623350552694 -0.914483035533 y2[1] (closed_form) = 0.623350552694 -0.914483035533 absolute error = 1.204e-15 relative error = 1.088e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.32731139356 -0.259501675023 y1[1] (closed_form) = 2.32731139356 -0.259501675023 absolute error = 8.022e-15 relative error = 3.426e-13 % Correct digits = 14 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=7262.8MB, alloc=44.3MB, time=94.72 x[1] = 0.2766 0.85 h = 0.003 0.006 y2[1] (numeric) = 0.62217643392 -0.919773505505 y2[1] (closed_form) = 0.62217643392 -0.919773505505 absolute error = 1.217e-15 relative error = 1.096e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.33094217826 -0.261102331502 y1[1] (closed_form) = 2.33094217826 -0.261102331502 absolute error = 9.020e-15 relative error = 3.846e-13 % Correct digits = 14 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 x[1] = 0.2796 0.856 h = 0.0001 0.005 y2[1] (numeric) = 0.616595268557 -0.9269814667 y2[1] (closed_form) = 0.616595268557 -0.9269814667 absolute error = 1.217e-15 relative error = 1.093e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.33534060599 -0.266156124286 y1[1] (closed_form) = 2.33534060599 -0.266156124286 absolute error = 9.020e-15 relative error = 3.838e-13 % Correct digits = 14 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=7310.3MB, alloc=44.3MB, time=95.34 x[1] = 0.2797 0.861 h = 0.0001 0.003 y2[1] (numeric) = 0.615125692523 -0.933642972525 y2[1] (closed_form) = 0.615125692523 -0.933642972525 absolute error = 1.315e-15 relative error = 1.176e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.3399537437 -0.268169848527 y1[1] (closed_form) = 2.3399537437 -0.268169848527 absolute error = 9.020e-15 relative error = 3.830e-13 % Correct digits = 14 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=7358.0MB, alloc=44.3MB, time=95.96 x[1] = 0.2798 0.864 h = 0.001 0.001 y2[1] (numeric) = 0.614185175693 -0.937640103926 y2[1] (closed_form) = 0.614185175693 -0.937640103926 absolute error = 1.315e-15 relative error = 1.173e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.34272213184 -0.269419445304 y1[1] (closed_form) = 2.34272213184 -0.269419445304 absolute error = 1.002e-14 relative error = 4.248e-13 % Correct digits = 14 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=7405.8MB, alloc=44.3MB, time=96.59 x[1] = 0.2808 0.865 h = 0.0001 0.004 y2[1] (numeric) = 0.612572096118 -0.938713020261 y2[1] (closed_form) = 0.612572096118 -0.938713020261 absolute error = 1.315e-15 relative error = 1.173e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.34327368726 -0.270744243139 y1[1] (closed_form) = 2.34327368726 -0.270744243139 absolute error = 1.002e-14 relative error = 4.247e-13 % Correct digits = 14 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 x[1] = 0.2809 0.869 h = 0.003 0.006 y2[1] (numeric) = 0.611351314844 -0.944066404719 y2[1] (closed_form) = 0.611351314844 -0.944066404719 absolute error = 1.315e-15 relative error = 1.169e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.34700043743 -0.272390532846 y1[1] (closed_form) = 2.34700043743 -0.272390532846 absolute error = 9.020e-15 relative error = 3.818e-13 % Correct digits = 14 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=7453.5MB, alloc=44.3MB, time=97.21 x[1] = 0.2839 0.875 h = 0.0001 0.005 y2[1] (numeric) = 0.605653661186 -0.951336983551 y2[1] (closed_form) = 0.605653661186 -0.951336983551 absolute error = 1.404e-15 relative error = 1.245e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.35151216048 -0.277582597783 y1[1] (closed_form) = 2.35151216048 -0.277582597783 absolute error = 1.002e-14 relative error = 4.231e-13 % Correct digits = 14 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=7501.2MB, alloc=44.3MB, time=97.83 x[1] = 0.284 0.88 h = 0.0001 0.003 y2[1] (numeric) = 0.604125186478 -0.958078503676 y2[1] (closed_form) = 0.604125186478 -0.958078503676 absolute error = 1.404e-15 relative error = 1.239e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.35624617846 -0.279653616731 y1[1] (closed_form) = 2.35624617846 -0.279653616731 absolute error = 9.020e-15 relative error = 3.801e-13 % Correct digits = 14 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=7549.1MB, alloc=44.3MB, time=98.46 x[1] = 0.2841 0.883 h = 0.001 0.001 y2[1] (numeric) = 0.603148532263 -0.96212347061 y2[1] (closed_form) = 0.603148532263 -0.96212347061 absolute error = 1.404e-15 relative error = 1.236e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.35908684304 -0.280938715146 y1[1] (closed_form) = 2.35908684304 -0.280938715146 absolute error = 9.020e-15 relative error = 3.797e-13 % Correct digits = 14 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 x[1] = 0.2851 0.884 h = 0.001 0.003 y2[1] (numeric) = 0.601507544222 -0.96320122134 y2[1] (closed_form) = 0.601507544222 -0.96320122134 absolute error = 1.404e-15 relative error = 1.236e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.35965183365 -0.28229904936 y1[1] (closed_form) = 2.35965183365 -0.28229904936 absolute error = 1.002e-14 relative error = 4.215e-13 % Correct digits = 14 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=7596.8MB, alloc=44.3MB, time=99.08 x[1] = 0.2861 0.887 h = 0.0001 0.004 y2[1] (numeric) = 0.599296504924 -0.967000537974 y2[1] (closed_form) = 0.599296504924 -0.967000537974 absolute error = 1.503e-15 relative error = 1.321e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.36214753773 -0.284462941475 y1[1] (closed_form) = 2.36214753773 -0.284462941475 absolute error = 9.020e-15 relative error = 3.791e-13 % Correct digits = 14 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=7644.7MB, alloc=44.3MB, time=99.70 x[1] = 0.2862 0.891 h = 0.003 0.006 y2[1] (numeric) = 0.598018843856 -0.972428267003 y2[1] (closed_form) = 0.598018843856 -0.972428267003 absolute error = 1.503e-15 relative error = 1.317e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.36598625611 -0.286165279694 y1[1] (closed_form) = 2.36598625611 -0.286165279694 absolute error = 9.020e-15 relative error = 3.785e-13 % Correct digits = 14 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 x[1] = 0.2892 0.897 h = 0.0001 0.005 y2[1] (numeric) = 0.592180892694 -0.979771578895 y2[1] (closed_form) = 0.592180892694 -0.979771578895 absolute error = 1.603e-15 relative error = 1.400e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.37062816088 -0.291522954273 y1[1] (closed_form) = 2.37062816088 -0.291522954273 absolute error = 9.020e-15 relative error = 3.776e-13 % Correct digits = 14 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=7692.5MB, alloc=44.3MB, time=100.32 x[1] = 0.2893 0.902 h = 0.0001 0.003 y2[1] (numeric) = 0.590580621729 -0.986607633921 y2[1] (closed_form) = 0.590580621729 -0.986607633921 absolute error = 1.603e-15 relative error = 1.394e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.37550323701 -0.293664364581 y1[1] (closed_form) = 2.37550323701 -0.293664364581 absolute error = 1.002e-14 relative error = 4.185e-13 % Correct digits = 14 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=7740.2MB, alloc=44.3MB, time=100.94 x[1] = 0.2894 0.905 h = 0.001 0.001 y2[1] (numeric) = 0.589559940052 -0.990709095211 y2[1] (closed_form) = 0.589559940052 -0.990709095211 absolute error = 1.603e-15 relative error = 1.391e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.37842821701 -0.294993018434 y1[1] (closed_form) = 2.37842821701 -0.294993018434 absolute error = 1.001e-14 relative error = 4.178e-13 % Correct digits = 14 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=7788.2MB, alloc=44.3MB, time=101.57 x[1] = 0.2904 0.906 h = 0.001 0.003 y2[1] (numeric) = 0.587885527746 -0.991792119412 y2[1] (closed_form) = 0.587885527746 -0.991792119412 absolute error = 1.603e-15 relative error = 1.390e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.37900819058 -0.29639554621 y1[1] (closed_form) = 2.37900819058 -0.29639554621 absolute error = 1.001e-14 relative error = 4.176e-13 % Correct digits = 14 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 x[1] = 0.2914 0.909 h = 0.0001 0.004 y2[1] (numeric) = 0.585612702213 -0.995635482114 y2[1] (closed_form) = 0.585612702213 -0.995635482114 absolute error = 1.603e-15 relative error = 1.388e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.38157608051 -0.298629009893 y1[1] (closed_form) = 2.38157608051 -0.298629009893 absolute error = 1.001e-14 relative error = 4.171e-13 % Correct digits = 14 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=7835.7MB, alloc=44.3MB, time=102.18 x[1] = 0.2915 0.913 h = 0.003 0.006 y2[1] (numeric) = 0.584276312995 -1.00113973237 y2[1] (closed_form) = 0.584276312995 -1.00113973237 absolute error = 1.005e-15 relative error = 8.670e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.38552812024 -0.300389068015 y1[1] (closed_form) = 2.38552812024 -0.300389068015 absolute error = 1.001e-14 relative error = 4.164e-13 % Correct digits = 14 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=7883.6MB, alloc=44.3MB, time=102.81 x[1] = 0.2945 0.919 h = 0.0001 0.005 y2[1] (numeric) = 0.578293690083 -1.00855776379 y2[1] (closed_form) = 0.578293690083 -1.00855776379 absolute error = 1.005e-15 relative error = 8.644e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.39030107357 -0.305915877496 y1[1] (closed_form) = 2.39030107357 -0.305915877496 absolute error = 9.014e-15 relative error = 3.741e-13 % Correct digits = 14 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=7931.4MB, alloc=44.3MB, time=103.43 x[1] = 0.2946 0.924 h = 0.0001 0.003 y2[1] (numeric) = 0.576619298973 -1.01549109722 y2[1] (closed_form) = 0.576619298973 -1.01549109722 absolute error = 1.005e-15 relative error = 8.606e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.39531893111 -0.308129792437 y1[1] (closed_form) = 2.39531893111 -0.308129792437 absolute error = 9.014e-15 relative error = 3.732e-13 % Correct digits = 14 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 x[1] = 0.2947 0.927 h = 0.001 0.001 y2[1] (numeric) = 0.575553167947 -1.01965068477 y2[1] (closed_form) = 0.575553167947 -1.01965068477 absolute error = 1.020e-15 relative error = 8.710e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.39832925022 -0.309503289647 y1[1] (closed_form) = 2.39832925022 -0.309503289647 absolute error = 9.014e-15 relative error = 3.727e-13 % Correct digits = 14 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=7979.2MB, alloc=44.3MB, time=104.05 x[1] = 0.2957 0.928 h = 0.001 0.003 y2[1] (numeric) = 0.573844315394 -1.02073908572 y2[1] (closed_form) = 0.573844315394 -1.02073908572 absolute error = 1.020e-15 relative error = 8.709e-14 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.39892414409 -0.310948785691 y1[1] (closed_form) = 2.39892414409 -0.310948785691 absolute error = 9.014e-15 relative error = 3.726e-13 % Correct digits = 14 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=8027.1MB, alloc=44.3MB, time=104.67 x[1] = 0.2967 0.931 h = 0.0001 0.004 y2[1] (numeric) = 0.571507771053 -1.0246277167 y2[1] (closed_form) = 0.571507771053 -1.0246277167 absolute error = 1.005e-15 relative error = 8.566e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.40156486972 -0.313253438106 y1[1] (closed_form) = 2.40156486972 -0.313253438106 absolute error = 9.020e-15 relative error = 3.724e-13 % Correct digits = 14 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=8074.9MB, alloc=44.3MB, time=105.30 x[1] = 0.2968 0.935 h = 0.003 0.006 y2[1] (numeric) = 0.570110760705 -1.03021068602 y2[1] (closed_form) = 0.570110760705 -1.03021068602 absolute error = 1.020e-15 relative error = 8.661e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.40563162216 -0.315072940267 y1[1] (closed_form) = 2.40563162216 -0.315072940267 absolute error = 9.020e-15 relative error = 3.718e-13 % Correct digits = 14 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 x[1] = 0.2998 0.941 h = 0.0001 0.005 y2[1] (numeric) = 0.563979008412 -1.03770542376 y2[1] (closed_form) = 0.563979008412 -1.03770542376 absolute error = 1.020e-15 relative error = 8.635e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.41053651121 -0.320772517585 y1[1] (closed_form) = 2.41053651121 -0.320772517585 absolute error = 9.014e-15 relative error = 3.707e-13 % Correct digits = 14 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=8122.4MB, alloc=44.3MB, time=105.91 x[1] = 0.2999 0.946 h = 0.0001 0.003 y2[1] (numeric) = 0.562228116787 -1.04473880616 y2[1] (closed_form) = 0.562228116787 -1.04473880616 absolute error = 1.020e-15 relative error = 8.596e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.41569892158 -0.323061116788 y1[1] (closed_form) = 2.41569892158 -0.323061116788 absolute error = 8.016e-15 relative error = 3.289e-13 % Correct digits = 14 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=8170.1MB, alloc=44.3MB, time=106.53 x[1] = 0.3 0.949 h = 0.001 0.001 y2[1] (numeric) = 0.561115080251 -1.04895816779 y2[1] (closed_form) = 0.561115080251 -1.04895816779 absolute error = 1.020e-15 relative error = 8.573e-14 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.41879563195 -0.324480785622 y1[1] (closed_form) = 2.41879563195 -0.324480785622 absolute error = 8.016e-15 relative error = 3.284e-13 % Correct digits = 14 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=8218.0MB, alloc=44.3MB, time=107.16 x[1] = 0.301 0.95 h = 0.001 0.003 y2[1] (numeric) = 0.55937075451 -1.05005204317 y2[1] (closed_form) = 0.55937075451 -1.05005204317 absolute error = 2.010e-15 relative error = 1.689e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.41940538022 -0.325970047709 y1[1] (closed_form) = 2.41940538022 -0.325970047709 absolute error = 8.016e-15 relative error = 3.283e-13 % Correct digits = 14 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 x[1] = 0.302 0.953 h = 0.0001 0.004 y2[1] (numeric) = 0.55696851918 -1.05398717043 y2[1] (closed_form) = 0.55696851918 -1.05398717043 absolute error = 1.020e-15 relative error = 8.555e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.42211960806 -0.328347555463 y1[1] (closed_form) = 2.42211960806 -0.328347555463 absolute error = 8.016e-15 relative error = 3.279e-13 % Correct digits = 14 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=8265.5MB, alloc=44.3MB, time=107.78 x[1] = 0.3021 0.957 h = 0.003 0.006 y2[1] (numeric) = 0.555508948727 -1.05965107841 y2[1] (closed_form) = 0.555508948727 -1.05965107841 absolute error = 1.020e-15 relative error = 8.524e-14 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.42630250298 -0.330228279655 y1[1] (closed_form) = 2.42630250298 -0.330228279655 absolute error = 9.014e-15 relative error = 3.681e-13 % Correct digits = 14 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=8313.3MB, alloc=44.3MB, time=108.40 x[1] = 0.3051 0.963 h = 0.0001 0.005 y2[1] (numeric) = 0.549223523542 -1.06722450947 y2[1] (closed_form) = 0.549223523542 -1.06722450947 absolute error = 1.020e-15 relative error = 8.497e-14 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.43134023474 -0.336104367285 y1[1] (closed_form) = 2.43134023474 -0.336104367285 absolute error = 9.020e-15 relative error = 3.675e-13 % Correct digits = 14 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=8361.2MB, alloc=44.3MB, time=109.04 x[1] = 0.3052 0.968 h = 0.0001 0.003 y2[1] (numeric) = 0.547393692821 -1.07436073918 y2[1] (closed_form) = 0.547393692821 -1.07436073918 absolute error = 1.020e-15 relative error = 8.458e-14 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.43664901787 -0.338469898138 y1[1] (closed_form) = 2.43664901787 -0.338469898138 absolute error = 9.020e-15 relative error = 3.667e-13 % Correct digits = 14 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 x[1] = 0.3053 0.971 h = 0.001 0.001 y2[1] (numeric) = 0.546232259285 -1.07864153901 y2[1] (closed_form) = 0.546232259285 -1.07864153901 absolute error = 2.010e-15 relative error = 1.662e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.43983320027 -0.339937108066 y1[1] (closed_form) = 2.43983320027 -0.339937108066 absolute error = 9.020e-15 relative error = 3.662e-13 % Correct digits = 14 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=8409.0MB, alloc=44.3MB, time=109.67 x[1] = 0.3063 0.972 h = 0.0001 0.004 y2[1] (numeric) = 0.544451409969 -1.07974098074 y2[1] (closed_form) = 0.544451409969 -1.07974098074 absolute error = 1.020e-15 relative error = 8.433e-14 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.44045773362 -0.341470957387 y1[1] (closed_form) = 2.44045773362 -0.341470957387 absolute error = 1.002e-14 relative error = 4.065e-13 % Correct digits = 14 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=8456.9MB, alloc=44.3MB, time=110.29 x[1] = 0.3064 0.976 h = 0.003 0.006 y2[1] (numeric) = 0.542937401565 -1.08547712996 y2[1] (closed_form) = 0.542937401565 -1.08547712996 absolute error = 2.010e-15 relative error = 1.656e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.4447425337 -0.343404437807 y1[1] (closed_form) = 2.4447425337 -0.343404437807 absolute error = 9.020e-15 relative error = 3.654e-13 % Correct digits = 14 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=8504.8MB, alloc=44.3MB, time=110.92 x[1] = 0.3094 0.982 h = 0.0001 0.005 y2[1] (numeric) = 0.536516963721 -1.09312179461 y2[1] (closed_form) = 0.536516963721 -1.09312179461 absolute error = 2.010e-15 relative error = 1.651e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.44989751851 -0.349433944067 y1[1] (closed_form) = 2.44989751851 -0.349433944067 absolute error = 9.020e-15 relative error = 3.645e-13 % Correct digits = 14 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 x[1] = 0.3095 0.987 h = 0.0001 0.003 y2[1] (numeric) = 0.53461845737 -1.10034979538 y2[1] (closed_form) = 0.53461845737 -1.10034979538 absolute error = 3.007e-15 relative error = 2.458e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.45533474314 -0.351865773576 y1[1] (closed_form) = 2.45533474314 -0.351865773576 absolute error = 9.020e-15 relative error = 3.636e-13 % Correct digits = 14 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=8552.5MB, alloc=44.3MB, time=111.54 x[1] = 0.3096 0.99 h = 0.001 0.001 y2[1] (numeric) = 0.533414902345 -1.10468542586 y2[1] (closed_form) = 0.533414902345 -1.10468542586 absolute error = 3.007e-15 relative error = 2.451e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.45859569527 -0.353373974005 y1[1] (closed_form) = 2.45859569527 -0.353373974005 absolute error = 9.027e-15 relative error = 3.634e-13 % Correct digits = 14 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=8600.5MB, alloc=44.3MB, time=112.16 x[1] = 0.3106 0.991 h = 0.001 0.003 y2[1] (numeric) = 0.531601827622 -1.10579018039 y2[1] (closed_form) = 0.531601827622 -1.10579018039 absolute error = 3.007e-15 relative error = 2.451e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.4592334417 -0.354946703337 y1[1] (closed_form) = 2.4592334417 -0.354946703337 absolute error = 1.002e-14 relative error = 4.034e-13 % Correct digits = 14 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 x[1] = 0.3116 0.994 h = 0.0001 0.004 y2[1] (numeric) = 0.529072555714 -1.10981595482 y2[1] (closed_form) = 0.529072555714 -1.10981595482 absolute error = 3.007e-15 relative error = 2.445e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.46208718745 -0.357463491725 y1[1] (closed_form) = 2.46208718745 -0.357463491725 absolute error = 1.002e-14 relative error = 4.029e-13 % Correct digits = 14 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=8648.2MB, alloc=44.3MB, time=112.78 x[1] = 0.3117 0.998 h = 0.003 0.006 y2[1] (numeric) = 0.527492279055 -1.11563725712 y2[1] (closed_form) = 0.527492279055 -1.11563725712 absolute error = 3.007e-15 relative error = 2.436e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.46649091638 -0.35946163176 y1[1] (closed_form) = 2.46649091638 -0.35946163176 absolute error = 1.002e-14 relative error = 4.022e-13 % Correct digits = 14 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=8696.0MB, alloc=44.3MB, time=113.41 x[1] = 0.3147 1.004 h = 0.0001 0.005 y2[1] (numeric) = 0.520909500285 -1.12336436903 y2[1] (closed_form) = 0.520909500285 -1.12336436903 absolute error = 3.007e-15 relative error = 2.428e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.47178053067 -0.365674899012 y1[1] (closed_form) = 2.47178053067 -0.365674899012 absolute error = 9.027e-15 relative error = 3.613e-13 % Correct digits = 14 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=8743.9MB, alloc=44.3MB, time=114.03 x[1] = 0.3148 1.009 h = 0.0001 0.003 y2[1] (numeric) = 0.518927390356 -1.13070053128 y2[1] (closed_form) = 0.518927390356 -1.13070053128 absolute error = 3.007e-15 relative error = 2.417e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.47736767334 -0.368188004331 y1[1] (closed_form) = 2.47736767334 -0.368188004331 absolute error = 1.002e-14 relative error = 4.002e-13 % Correct digits = 14 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 x[1] = 0.3149 1.012 h = 0.001 0.001 y2[1] (numeric) = 0.517672585626 -1.13510076014 y2[1] (closed_form) = 0.517672585626 -1.13510076014 absolute error = 3.007e-15 relative error = 2.410e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.48071820284 -0.369746393097 y1[1] (closed_form) = 2.48071820284 -0.369746393097 absolute error = 1.002e-14 relative error = 3.997e-13 % Correct digits = 14 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=8791.6MB, alloc=44.3MB, time=114.65 x[1] = 0.3159 1.013 h = 0.001 0.003 y2[1] (numeric) = 0.515820985559 -1.13621124901 y2[1] (closed_form) = 0.515820985559 -1.13621124901 absolute error = 4.011e-15 relative error = 3.215e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.4813706059 -0.371365302207 y1[1] (closed_form) = 2.4813706059 -0.371365302207 absolute error = 1.002e-14 relative error = 3.995e-13 % Correct digits = 14 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=8839.3MB, alloc=44.3MB, time=115.27 x[1] = 0.3169 1.016 h = 0.0001 0.004 y2[1] (numeric) = 0.513220166158 -1.14028709067 y2[1] (closed_form) = 0.513220166158 -1.14028709067 absolute error = 4.005e-15 relative error = 3.203e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.48429987333 -0.373959986455 y1[1] (closed_form) = 2.48429987333 -0.373959986455 absolute error = 1.002e-14 relative error = 3.990e-13 % Correct digits = 14 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=8887.0MB, alloc=44.3MB, time=115.89 x[1] = 0.317 1.02 h = 0.003 0.006 y2[1] (numeric) = 0.51157154313 -1.14619583156 y2[1] (closed_form) = 0.51157154313 -1.14619583156 absolute error = 4.005e-15 relative error = 3.191e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.48882407287 -0.37602472413 y1[1] (closed_form) = 2.48882407287 -0.37602472413 absolute error = 1.002e-14 relative error = 3.983e-13 % Correct digits = 14 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 x[1] = 0.32 1.026 h = 0.0001 0.005 y2[1] (numeric) = 0.504821620095 -1.15400737847 y2[1] (closed_form) = 0.504821620095 -1.15400737847 absolute error = 4.005e-15 relative error = 3.180e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.49424927924 -0.382425818777 y1[1] (closed_form) = 2.49424927924 -0.382425818777 absolute error = 1.002e-14 relative error = 3.973e-13 % Correct digits = 14 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=8934.6MB, alloc=44.3MB, time=116.51 x[1] = 0.3201 1.031 h = 0.0001 0.003 y2[1] (numeric) = 0.502753291975 -1.16145458467 y2[1] (closed_form) = 0.502753291975 -1.16145458467 absolute error = 3.007e-15 relative error = 2.376e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.49998830116 -0.385022648709 y1[1] (closed_form) = 2.49998830116 -0.385022648709 absolute error = 1.103e-14 relative error = 4.360e-13 % Correct digits = 14 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=8982.5MB, alloc=44.3MB, time=117.14 x[1] = 0.3202 1.034 h = 0.001 0.001 y2[1] (numeric) = 0.501445639235 -1.16592112543 y2[1] (closed_form) = 0.501445639235 -1.16592112543 absolute error = 4.005e-15 relative error = 3.156e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.50342957217 -0.386632717719 y1[1] (closed_form) = 2.50342957217 -0.386632717719 absolute error = 1.103e-14 relative error = 4.354e-13 % Correct digits = 14 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=9030.5MB, alloc=44.3MB, time=117.76 x[1] = 0.3212 1.035 h = 0.001 0.003 y2[1] (numeric) = 0.499554410652 -1.1670374231 y2[1] (closed_form) = 0.499554410652 -1.1670374231 absolute error = 3.007e-15 relative error = 2.368e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.50409655175 -0.388298696857 y1[1] (closed_form) = 2.50409655175 -0.388298696857 absolute error = 1.104e-14 relative error = 4.355e-13 % Correct digits = 14 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 x[1] = 0.3222 1.038 h = 0.0001 0.004 y2[1] (numeric) = 0.496879907427 -1.1711645837 y2[1] (closed_form) = 0.496879907427 -1.1711645837 absolute error = 3.002e-15 relative error = 2.359e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.50710207125 -0.390973143098 y1[1] (closed_form) = 2.50710207125 -0.390973143098 absolute error = 1.004e-14 relative error = 3.957e-13 % Correct digits = 14 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=9078.1MB, alloc=44.3MB, time=118.38 x[1] = 0.3223 1.042 h = 0.003 0.006 y2[1] (numeric) = 0.495160808362 -1.17716307263 y2[1] (closed_form) = 0.495160808362 -1.17716307263 absolute error = 3.007e-15 relative error = 2.354e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.51174832255 -0.393106474897 y1[1] (closed_form) = 2.51174832255 -0.393106474897 absolute error = 1.004e-14 relative error = 3.949e-13 % Correct digits = 14 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=9126.0MB, alloc=44.3MB, time=119.00 x[1] = 0.3253 1.048 h = 0.0001 0.005 y2[1] (numeric) = 0.488238841827 -1.18506104181 y2[1] (closed_form) = 0.488238841827 -1.18506104181 absolute error = 3.007e-15 relative error = 2.346e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.51731010164 -0.399699580598 y1[1] (closed_form) = 2.51731010164 -0.399699580598 absolute error = 1.104e-14 relative error = 4.330e-13 % Correct digits = 14 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=9173.8MB, alloc=44.3MB, time=119.63 x[1] = 0.3254 1.053 h = 0.0001 0.003 y2[1] (numeric) = 0.486081615699 -1.19262220492 y2[1] (closed_form) = 0.486081615699 -1.19262220492 absolute error = 3.007e-15 relative error = 2.335e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.52320301373 -0.402382657538 y1[1] (closed_form) = 2.52320301373 -0.402382657538 absolute error = 1.004e-14 relative error = 3.930e-13 % Correct digits = 14 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 x[1] = 0.3255 1.056 h = 0.001 0.001 y2[1] (numeric) = 0.484719477083 -1.19715678901 y2[1] (closed_form) = 0.484719477083 -1.19715678901 absolute error = 3.007e-15 relative error = 2.328e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.52673621971 -0.404045943426 y1[1] (closed_form) = 2.52673621971 -0.404045943426 absolute error = 1.004e-14 relative error = 3.924e-13 % Correct digits = 14 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=9221.4MB, alloc=44.3MB, time=120.24 x[1] = 0.3265 1.057 h = 0.001 0.003 y2[1] (numeric) = 0.482787497389 -1.19827896336 y2[1] (closed_form) = 0.482787497389 -1.19827896336 absolute error = 3.007e-15 relative error = 2.327e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.52741769136 -0.405759907701 y1[1] (closed_form) = 2.52741769136 -0.405759907701 absolute error = 1.104e-14 relative error = 4.312e-13 % Correct digits = 14 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=9269.3MB, alloc=44.3MB, time=120.87 x[1] = 0.3275 1.06 h = 0.0001 0.004 y2[1] (numeric) = 0.480037128446 -1.20245870083 y2[1] (closed_form) = 0.480037128446 -1.20245870083 absolute error = 3.007e-15 relative error = 2.322e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.53050020949 -0.408516036216 y1[1] (closed_form) = 2.53050020949 -0.408516036216 absolute error = 1.004e-14 relative error = 3.917e-13 % Correct digits = 14 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=9317.2MB, alloc=44.3MB, time=121.50 x[1] = 0.3276 1.064 h = 0.003 0.006 y2[1] (numeric) = 0.478245370613 -1.20854927172 y2[1] (closed_form) = 0.478245370613 -1.20854927172 absolute error = 3.007e-15 relative error = 2.313e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.53527013335 -0.410720018362 y1[1] (closed_form) = 2.53527013335 -0.410720018362 absolute error = 1.004e-14 relative error = 3.909e-13 % Correct digits = 14 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 x[1] = 0.3306 1.07 h = 0.0001 0.005 y2[1] (numeric) = 0.471146362751 -1.21653564971 y2[1] (closed_form) = 0.471146362751 -1.21653564971 absolute error = 3.015e-15 relative error = 2.311e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.54096948326 -0.417509438169 y1[1] (closed_form) = 2.54096948326 -0.417509438169 absolute error = 1.004e-14 relative error = 3.899e-13 % Correct digits = 14 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=9364.8MB, alloc=44.3MB, time=122.12 x[1] = 0.3307 1.075 h = 0.0001 0.003 y2[1] (numeric) = 0.468897491688 -1.22421371394 y2[1] (closed_form) = 0.468897491688 -1.22421371394 absolute error = 3.007e-15 relative error = 2.294e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.5470183465 -0.420281359725 y1[1] (closed_form) = 2.5470183465 -0.420281359725 absolute error = 1.004e-14 relative error = 3.889e-13 % Correct digits = 14 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=9412.7MB, alloc=44.3MB, time=122.74 x[1] = 0.3308 1.078 h = 0.001 0.001 y2[1] (numeric) = 0.467479188621 -1.22881809111 y2[1] (closed_form) = 0.467479188621 -1.22881809111 absolute error = 3.007e-15 relative error = 2.287e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.55064471041 -0.421999444826 y1[1] (closed_form) = 2.55064471041 -0.421999444826 absolute error = 1.004e-14 relative error = 3.884e-13 % Correct digits = 14 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=9460.5MB, alloc=44.3MB, time=123.36 x[1] = 0.3318 1.079 h = 0.0001 0.004 y2[1] (numeric) = 0.465505315271 -1.2299462032 y2[1] (closed_form) = 0.465505315271 -1.2299462032 absolute error = 3.015e-15 relative error = 2.293e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.5513405851 -0.423762334605 y1[1] (closed_form) = 2.5513405851 -0.423762334605 absolute error = 1.004e-14 relative error = 3.882e-13 % Correct digits = 14 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 x[1] = 0.3319 1.083 h = 0.003 0.006 y2[1] (numeric) = 0.463650360851 -1.23611882512 y2[1] (closed_form) = 0.463650360851 -1.23611882512 absolute error = 3.007e-15 relative error = 2.277e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.55621916659 -0.426027323161 y1[1] (closed_form) = 2.55621916659 -0.426027323161 absolute error = 1.003e-14 relative error = 3.871e-13 % Correct digits = 14 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=9508.2MB, alloc=44.3MB, time=123.98 x[1] = 0.3349 1.089 h = 0.0001 0.005 y2[1] (numeric) = 0.456395967599 -1.2441850843 y2[1] (closed_form) = 0.456395967599 -1.2441850843 absolute error = 3.007e-15 relative error = 2.269e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.5620401556 -0.432987606916 y1[1] (closed_form) = 2.5620401556 -0.432987606916 absolute error = 1.003e-14 relative error = 3.861e-13 % Correct digits = 14 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=9555.9MB, alloc=44.3MB, time=124.60 x[1] = 0.335 1.094 h = 0.0001 0.003 y2[1] (numeric) = 0.454067400145 -1.2519672926 y2[1] (closed_form) = 0.454067400145 -1.2519672926 absolute error = 3.007e-15 relative error = 2.258e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.56822604706 -0.435836249668 y1[1] (closed_form) = 2.56822604706 -0.435836249668 absolute error = 1.003e-14 relative error = 3.851e-13 % Correct digits = 14 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 x[1] = 0.3351 1.097 h = 0.001 0.001 y2[1] (numeric) = 0.452600236572 -1.25663385777 y2[1] (closed_form) = 0.452600236572 -1.25663385777 absolute error = 3.007e-15 relative error = 2.251e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.57193427948 -0.437601676763 y1[1] (closed_form) = 2.57193427948 -0.437601676763 absolute error = 9.045e-15 relative error = 3.467e-13 % Correct digits = 14 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=9603.6MB, alloc=44.3MB, time=125.22 x[1] = 0.3361 1.098 h = 0.001 0.003 y2[1] (numeric) = 0.450589443603 -1.25776764231 y2[1] (closed_form) = 0.450589443603 -1.25776764231 absolute error = 3.007e-15 relative error = 2.250e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.57264307537 -0.439407282554 y1[1] (closed_form) = 2.57264307537 -0.439407282554 absolute error = 1.004e-14 relative error = 3.847e-13 % Correct digits = 14 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=9651.5MB, alloc=44.3MB, time=125.84 x[1] = 0.3371 1.101 h = 0.0001 0.004 y2[1] (numeric) = 0.447692599597 -1.2620495499 y2[1] (closed_form) = 0.447692599597 -1.2620495499 absolute error = 3.007e-15 relative error = 2.245e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.57587194149 -0.44231976453 y1[1] (closed_form) = 2.57587194149 -0.44231976453 absolute error = 9.045e-15 relative error = 3.461e-13 % Correct digits = 14 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=9699.4MB, alloc=44.3MB, time=126.47 x[1] = 0.3372 1.105 h = 0.003 0.006 y2[1] (numeric) = 0.44576080685 -1.26831869129 y2[1] (closed_form) = 0.44576080685 -1.26831869129 absolute error = 3.007e-15 relative error = 2.236e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.58087734412 -0.444659372678 y1[1] (closed_form) = 2.58087734412 -0.444659372678 absolute error = 9.055e-15 relative error = 3.458e-13 % Correct digits = 14 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 x[1] = 0.3402 1.111 h = 0.0001 0.005 y2[1] (numeric) = 0.438319824271 -1.27647711538 y2[1] (closed_form) = 0.438319824271 -1.27647711538 absolute error = 3.007e-15 relative error = 2.228e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.58683786057 -0.451824290492 y1[1] (closed_form) = 2.58683786057 -0.451824290492 absolute error = 9.055e-15 relative error = 3.448e-13 % Correct digits = 14 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=9747.0MB, alloc=44.3MB, time=127.09 x[1] = 0.3403 1.116 h = 0.0001 0.003 y2[1] (numeric) = 0.435894351198 -1.28438182348 y2[1] (closed_form) = 0.435894351198 -1.28438182348 absolute error = 3.007e-15 relative error = 2.217e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.59318370566 -0.454766791343 y1[1] (closed_form) = 2.59318370566 -0.454766791343 absolute error = 9.055e-15 relative error = 3.440e-13 % Correct digits = 14 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=9794.7MB, alloc=44.3MB, time=127.71 x[1] = 0.3404 1.119 h = 0.001 0.001 y2[1] (numeric) = 0.434367808725 -1.28912150893 y2[1] (closed_form) = 0.434367808725 -1.28912150893 absolute error = 3.015e-15 relative error = 2.216e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.59698747101 -0.456590071714 y1[1] (closed_form) = 2.59698747101 -0.456590071714 absolute error = 9.055e-15 relative error = 3.434e-13 % Correct digits = 14 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=9842.7MB, alloc=44.3MB, time=128.33 x[1] = 0.3414 1.12 h = 0.001 0.003 y2[1] (numeric) = 0.432312941681 -1.29026134001 y2[1] (closed_form) = 0.432312941681 -1.29026134001 absolute error = 4.005e-15 relative error = 2.943e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.59771050312 -0.458446422643 y1[1] (closed_form) = 2.59771050312 -0.458446422643 absolute error = 9.055e-15 relative error = 3.433e-13 % Correct digits = 14 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 x[1] = 0.3424 1.123 h = 0.0001 0.004 y2[1] (numeric) = 0.429333742073 -1.29459948589 y2[1] (closed_form) = 0.429333742073 -1.29459948589 absolute error = 4.005e-15 relative error = 2.936e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.60101861699 -0.461446379376 y1[1] (closed_form) = 2.60101861699 -0.461446379376 absolute error = 9.055e-15 relative error = 3.428e-13 % Correct digits = 14 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=9890.3MB, alloc=44.3MB, time=128.95 x[1] = 0.3425 1.127 h = 0.003 0.006 y2[1] (numeric) = 0.427322768176 -1.30096755446 y2[1] (closed_form) = 0.427322768176 -1.30096755446 absolute error = 4.005e-15 relative error = 2.925e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.60615257722 -0.463862841145 y1[1] (closed_form) = 2.60615257722 -0.463862841145 absolute error = 9.055e-15 relative error = 3.421e-13 % Correct digits = 14 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=9938.2MB, alloc=44.3MB, time=129.57 x[1] = 0.3455 1.133 h = 0.0001 0.005 y2[1] (numeric) = 0.419689901068 -1.30922012769 y2[1] (closed_form) = 0.419689901068 -1.30922012769 absolute error = 4.005e-15 relative error = 2.913e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.61225366766 -0.471237049766 y1[1] (closed_form) = 2.61225366766 -0.471237049766 absolute error = 9.055e-15 relative error = 3.411e-13 % Correct digits = 14 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=9985.9MB, alloc=44.3MB, time=130.19 x[1] = 0.3456 1.138 h = 0.0001 0.003 y2[1] (numeric) = 0.417164573029 -1.31725037387 y2[1] (closed_form) = 0.417164573029 -1.31725037387 absolute error = 4.005e-15 relative error = 2.899e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.61876167334 -0.474276230234 y1[1] (closed_form) = 2.61876167334 -0.474276230234 absolute error = 8.075e-15 relative error = 3.034e-13 % Correct digits = 15 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 x[1] = 0.3457 1.141 h = 0.001 0.001 y2[1] (numeric) = 0.415576850293 -1.3220649845 y2[1] (closed_form) = 0.415576850293 -1.3220649845 absolute error = 4.005e-15 relative error = 2.890e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.62266228062 -0.476159082261 y1[1] (closed_form) = 2.62266228062 -0.476159082261 absolute error = 8.062e-15 relative error = 3.025e-13 % Correct digits = 15 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=10033.7MB, alloc=44.3MB, time=130.81 x[1] = 0.3467 1.142 h = 0.001 0.003 y2[1] (numeric) = 0.413476706483 -1.32321090258 y2[1] (closed_form) = 0.413476706483 -1.32321090258 absolute error = 5.004e-15 relative error = 3.610e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.62339944566 -0.478067193304 y1[1] (closed_form) = 2.62339944566 -0.478067193304 absolute error = 8.062e-15 relative error = 3.023e-13 % Correct digits = 15 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=10081.5MB, alloc=44.3MB, time=131.44 x[1] = 0.3477 1.145 h = 0.0001 0.004 y2[1] (numeric) = 0.410412781256 -1.32760656979 y2[1] (closed_form) = 0.410412781256 -1.32760656979 absolute error = 5.001e-15 relative error = 3.599e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.6267876159 -0.481156764054 y1[1] (closed_form) = 2.6267876159 -0.481156764054 absolute error = 8.062e-15 relative error = 3.019e-13 % Correct digits = 15 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=10129.5MB, alloc=44.3MB, time=132.06 x[1] = 0.3478 1.149 h = 0.003 0.006 y2[1] (numeric) = 0.408320224215 -1.33407599991 y2[1] (closed_form) = 0.408320224215 -1.33407599991 absolute error = 5.001e-15 relative error = 3.585e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.63205191084 -0.483652378496 y1[1] (closed_form) = 2.63205191084 -0.483652378496 absolute error = 8.062e-15 relative error = 3.013e-13 % Correct digits = 15 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 x[1] = 0.3508 1.155 h = 0.0001 0.005 y2[1] (numeric) = 0.400490067932 -1.3424247047 y2[1] (closed_form) = 0.400490067932 -1.3424247047 absolute error = 5.001e-15 relative error = 3.570e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.63829463711 -0.491240662874 y1[1] (closed_form) = 2.63829463711 -0.491240662874 absolute error = 7.058e-15 relative error = 2.630e-13 % Correct digits = 15 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=10177.0MB, alloc=44.3MB, time=132.68 x[1] = 0.3509 1.16 h = 0.0001 0.003 y2[1] (numeric) = 0.397861860778 -1.35058356117 y2[1] (closed_form) = 0.397861860778 -1.35058356117 absolute error = 4.001e-15 relative error = 2.842e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.64496706174 -0.494379426373 y1[1] (closed_form) = 2.64496706174 -0.494379426373 absolute error = 7.058e-15 relative error = 2.623e-13 % Correct digits = 15 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=10224.9MB, alloc=44.3MB, time=133.30 x[1] = 0.351 1.163 h = 0.001 0.001 y2[1] (numeric) = 0.396211111046 -1.3554749218 y2[1] (closed_form) = 0.396211111046 -1.3554749218 absolute error = 4.005e-15 relative error = 2.836e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.64896585022 -0.496323618183 y1[1] (closed_form) = 2.64896585022 -0.496323618183 absolute error = 7.071e-15 relative error = 2.624e-13 % Correct digits = 15 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=10272.8MB, alloc=44.3MB, time=133.92 x[1] = 0.352 1.164 h = 0.001 0.003 y2[1] (numeric) = 0.394064465719 -1.35662695953 y2[1] (closed_form) = 0.394064465719 -1.35662695953 absolute error = 4.005e-15 relative error = 2.835e-13 % Correct digits = 15 h = 0.001 0.003 y1[1] (numeric) = 2.64971703927 -0.49828453121 y1[1] (closed_form) = 2.64971703927 -0.49828453121 absolute error = 7.071e-15 relative error = 2.623e-13 % Correct digits = 15 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 x[1] = 0.353 1.167 h = 0.0001 0.004 y2[1] (numeric) = 0.390913392813 -1.36108143761 y2[1] (closed_form) = 0.390913392813 -1.36108143761 absolute error = 4.005e-15 relative error = 2.828e-13 % Correct digits = 15 h = 0.0001 0.004 y1[1] (numeric) = 2.65318609007 -0.501465914766 y1[1] (closed_form) = 2.65318609007 -0.501465914766 absolute error = 7.071e-15 relative error = 2.619e-13 % Correct digits = 15 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=10320.6MB, alloc=44.3MB, time=134.55 x[1] = 0.3531 1.171 h = 0.003 0.006 y2[1] (numeric) = 0.388736789796 -1.3676546908 y2[1] (closed_form) = 0.388736789796 -1.3676546908 absolute error = 4.001e-15 relative error = 2.814e-13 % Correct digits = 15 h = 0.003 0.006 y1[1] (numeric) = 2.65858253782 -0.504043047413 y1[1] (closed_form) = 2.65858253782 -0.504043047413 absolute error = 7.071e-15 relative error = 2.613e-13 % Correct digits = 15 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=10368.4MB, alloc=44.3MB, time=135.17 x[1] = 0.3561 1.177 h = 0.0001 0.005 y2[1] (numeric) = 0.380703827328 -1.37610150738 y2[1] (closed_form) = 0.380703827328 -1.37610150738 absolute error = 4.001e-15 relative error = 2.802e-13 % Correct digits = 15 h = 0.0001 0.005 y1[1] (numeric) = 2.6649679764 -0.511850323136 y1[1] (closed_form) = 2.6649679764 -0.511850323136 absolute error = 7.071e-15 relative error = 2.606e-13 % Correct digits = 15 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=10416.3MB, alloc=44.3MB, time=135.80 x[1] = 0.3562 1.182 h = 0.0001 0.003 y2[1] (numeric) = 0.377969640007 -1.38439208101 y2[1] (closed_form) = 0.377969640007 -1.38439208101 absolute error = 4.001e-15 relative error = 2.788e-13 % Correct digits = 15 h = 0.0001 0.003 y1[1] (numeric) = 2.67180713007 -0.515091656827 y1[1] (closed_form) = 2.67180713007 -0.515091656827 absolute error = 7.071e-15 relative error = 2.599e-13 % Correct digits = 15 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 x[1] = 0.3563 1.185 h = 0.001 0.001 y2[1] (numeric) = 0.376253969915 -1.38936203674 y2[1] (closed_form) = 0.376253969915 -1.38936203674 absolute error = 4.005e-15 relative error = 2.782e-13 % Correct digits = 15 h = 0.001 0.001 y1[1] (numeric) = 2.67590546946 -0.51709900741 y1[1] (closed_form) = 2.67590546946 -0.51709900741 absolute error = 7.071e-15 relative error = 2.594e-13 % Correct digits = 15 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=10464.1MB, alloc=44.3MB, time=136.41 x[1] = 0.3573 1.186 h = 0.0001 0.004 y2[1] (numeric) = 0.37405957569 -1.39052021872 y2[1] (closed_form) = 0.37405957569 -1.39052021872 absolute error = 5.001e-15 relative error = 3.473e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.67667056769 -0.519113791637 y1[1] (closed_form) = 2.67667056769 -0.519113791637 absolute error = 7.071e-15 relative error = 2.593e-13 % Correct digits = 15 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=10512.0MB, alloc=44.3MB, time=137.04 x[1] = 0.3574 1.19 h = 0.003 0.006 y2[1] (numeric) = 0.371809885989 -1.3971858739 y2[1] (closed_form) = 0.371809885989 -1.3971858739 absolute error = 5.004e-15 relative error = 3.461e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.68218326618 -0.521761434123 y1[1] (closed_form) = 2.68218326618 -0.521761434123 absolute error = 7.071e-15 relative error = 2.588e-13 % Correct digits = 15 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 x[1] = 0.3604 1.196 h = 0.0001 0.005 y2[1] (numeric) = 0.363599049611 -1.40572123301 y2[1] (closed_form) = 0.363599049611 -1.40572123301 absolute error = 5.004e-15 relative error = 3.446e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.68869511025 -0.529759530445 y1[1] (closed_form) = 2.68869511025 -0.529759530445 absolute error = 7.071e-15 relative error = 2.580e-13 % Correct digits = 15 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=10559.7MB, alloc=44.3MB, time=137.66 x[1] = 0.3605 1.201 h = 0.0001 0.003 y2[1] (numeric) = 0.360772714603 -1.41412901341 y2[1] (closed_form) = 0.360772714603 -1.41412901341 absolute error = 5.004e-15 relative error = 3.429e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.69568094018 -0.53308958603 y1[1] (closed_form) = 2.69568094018 -0.53308958603 absolute error = 7.071e-15 relative error = 2.573e-13 % Correct digits = 15 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=10607.5MB, alloc=44.3MB, time=138.28 x[1] = 0.3606 1.204 h = 0.001 0.001 y2[1] (numeric) = 0.35900057703 -1.41916891938 y2[1] (closed_form) = 0.35900057703 -1.41916891938 absolute error = 6.003e-15 relative error = 4.101e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.69986687271 -0.535151589235 y1[1] (closed_form) = 2.69986687271 -0.535151589235 absolute error = 7.071e-15 relative error = 2.569e-13 % Correct digits = 15 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=10655.4MB, alloc=44.3MB, time=138.91 x[1] = 0.3616 1.205 h = 0.001 0.003 y2[1] (numeric) = 0.356764139011 -1.42033299292 y2[1] (closed_form) = 0.356764139011 -1.42033299292 absolute error = 6.003e-15 relative error = 4.099e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.70064450637 -0.537213457703 y1[1] (closed_form) = 2.70064450637 -0.537213457703 absolute error = 7.058e-15 relative error = 2.563e-13 % Correct digits = 15 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 x[1] = 0.3626 1.208 h = 0.0001 0.004 y2[1] (numeric) = 0.353445011201 -1.42490146738 y2[1] (closed_form) = 0.353445011201 -1.42490146738 absolute error = 6.001e-15 relative error = 4.088e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.7042674619 -0.540570757159 y1[1] (closed_form) = 2.7042674619 -0.540570757159 absolute error = 7.058e-15 relative error = 2.559e-13 % Correct digits = 15 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=10703.1MB, alloc=44.3MB, time=139.52 x[1] = 0.3627 1.212 h = 0.003 0.006 y2[1] (numeric) = 0.351106555132 -1.43167563134 y2[1] (closed_form) = 0.351106555132 -1.43167563134 absolute error = 6.001e-15 relative error = 4.071e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.70991583633 -0.543304478862 y1[1] (closed_form) = 2.70991583633 -0.543304478862 absolute error = 7.071e-15 relative error = 2.558e-13 % Correct digits = 15 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=10751.0MB, alloc=44.3MB, time=140.16 x[1] = 0.3657 1.218 h = 0.0001 0.005 y2[1] (numeric) = 0.342682360895 -1.44031284887 y2[1] (closed_form) = 0.342682360895 -1.44031284887 absolute error = 6.001e-15 relative error = 4.053e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.71657249485 -0.551531056354 y1[1] (closed_form) = 2.71657249485 -0.551531056354 absolute error = 7.071e-15 relative error = 2.551e-13 % Correct digits = 15 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=10798.9MB, alloc=44.3MB, time=140.79 x[1] = 0.3658 1.223 h = 0.0001 0.003 y2[1] (numeric) = 0.339744101382 -1.44885826136 y2[1] (closed_form) = 0.339744101382 -1.44885826136 absolute error = 6.003e-15 relative error = 4.034e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.72372952933 -0.554969440997 y1[1] (closed_form) = 2.72372952933 -0.554969440997 absolute error = 7.071e-15 relative error = 2.544e-13 % Correct digits = 15 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 x[1] = 0.3659 1.226 h = 0.001 0.001 y2[1] (numeric) = 0.337903414331 -1.45398027503 y2[1] (closed_form) = 0.337903414331 -1.45398027503 absolute error = 7.003e-15 relative error = 4.691e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.7280176664 -0.557098109841 y1[1] (closed_form) = 2.7280176664 -0.557098109841 absolute error = 7.071e-15 relative error = 2.540e-13 % Correct digits = 15 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=10846.7MB, alloc=44.3MB, time=141.42 x[1] = 0.3669 1.227 h = 0.001 0.003 y2[1] (numeric) = 0.335616844184 -1.45515053172 y2[1] (closed_form) = 0.335616844184 -1.45515053172 absolute error = 7.003e-15 relative error = 4.689e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.72880899229 -0.559215914983 y1[1] (closed_form) = 2.72880899229 -0.559215914983 absolute error = 7.071e-15 relative error = 2.539e-13 % Correct digits = 15 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=10894.5MB, alloc=44.3MB, time=142.04 x[1] = 0.3679 1.23 h = 0.0001 0.004 y2[1] (numeric) = 0.332203355287 -1.459781573 y2[1] (closed_form) = 0.332203355287 -1.459781573 absolute error = 7.003e-15 relative error = 4.678e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.7325152998 -0.56267164658 y1[1] (closed_form) = 2.7325152998 -0.56267164658 absolute error = 7.071e-15 relative error = 2.535e-13 % Correct digits = 15 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=10942.4MB, alloc=44.3MB, time=142.66 x[1] = 0.368 1.234 h = 0.003 0.006 y2[1] (numeric) = 0.329773486839 -1.46666678888 y2[1] (closed_form) = 0.329773486839 -1.46666678888 absolute error = 6.003e-15 relative error = 3.993e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.73830128785 -0.565494011167 y1[1] (closed_form) = 2.73830128785 -0.565494011167 absolute error = 7.071e-15 relative error = 2.529e-13 % Correct digits = 15 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 x[1] = 0.371 1.24 h = 0.0001 0.005 y2[1] (numeric) = 0.32113007961 -1.47540783806 y2[1] (closed_form) = 0.32113007961 -1.47540783806 absolute error = 6.003e-15 relative error = 3.976e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.74510387715 -0.573954372964 y1[1] (closed_form) = 2.74510387715 -0.573954372964 absolute error = 7.058e-15 relative error = 2.517e-13 % Correct digits = 15 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=10989.9MB, alloc=44.3MB, time=143.28 x[1] = 0.3711 1.245 h = 0.0001 0.003 y2[1] (numeric) = 0.318076563029 -1.48409409343 y2[1] (closed_form) = 0.318076563029 -1.48409409343 absolute error = 6.003e-15 relative error = 3.955e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.75243457734 -0.577504323451 y1[1] (closed_form) = 2.75243457734 -0.577504323451 absolute error = 7.058e-15 relative error = 2.509e-13 % Correct digits = 15 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=11037.8MB, alloc=44.3MB, time=143.90 x[1] = 0.3712 1.248 h = 0.001 0.001 y2[1] (numeric) = 0.316165292745 -1.48930012076 y2[1] (closed_form) = 0.316165292745 -1.48930012076 absolute error = 6.003e-15 relative error = 3.943e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.75682637758 -0.579701628512 y1[1] (closed_form) = 2.75682637758 -0.579701628512 absolute error = 7.058e-15 relative error = 2.505e-13 % Correct digits = 15 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=11085.8MB, alloc=44.3MB, time=144.53 x[1] = 0.3722 1.249 h = 0.001 0.003 y2[1] (numeric) = 0.313827275047 -1.49047656089 y2[1] (closed_form) = 0.313827275047 -1.49047656089 absolute error = 6.003e-15 relative error = 3.941e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.75763126256 -0.581876520435 y1[1] (closed_form) = 2.75763126256 -0.581876520435 absolute error = 7.058e-15 relative error = 2.504e-13 % Correct digits = 15 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 x[1] = 0.3732 1.252 h = 0.0001 0.004 y2[1] (numeric) = 0.310316788734 -1.4951714843 y2[1] (closed_form) = 0.310316788734 -1.4951714843 absolute error = 7.001e-15 relative error = 4.585e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.76142180591 -0.585433124095 y1[1] (closed_form) = 2.76142180591 -0.585433124095 absolute error = 8.050e-15 relative error = 2.852e-13 % Correct digits = 15 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=11133.5MB, alloc=44.3MB, time=145.14 x[1] = 0.3733 1.256 h = 0.003 0.006 y2[1] (numeric) = 0.30779279432 -1.50217032453 y2[1] (closed_form) = 0.30779279432 -1.50217032453 absolute error = 7.001e-15 relative error = 4.566e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.76734738731 -0.588346767742 y1[1] (closed_form) = 2.76734738731 -0.588346767742 absolute error = 8.050e-15 relative error = 2.845e-13 % Correct digits = 15 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=11181.3MB, alloc=44.3MB, time=145.77 x[1] = 0.3763 1.262 h = 0.0001 0.005 y2[1] (numeric) = 0.298924194804 -1.51101717482 y2[1] (closed_form) = 0.298924194804 -1.51101717482 absolute error = 7.001e-15 relative error = 4.545e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.77429703575 -0.597046357601 y1[1] (closed_form) = 2.77429703575 -0.597046357601 absolute error = 7.058e-15 relative error = 2.487e-13 % Correct digits = 15 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=11229.2MB, alloc=44.3MB, time=146.40 x[1] = 0.3764 1.267 h = 0.0001 0.003 y2[1] (numeric) = 0.295752003199 -1.51984752119 y2[1] (closed_form) = 0.295752003199 -1.51984752119 absolute error = 7.001e-15 relative error = 4.521e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.78180391598 -0.600711202083 y1[1] (closed_form) = 2.78180391598 -0.600711202083 absolute error = 7.046e-15 relative error = 2.476e-13 % Correct digits = 15 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 x[1] = 0.3765 1.27 h = 0.001 0.001 y2[1] (numeric) = 0.293768064154 -1.52513948999 y2[1] (closed_form) = 0.293768064154 -1.52513948999 absolute error = 7.001e-15 relative error = 4.507e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.78630086924 -0.602979169409 y1[1] (closed_form) = 2.78630086924 -0.602979169409 absolute error = 7.046e-15 relative error = 2.471e-13 % Correct digits = 15 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=11277.0MB, alloc=44.3MB, time=147.02 x[1] = 0.3775 1.271 h = 0.001 0.003 y2[1] (numeric) = 0.291377258581 -1.52632210466 y2[1] (closed_form) = 0.291377258581 -1.52632210466 absolute error = 7.001e-15 relative error = 4.505e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.78711917307 -0.605212327408 y1[1] (closed_form) = 2.78711917307 -0.605212327408 absolute error = 7.046e-15 relative error = 2.470e-13 % Correct digits = 15 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=11324.7MB, alloc=44.3MB, time=147.65 x[1] = 0.3785 1.274 h = 0.0001 0.004 y2[1] (numeric) = 0.287767079402 -1.53108223201 y2[1] (closed_form) = 0.287767079402 -1.53108223201 absolute error = 7.001e-15 relative error = 4.494e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.79099485099 -0.608872308692 y1[1] (closed_form) = 2.79099485099 -0.608872308692 absolute error = 7.046e-15 relative error = 2.466e-13 % Correct digits = 15 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 x[1] = 0.3786 1.278 h = 0.003 0.006 y2[1] (numeric) = 0.285146176023 -1.53819729889 y2[1] (closed_form) = 0.285146176023 -1.53819729889 absolute error = 7.001e-15 relative error = 4.475e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.79706204783 -0.611879941745 y1[1] (closed_form) = 2.79706204783 -0.611879941745 absolute error = 7.046e-15 relative error = 2.461e-13 % Correct digits = 15 memory used=11372.7MB, alloc=44.3MB, time=148.27 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 x[1] = 0.3816 1.284 h = 0.0001 0.005 y2[1] (numeric) = 0.276046277582 -1.54715191543 y2[1] (closed_form) = 0.276046277582 -1.54715191543 absolute error = 7.001e-15 relative error = 4.455e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.80415989502 -0.620824346788 y1[1] (closed_form) = 2.80415989502 -0.620824346788 absolute error = 8.040e-15 relative error = 2.799e-13 % Correct digits = 15 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=11420.4MB, alloc=44.3MB, time=148.89 x[1] = 0.3817 1.289 h = 0.0001 0.003 y2[1] (numeric) = 0.272751905285 -1.55612963896 y2[1] (closed_form) = 0.272751905285 -1.55612963896 absolute error = 8.001e-15 relative error = 5.064e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.81184552312 -0.624607506889 y1[1] (closed_form) = 2.81184552312 -0.624607506889 absolute error = 8.040e-15 relative error = 2.791e-13 % Correct digits = 15 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=11468.3MB, alloc=44.3MB, time=149.52 x[1] = 0.3818 1.292 h = 0.001 0.001 y2[1] (numeric) = 0.270693158774 -1.56150949926 y2[1] (closed_form) = 0.270693158774 -1.56150949926 absolute error = 8.001e-15 relative error = 5.048e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.81644915075 -0.626948219266 y1[1] (closed_form) = 2.81644915075 -0.626948219266 absolute error = 9.045e-15 relative error = 3.135e-13 % Correct digits = 15 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 x[1] = 0.3828 1.293 h = 0.0001 0.004 y2[1] (numeric) = 0.268248199498 -1.56269827007 y2[1] (closed_form) = 0.268248199498 -1.56269827007 absolute error = 7.001e-15 relative error = 4.415e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.8172807257 -0.629240852333 y1[1] (closed_form) = 2.8172807257 -0.629240852333 absolute error = 9.045e-15 relative error = 3.133e-13 % Correct digits = 15 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=11516.1MB, alloc=44.3MB, time=150.14 x[1] = 0.3829 1.297 h = 0.003 0.006 y2[1] (numeric) = 0.265543024419 -1.56991668882 y2[1] (closed_form) = 0.265543024419 -1.56991668882 absolute error = 7.001e-15 relative error = 4.397e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.82347263713 -0.632329896104 y1[1] (closed_form) = 2.82347263713 -0.632329896104 absolute error = 9.045e-15 relative error = 3.126e-13 % Correct digits = 15 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=11563.9MB, alloc=44.3MB, time=150.76 x[1] = 0.3859 1.303 h = 0.0001 0.005 y2[1] (numeric) = 0.256240357398 -1.57896849362 y2[1] (closed_form) = 0.256240357398 -1.57896849362 absolute error = 8e-15 relative error = 5.001e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.83070197896 -0.641487831439 y1[1] (closed_form) = 2.83070197896 -0.641487831439 absolute error = 8.050e-15 relative error = 2.774e-13 % Correct digits = 15 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=11611.7MB, alloc=44.3MB, time=151.38 x[1] = 0.386 1.308 h = 0.0001 0.003 y2[1] (numeric) = 0.252839749623 -1.58807724939 y2[1] (closed_form) = 0.252839749623 -1.58807724939 absolute error = 8e-15 relative error = 4.975e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.83854503131 -0.645373474713 y1[1] (closed_form) = 2.83854503131 -0.645373474713 absolute error = 8.050e-15 relative error = 2.766e-13 % Correct digits = 15 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 x[1] = 0.3861 1.311 h = 0.001 0.001 y2[1] (numeric) = 0.250715936063 -1.59353526936 y2[1] (closed_form) = 0.250715936063 -1.59353526936 absolute error = 8e-15 relative error = 4.959e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.84324262448 -0.647777219775 y1[1] (closed_form) = 2.84324262448 -0.647777219775 absolute error = 9.035e-15 relative error = 3.098e-13 % Correct digits = 15 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=11659.5MB, alloc=44.3MB, time=152.00 x[1] = 0.3871 1.312 h = 0.001 0.003 y2[1] (numeric) = 0.248223322285 -1.59472998465 y2[1] (closed_form) = 0.248223322285 -1.59472998465 absolute error = 8e-15 relative error = 4.957e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.84408622712 -0.650121882632 y1[1] (closed_form) = 2.84408622712 -0.650121882632 absolute error = 9.035e-15 relative error = 3.097e-13 % Correct digits = 15 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=11707.2MB, alloc=44.3MB, time=152.63 x[1] = 0.3881 1.315 h = 0.0001 0.004 y2[1] (numeric) = 0.244421069164 -1.59961624775 y2[1] (closed_form) = 0.244421069164 -1.59961624775 absolute error = 9.001e-15 relative error = 5.562e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.8481240679 -0.65398008457 y1[1] (closed_form) = 2.8481240679 -0.65398008457 absolute error = 9.035e-15 relative error = 3.092e-13 % Correct digits = 15 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=11755.3MB, alloc=44.3MB, time=153.26 x[1] = 0.3882 1.319 h = 0.003 0.006 y2[1] (numeric) = 0.241613647269 -1.60695585189 y2[1] (closed_form) = 0.241613647269 -1.60695585189 absolute error = 9e-15 relative error = 5.538e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.85446150561 -0.657168339072 y1[1] (closed_form) = 2.85446150561 -0.657168339072 absolute error = 9.035e-15 relative error = 3.085e-13 % Correct digits = 15 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 x[1] = 0.3912 1.325 h = 0.0001 0.005 y2[1] (numeric) = 0.232067991474 -1.61611914291 y2[1] (closed_form) = 0.232067991474 -1.61611914291 absolute error = 9e-15 relative error = 5.512e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.86184126469 -0.666581863328 y1[1] (closed_form) = 2.86184126469 -0.666581863328 absolute error = 9.035e-15 relative error = 3.075e-13 % Correct digits = 15 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=11802.9MB, alloc=44.3MB, time=153.88 x[1] = 0.3913 1.33 h = 0.0001 0.003 y2[1] (numeric) = 0.22853847844 -1.62538153844 y2[1] (closed_form) = 0.22853847844 -1.62538153844 absolute error = 9e-15 relative error = 5.483e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.86986803033 -0.670592413166 y1[1] (closed_form) = 2.86986803033 -0.670592413166 absolute error = 9.045e-15 relative error = 3.069e-13 % Correct digits = 15 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=11850.7MB, alloc=44.3MB, time=154.50 x[1] = 0.3914 1.333 h = 0.001 0.001 y2[1] (numeric) = 0.226335755211 -1.63093116603 y2[1] (closed_form) = 0.226335755211 -1.63093116603 absolute error = 9e-15 relative error = 5.466e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.87467523962 -0.673072915352 y1[1] (closed_form) = 2.87467523962 -0.673072915352 absolute error = 9.045e-15 relative error = 3.064e-13 % Correct digits = 15 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=11898.8MB, alloc=44.3MB, time=155.13 x[1] = 0.3924 1.334 h = 0.001 0.003 y2[1] (numeric) = 0.223786375725 -1.63213199384 y2[1] (closed_form) = 0.223786375725 -1.63213199384 absolute error = 9e-15 relative error = 5.463e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.87553183267 -0.675479385724 y1[1] (closed_form) = 2.87553183267 -0.675479385724 absolute error = 9.035e-15 relative error = 3.059e-13 % Correct digits = 15 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 x[1] = 0.3934 1.337 h = 0.0001 0.004 y2[1] (numeric) = 0.219876394323 -1.63708731254 y2[1] (closed_form) = 0.219876394323 -1.63708731254 absolute error = 9e-15 relative error = 5.449e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.87965749225 -0.679448496513 y1[1] (closed_form) = 2.87965749225 -0.679448496513 absolute error = 8.040e-15 relative error = 2.717e-13 % Correct digits = 15 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=11946.6MB, alloc=44.3MB, time=155.75 x[1] = 0.3935 1.341 h = 0.003 0.006 y2[1] (numeric) = 0.216963733917 -1.64455079361 y2[1] (closed_form) = 0.216963733917 -1.64455079361 absolute error = 9e-15 relative error = 5.426e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.88614260204 -0.682738893345 y1[1] (closed_form) = 2.88614260204 -0.682738893345 absolute error = 8.040e-15 relative error = 2.711e-13 % Correct digits = 15 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=11994.4MB, alloc=44.3MB, time=156.38 x[1] = 0.3965 1.347 h = 0.0001 0.005 y2[1] (numeric) = 0.207168600224 -1.6538275224 y2[1] (closed_form) = 0.207168600224 -1.6538275224 absolute error = 9e-15 relative error = 5.400e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.89367394757 -0.692414019454 y1[1] (closed_form) = 2.89367394757 -0.692414019454 absolute error = 8.040e-15 relative error = 2.702e-13 % Correct digits = 15 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=12042.2MB, alloc=44.3MB, time=157.00 x[1] = 0.3966 1.352 h = 0.0001 0.003 y2[1] (numeric) = 0.203506412591 -1.66324695748 y2[1] (closed_form) = 0.203506412591 -1.66324695748 absolute error = 1.0e-14 relative error = 5.968e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.90188715077 -0.696553176342 y1[1] (closed_form) = 2.90188715077 -0.696553176342 absolute error = 8.040e-15 relative error = 2.694e-13 % Correct digits = 15 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 x[1] = 0.3967 1.355 h = 0.001 0.001 y2[1] (numeric) = 0.201222481151 -1.66889020918 y2[1] (closed_form) = 0.201222481151 -1.66889020918 absolute error = 1.0e-14 relative error = 5.949e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.9068055894 -0.699112687696 y1[1] (closed_form) = 2.9068055894 -0.699112687696 absolute error = 9.027e-15 relative error = 3.019e-13 % Correct digits = 15 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=12090.0MB, alloc=44.3MB, time=157.62 x[1] = 0.3977 1.356 h = 0.001 0.003 y2[1] (numeric) = 0.198614893581 -1.67009710244 y2[1] (closed_form) = 0.198614893581 -1.67009710244 absolute error = 1.0e-14 relative error = 5.946e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.90767500216 -0.701582262519 y1[1] (closed_form) = 2.90767500216 -0.701582262519 absolute error = 8.031e-15 relative error = 2.685e-13 % Correct digits = 15 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=12137.8MB, alloc=44.3MB, time=158.25 x[1] = 0.3987 1.359 h = 0.0001 0.004 y2[1] (numeric) = 0.194594245581 -1.67512282409 y2[1] (closed_form) = 0.194594245581 -1.67512282409 absolute error = 1.1e-14 relative error = 6.523e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.91188943585 -0.705665053945 y1[1] (closed_form) = 2.91188943585 -0.705665053945 absolute error = 9.027e-15 relative error = 3.013e-13 % Correct digits = 15 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=12185.8MB, alloc=44.3MB, time=158.87 x[1] = 0.3988 1.363 h = 0.003 0.006 y2[1] (numeric) = 0.191573278101 -1.68271290559 y2[1] (closed_form) = 0.191573278101 -1.68271290559 absolute error = 1.000e-14 relative error = 5.905e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.91852440707 -0.709060605717 y1[1] (closed_form) = 2.91852440707 -0.709060605717 absolute error = 9.027e-15 relative error = 3.006e-13 % Correct digits = 15 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 x[1] = 0.4018 1.369 h = 0.0001 0.005 y2[1] (numeric) = 0.181522037186 -1.69210501722 y2[1] (closed_form) = 0.181522037186 -1.69210501722 absolute error = 1.000e-14 relative error = 5.876e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.92620851635 -0.719003501232 y1[1] (closed_form) = 2.92620851635 -0.719003501232 absolute error = 9.027e-15 relative error = 2.996e-13 % Correct digits = 15 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=12233.4MB, alloc=44.3MB, time=159.49 x[1] = 0.4019 1.374 h = 0.0001 0.003 y2[1] (numeric) = 0.1777233085 -1.70168493229 y2[1] (closed_form) = 0.1777233085 -1.70168493229 absolute error = 1.000e-14 relative error = 5.845e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.93461093635 -0.723275067769 y1[1] (closed_form) = 2.93461093635 -0.723275067769 absolute error = 9.027e-15 relative error = 2.987e-13 % Correct digits = 15 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=12281.3MB, alloc=44.3MB, time=160.12 x[1] = 0.402 1.377 h = 0.001 0.001 y2[1] (numeric) = 0.175355811447 -1.70742384834 y2[1] (closed_form) = 0.175355811447 -1.70742384834 absolute error = 1.100e-14 relative error = 6.409e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.93964224984 -0.725915902298 y1[1] (closed_form) = 2.93964224984 -0.725915902298 absolute error = 9.027e-15 relative error = 2.981e-13 % Correct digits = 15 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 x[1] = 0.403 1.378 h = 0.001 0.003 y2[1] (numeric) = 0.172688545466 -1.70863674915 y2[1] (closed_form) = 0.172688545466 -1.70863674915 absolute error = 1.000e-14 relative error = 5.823e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.94052430274 -0.728449910272 y1[1] (closed_form) = 2.94052430274 -0.728449910272 absolute error = 8.031e-15 relative error = 2.651e-13 % Correct digits = 15 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=12329.2MB, alloc=44.3MB, time=160.74 x[1] = 0.404 1.381 h = 0.0001 0.004 y2[1] (numeric) = 0.168554225674 -1.71373422742 y2[1] (closed_form) = 0.168554225674 -1.71373422742 absolute error = 1.000e-14 relative error = 5.807e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 2.94482847982 -0.732649226652 y1[1] (closed_form) = 2.94482847982 -0.732649226652 absolute error = 9.027e-15 relative error = 2.975e-13 % Correct digits = 15 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=12376.9MB, alloc=44.3MB, time=161.36 x[1] = 0.4041 1.385 h = 0.003 0.006 y2[1] (numeric) = 0.165421803651 -1.72145366529 y2[1] (closed_form) = 0.165421803651 -1.72145366529 absolute error = 1.000e-14 relative error = 5.784e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.9516155456 -0.736153028866 y1[1] (closed_form) = 2.9516155456 -0.736153028866 absolute error = 8.031e-15 relative error = 2.640e-13 % Correct digits = 15 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=12424.9MB, alloc=44.3MB, time=161.98 x[1] = 0.4071 1.391 h = 0.0001 0.005 y2[1] (numeric) = 0.155107682519 -1.73096309771 y2[1] (closed_form) = 0.155107682519 -1.73096309771 absolute error = 1.000e-14 relative error = 5.755e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.95945360313 -0.74637001905 y1[1] (closed_form) = 2.95945360313 -0.74637001905 absolute error = 8.022e-15 relative error = 2.628e-13 % Correct digits = 15 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 x[1] = 0.4072 1.396 h = 0.0001 0.003 y2[1] (numeric) = 0.151168446647 -1.74070697454 y2[1] (closed_form) = 0.151168446647 -1.74070697454 absolute error = 1.000e-14 relative error = 5.724e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.96804807459 -0.750777902335 y1[1] (closed_form) = 2.96804807459 -0.750777902335 absolute error = 8.022e-15 relative error = 2.620e-13 % Correct digits = 15 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=12472.6MB, alloc=44.3MB, time=162.60 x[1] = 0.4073 1.399 h = 0.001 0.001 y2[1] (numeric) = 0.148714966166 -1.7465436193 y2[1] (closed_form) = 0.148714966166 -1.7465436193 absolute error = 1.000e-14 relative error = 5.706e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.97319394093 -0.753502437447 y1[1] (closed_form) = 2.97319394093 -0.753502437447 absolute error = 8.022e-15 relative error = 2.616e-13 % Correct digits = 15 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=12520.6MB, alloc=44.3MB, time=163.22 x[1] = 0.4083 1.4 h = 0.003 0.006 y2[1] (numeric) = 0.145986522838 -1.74776245861 y2[1] (closed_form) = 0.145986522838 -1.74776245861 absolute error = 1.000e-14 relative error = 5.703e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 2.97408844515 -0.756102239592 y1[1] (closed_form) = 2.97408844515 -0.756102239592 absolute error = 8.031e-15 relative error = 2.617e-13 % Correct digits = 15 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=12568.6MB, alloc=44.3MB, time=163.85 x[1] = 0.4113 1.406 h = 0.0001 0.005 y2[1] (numeric) = 0.135484550515 -1.75734688534 y2[1] (closed_form) = 0.135484550515 -1.75734688534 absolute error = 1.000e-14 relative error = 5.675e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 2.98202599317 -0.766515443146 y1[1] (closed_form) = 2.98202599317 -0.766515443146 absolute error = 8.031e-15 relative error = 2.608e-13 % Correct digits = 15 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 x[1] = 0.4114 1.411 h = 0.0001 0.003 y2[1] (numeric) = 0.131442071453 -1.76720192988 y2[1] (closed_form) = 0.131442071453 -1.76720192988 absolute error = 1.000e-14 relative error = 5.644e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 2.99075069374 -0.771024343915 y1[1] (closed_form) = 2.99075069374 -0.771024343915 absolute error = 8.031e-15 relative error = 2.600e-13 % Correct digits = 15 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=12616.3MB, alloc=44.3MB, time=164.47 x[1] = 0.4115 1.414 h = 0.001 0.001 y2[1] (numeric) = 0.128925484666 -1.77310477112 y2[1] (closed_form) = 0.128925484666 -1.77310477112 absolute error = 1.000e-14 relative error = 5.626e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 2.9959741684 -0.773810805567 y1[1] (closed_form) = 2.9959741684 -0.773810805567 absolute error = 8.031e-15 relative error = 2.595e-13 % Correct digits = 15 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=12664.3MB, alloc=44.3MB, time=165.10 x[1] = 0.4125 1.415 h = 0.001 0.003 y2[1] (numeric) = 0.12615392618 -1.77432606248 y2[1] (closed_form) = 0.12615392618 -1.77432606248 absolute error = 1.100e-14 relative error = 6.185e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 2.99687542396 -0.776456981128 y1[1] (closed_form) = 2.99687542396 -0.776456981128 absolute error = 8.031e-15 relative error = 2.594e-13 % Correct digits = 15 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=12712.2MB, alloc=44.3MB, time=165.72 x[1] = 0.4135 1.418 h = 0.0001 0.004 y2[1] (numeric) = 0.121818850459 -1.77954471017 y2[1] (closed_form) = 0.121818850459 -1.77954471017 absolute error = 1.100e-14 relative error = 6.168e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.00133021574 -0.780861952185 y1[1] (closed_form) = 3.00133021574 -0.780861952185 absolute error = 9.027e-15 relative error = 2.911e-13 % Correct digits = 15 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 x[1] = 0.4136 1.422 h = 0.003 0.006 y2[1] (numeric) = 0.118487526827 -1.78748584172 y2[1] (closed_form) = 0.118487526827 -1.78748584172 absolute error = 1.100e-14 relative error = 6.141e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.00837628302 -0.784559685562 y1[1] (closed_form) = 3.00837628302 -0.784559685562 absolute error = 8.031e-15 relative error = 2.583e-13 % Correct digits = 15 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=12759.9MB, alloc=44.3MB, time=166.34 x[1] = 0.4166 1.428 h = 0.0001 0.005 y2[1] (numeric) = 0.107710858102 -1.79719066332 y2[1] (closed_form) = 0.107710858102 -1.79719066332 absolute error = 1.100e-14 relative error = 6.111e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.016469624 -0.795258056813 y1[1] (closed_form) = 3.016469624 -0.795258056813 absolute error = 8.031e-15 relative error = 2.574e-13 % Correct digits = 15 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=12807.7MB, alloc=44.3MB, time=166.96 x[1] = 0.4167 1.433 h = 0.0001 0.003 y2[1] (numeric) = 0.103520854012 -1.8072155364 y2[1] (closed_form) = 0.103520854012 -1.8072155364 absolute error = 1.200e-14 relative error = 6.630e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.02539118289 -0.799910187411 y1[1] (closed_form) = 3.02539118289 -0.799910187411 absolute error = 8.031e-15 relative error = 2.566e-13 % Correct digits = 15 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=12855.7MB, alloc=44.3MB, time=167.58 x[1] = 0.4168 1.436 h = 0.001 0.001 y2[1] (numeric) = 0.10091400799 -1.81321958215 y2[1] (closed_form) = 0.10091400799 -1.81321958215 absolute error = 1.100e-14 relative error = 6.058e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.03073205346 -0.802784554454 y1[1] (closed_form) = 3.03073205346 -0.802784554454 absolute error = 8.031e-15 relative error = 2.561e-13 % Correct digits = 15 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 x[1] = 0.4178 1.437 h = 0.001 0.003 y2[1] (numeric) = 0.0980786777538 -1.81444662962 y2[1] (closed_form) = 0.0980786777538 -1.81444662962 absolute error = 1.100e-14 relative error = 6.055e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.03164538336 -0.805498891064 y1[1] (closed_form) = 3.03164538336 -0.805498891064 absolute error = 8.022e-15 relative error = 2.558e-13 % Correct digits = 15 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=12903.4MB, alloc=44.3MB, time=168.20 x[1] = 0.4188 1.44 h = 0.0001 0.004 y2[1] (numeric) = 0.0936214734435 -1.8197406215 y2[1] (closed_form) = 0.0936214734435 -1.8197406215 absolute error = 1.100e-14 relative error = 6.038e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.03619251354 -0.81002842917 y1[1] (closed_form) = 3.03619251354 -0.81002842917 absolute error = 8.022e-15 relative error = 2.553e-13 % Correct digits = 15 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=12951.4MB, alloc=44.3MB, time=168.83 x[1] = 0.4189 1.444 h = 0.003 0.006 y2[1] (numeric) = 0.0901697558186 -1.82781859604 y2[1] (closed_form) = 0.0901697558186 -1.82781859604 absolute error = 1.100e-14 relative error = 6.012e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.04339681219 -0.813843219109 y1[1] (closed_form) = 3.04339681219 -0.813843219109 absolute error = 7.035e-15 relative error = 2.233e-13 % Correct digits = 15 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=12999.3MB, alloc=44.3MB, time=169.46 x[1] = 0.4219 1.45 h = 0.0001 0.005 y2[1] (numeric) = 0.0791112140249 -1.83764572385 y2[1] (closed_form) = 0.0791112140249 -1.83764572385 absolute error = 1.200e-14 relative error = 6.525e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.05164714102 -0.8248335232 y1[1] (closed_form) = 3.05164714102 -0.8248335232 absolute error = 7.026e-15 relative error = 2.223e-13 % Correct digits = 15 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 x[1] = 0.422 1.455 h = 0.0001 0.003 y2[1] (numeric) = 0.0747694366112 -1.84784401885 y2[1] (closed_form) = 0.0747694366112 -1.84784401885 absolute error = 1.200e-14 relative error = 6.490e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.06076854081 -0.829633085305 y1[1] (closed_form) = 3.06076854081 -0.829633085305 absolute error = 7.026e-15 relative error = 2.215e-13 % Correct digits = 15 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=13047.0MB, alloc=44.3MB, time=170.09 x[1] = 0.4221 1.458 h = 0.001 0.001 y2[1] (numeric) = 0.0720697425848 -1.85395139853 y2[1] (closed_form) = 0.0720697425848 -1.85395139853 absolute error = 1.200e-14 relative error = 6.469e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.06622857195 -0.832597913813 y1[1] (closed_form) = 3.06622857195 -0.832597913813 absolute error = 8.022e-15 relative error = 2.525e-13 % Correct digits = 15 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=13094.9MB, alloc=44.3MB, time=170.71 x[1] = 0.4231 1.459 h = 0.001 0.003 y2[1] (numeric) = 0.0691690617365 -1.85518410029 y2[1] (closed_form) = 0.0691690617365 -1.85518410029 absolute error = 1.200e-14 relative error = 6.465e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.06715375957 -0.835381862006 y1[1] (closed_form) = 3.06715375957 -0.835381862006 absolute error = 7.018e-15 relative error = 2.208e-13 % Correct digits = 15 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 x[1] = 0.4241 1.462 h = 0.0001 0.004 y2[1] (numeric) = 0.0645864620426 -1.86055481053 y2[1] (closed_form) = 0.0645864620426 -1.86055481053 absolute error = 1.300e-14 relative error = 6.984e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.07179424493 -0.840039092751 y1[1] (closed_form) = 3.07179424493 -0.840039092751 absolute error = 8.016e-15 relative error = 2.517e-13 % Correct digits = 15 memory used=13142.7MB, alloc=44.3MB, time=171.33 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 x[1] = 0.4242 1.466 h = 0.003 0.006 y2[1] (numeric) = 0.0610108927813 -1.86877250597 y2[1] (closed_form) = 0.0610108927813 -1.86877250597 absolute error = 1.300e-14 relative error = 6.953e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.07915916988 -0.843974358672 y1[1] (closed_form) = 3.07915916988 -0.843974358672 absolute error = 8.016e-15 relative error = 2.511e-13 % Correct digits = 15 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=13190.6MB, alloc=44.3MB, time=171.96 x[1] = 0.4272 1.472 h = 0.0001 0.005 y2[1] (numeric) = 0.0496631442181 -1.87872384136 y2[1] (closed_form) = 0.0496631442181 -1.87872384136 absolute error = 1.300e-14 relative error = 6.918e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.08756768493 -0.855263530456 y1[1] (closed_form) = 3.08756768493 -0.855263530456 absolute error = 8.016e-15 relative error = 2.502e-13 % Correct digits = 15 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=13238.4MB, alloc=44.3MB, time=172.59 x[1] = 0.4273 1.477 h = 0.0001 0.003 y2[1] (numeric) = 0.045165235542 -1.88909919533 y2[1] (closed_form) = 0.045165235542 -1.88909919533 absolute error = 1.300e-14 relative error = 6.880e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.09689196493 -0.860214839571 y1[1] (closed_form) = 3.09689196493 -0.860214839571 absolute error = 8.022e-15 relative error = 2.496e-13 % Correct digits = 15 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 x[1] = 0.4274 1.48 h = 0.001 0.001 y2[1] (numeric) = 0.0423700383094 -1.89531206382 y2[1] (closed_form) = 0.0423700383094 -1.89531206382 absolute error = 1.300e-14 relative error = 6.859e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.10247295456 -0.863272754653 y1[1] (closed_form) = 3.10247295456 -0.863272754653 absolute error = 9.020e-15 relative error = 2.801e-13 % Correct digits = 15 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=13286.2MB, alloc=44.3MB, time=173.21 x[1] = 0.4284 1.481 h = 0.0001 0.004 y2[1] (numeric) = 0.0394023968753 -1.8965503054 y2[1] (closed_form) = 0.0394023968753 -1.8965503054 absolute error = 1.200e-14 relative error = 6.327e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.10340977243 -0.866127799464 y1[1] (closed_form) = 3.10340977243 -0.866127799464 absolute error = 9.020e-15 relative error = 2.799e-13 % Correct digits = 15 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=13334.1MB, alloc=44.3MB, time=173.84 x[1] = 0.4285 1.485 h = 0.003 0.006 y2[1] (numeric) = 0.0357190951862 -1.90489213211 y2[1] (closed_form) = 0.0357190951862 -1.90489213211 absolute error = 1.300e-14 relative error = 6.824e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.11091640365 -0.870167622718 y1[1] (closed_form) = 3.11091640365 -0.870167622718 absolute error = 9.020e-15 relative error = 2.792e-13 % Correct digits = 15 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=13382.1MB, alloc=44.3MB, time=174.46 x[1] = 0.4315 1.491 h = 0.0001 0.005 y2[1] (numeric) = 0.0241179219349 -1.91495546245 y2[1] (closed_form) = 0.0241179219349 -1.91495546245 absolute error = 1.300e-14 relative error = 6.790e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.11946571737 -0.881717831422 y1[1] (closed_form) = 3.11946571737 -0.881717831422 absolute error = 9.014e-15 relative error = 2.781e-13 % Correct digits = 15 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 x[1] = 0.4316 1.496 h = 0.0001 0.003 y2[1] (numeric) = 0.0194842140563 -1.92548810173 y2[1] (closed_form) = 0.0194842140563 -1.92548810173 absolute error = 1.200e-14 relative error = 6.233e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.12896898703 -0.886800836883 y1[1] (closed_form) = 3.12896898703 -0.886800836883 absolute error = 9.020e-15 relative error = 2.773e-13 % Correct digits = 15 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=13429.6MB, alloc=44.3MB, time=175.08 x[1] = 0.4317 1.499 h = 0.001 0.001 y2[1] (numeric) = 0.0166059246429 -1.93179469868 y2[1] (closed_form) = 0.0166059246429 -1.93179469868 absolute error = 1.200e-14 relative error = 6.213e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.13465671163 -0.88993956318 y1[1] (closed_form) = 3.13465671163 -0.88993956318 absolute error = 9.014e-15 relative error = 2.766e-13 % Correct digits = 15 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=13477.5MB, alloc=44.3MB, time=175.70 x[1] = 0.4327 1.5 h = 0.001 0.003 y2[1] (numeric) = 0.0135793961587 -1.93303843142 y2[1] (closed_form) = 0.0135793961587 -1.93303843142 absolute error = 1.200e-14 relative error = 6.209e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.13560422134 -0.892856886926 y1[1] (closed_form) = 3.13560422134 -0.892856886926 absolute error = 9.014e-15 relative error = 2.765e-13 % Correct digits = 15 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=13525.5MB, alloc=44.3MB, time=176.33 x[1] = 0.4337 1.503 h = 0.0001 0.004 y2[1] (numeric) = 0.0087554645371 -1.93855716263 y2[1] (closed_form) = 0.0087554645371 -1.93855716263 absolute error = 1.300e-14 relative error = 6.707e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.1404227814 -0.897759176755 y1[1] (closed_form) = 3.1404227814 -0.897759176755 absolute error = 9.014e-15 relative error = 2.760e-13 % Correct digits = 15 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 x[1] = 0.4338 1.507 h = 0.003 0.006 y2[1] (numeric) = 0.00494167384628 -1.94704420219 y2[1] (closed_form) = 0.00494167384628 -1.94704420219 absolute error = 1.200e-14 relative error = 6.164e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.14809465904 -0.901926056482 y1[1] (closed_form) = 3.14809465904 -0.901926056482 absolute error = 9.014e-15 relative error = 2.753e-13 % Correct digits = 15 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=13573.2MB, alloc=44.3MB, time=176.95 x[1] = 0.4368 1.513 h = 0.0001 0.005 y2[1] (numeric) = -0.00696276113512 -1.95723534058 y2[1] (closed_form) = -0.00696276113512 -1.95723534058 absolute error = 1.300e-14 relative error = 6.642e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.15680448203 -0.913788486239 y1[1] (closed_form) = 3.15680448203 -0.913788486239 absolute error = 9.009e-15 relative error = 2.741e-13 % Correct digits = 15 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=13621.1MB, alloc=44.3MB, time=177.58 x[1] = 0.4369 1.518 h = 0.0001 0.003 y2[1] (numeric) = -0.0117609663722 -1.96795198011 y2[1] (closed_form) = -0.0117609663722 -1.96795198011 absolute error = 1.301e-14 relative error = 6.609e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.16651649436 -0.919031543195 y1[1] (closed_form) = 3.16651649436 -0.919031543195 absolute error = 9.014e-15 relative error = 2.734e-13 % Correct digits = 15 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=13669.0MB, alloc=44.3MB, time=178.20 x[1] = 0.437 1.521 h = 0.001 0.001 y2[1] (numeric) = -0.0147398560031 -1.97436817816 y2[1] (closed_form) = -0.0147398560031 -1.97436817816 absolute error = 1.300e-14 relative error = 6.584e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.17232864536 -0.922268407721 y1[1] (closed_form) = 3.17232864536 -0.922268407721 absolute error = 8.016e-15 relative error = 2.426e-13 % Correct digits = 15 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 x[1] = 0.438 1.522 h = 0.001 0.003 y2[1] (numeric) = -0.0178364278409 -1.97561722263 y2[1] (closed_form) = -0.0178364278409 -1.97561722263 absolute error = 1.301e-14 relative error = 6.583e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.17328735042 -0.925259688404 y1[1] (closed_form) = 3.17328735042 -0.925259688404 absolute error = 9.014e-15 relative error = 2.727e-13 % Correct digits = 15 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=13716.8MB, alloc=44.3MB, time=178.82 x[1] = 0.439 1.525 h = 0.0001 0.004 y2[1] (numeric) = -0.0227955046563 -1.98121667646 y2[1] (closed_form) = -0.0227955046563 -1.98121667646 absolute error = 1.302e-14 relative error = 6.570e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.17820228454 -0.930299047435 y1[1] (closed_form) = 3.17820228454 -0.930299047435 absolute error = 8.010e-15 relative error = 2.419e-13 % Correct digits = 15 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=13764.7MB, alloc=44.3MB, time=179.45 x[1] = 0.4391 1.529 h = 0.003 0.006 y2[1] (numeric) = -0.026743502471 -1.98985190887 y2[1] (closed_form) = -0.026743502471 -1.98985190887 absolute error = 1.300e-14 relative error = 6.535e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.1860419346 -0.934596672629 y1[1] (closed_form) = 3.1860419346 -0.934596672629 absolute error = 8.010e-15 relative error = 2.412e-13 % Correct digits = 15 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=13812.5MB, alloc=44.3MB, time=180.08 x[1] = 0.4421 1.535 h = 0.0001 0.005 y2[1] (numeric) = -0.0389590034397 -2.00017272536 y2[1] (closed_form) = -0.0389590034397 -2.00017272536 absolute error = 1.400e-14 relative error = 6.998e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.19491347133 -0.946778763074 y1[1] (closed_form) = 3.19491347133 -0.946778763074 absolute error = 8.010e-15 relative error = 2.404e-13 % Correct digits = 15 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 x[1] = 0.4422 1.54 h = 0.0001 0.003 y2[1] (numeric) = -0.0439263929567 -2.01107713205 y2[1] (closed_form) = -0.0439263929567 -2.01107713205 absolute error = 1.302e-14 relative error = 6.472e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.20483743149 -0.952186526969 y1[1] (closed_form) = 3.20483743149 -0.952186526969 absolute error = 8.010e-15 relative error = 2.396e-13 % Correct digits = 15 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=13860.2MB, alloc=44.3MB, time=180.70 x[1] = 0.4423 1.543 h = 0.001 0.001 y2[1] (numeric) = -0.0470087373198 -2.01760516178 y2[1] (closed_form) = -0.0470087373198 -2.01760516178 absolute error = 1.3e-14 relative error = 6.442e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.21077590389 -0.955524360982 y1[1] (closed_form) = 3.21077590389 -0.955524360982 absolute error = 9.009e-15 relative error = 2.689e-13 % Correct digits = 15 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=13908.2MB, alloc=44.3MB, time=181.32 x[1] = 0.4433 1.544 h = 0.001 0.003 y2[1] (numeric) = -0.0501770556081 -2.01885936525 y2[1] (closed_form) = -0.0501770556081 -2.01885936525 absolute error = 1.301e-14 relative error = 6.445e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.21174554377 -0.95859118598 y1[1] (closed_form) = 3.21174554377 -0.95859118598 absolute error = 9.005e-15 relative error = 2.687e-13 % Correct digits = 15 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=13956.0MB, alloc=44.3MB, time=181.94 x[1] = 0.4443 1.547 h = 0.0001 0.004 y2[1] (numeric) = -0.0552748444654 -2.02454093809 y2[1] (closed_form) = -0.0552748444654 -2.02454093809 absolute error = 1.300e-14 relative error = 6.419e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.21675791752 -0.963771058023 y1[1] (closed_form) = 3.21675791752 -0.963771058023 absolute error = 9.009e-15 relative error = 2.683e-13 % Correct digits = 15 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 x[1] = 0.4444 1.551 h = 0.003 0.006 y2[1] (numeric) = -0.0593608632754 -2.0333273796 y2[1] (closed_form) = -0.0593608632754 -2.0333273796 absolute error = 1.301e-14 relative error = 6.393e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.224767912 -0.968203216414 y1[1] (closed_form) = 3.224767912 -0.968203216414 absolute error = 9.009e-15 relative error = 2.676e-13 % Correct digits = 15 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=14003.7MB, alloc=44.3MB, time=182.57 x[1] = 0.4474 1.557 h = 0.0001 0.005 y2[1] (numeric) = -0.071895406554 -2.0437797308 y2[1] (closed_form) = -0.071895406554 -2.0437797308 absolute error = 1.400e-14 relative error = 6.846e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.23380236612 -0.98071259064 y1[1] (closed_form) = 3.23380236612 -0.98071259064 absolute error = 1.001e-14 relative error = 2.962e-13 % Correct digits = 15 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=14051.5MB, alloc=44.3MB, time=183.19 x[1] = 0.4475 1.562 h = 0.0001 0.003 y2[1] (numeric) = -0.0770367881978 -2.05487571776 y2[1] (closed_form) = -0.0770367881978 -2.05487571776 absolute error = 1.400e-14 relative error = 6.810e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.24394153748 -0.98628984144 y1[1] (closed_form) = 3.24394153748 -0.98628984144 absolute error = 1.001e-14 relative error = 2.952e-13 % Correct digits = 15 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 x[1] = 0.4476 1.565 h = 0.001 0.001 y2[1] (numeric) = -0.0802255150563 -2.06151783657 y2[1] (closed_form) = -0.0802255150563 -2.06151783657 absolute error = 1.401e-14 relative error = 6.792e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.25000826033 -0.98973155169 y1[1] (closed_form) = 3.25000826033 -0.98973155169 absolute error = 1.001e-14 relative error = 2.946e-13 % Correct digits = 15 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=14099.4MB, alloc=44.3MB, time=183.81 x[1] = 0.4486 1.566 h = 0.001 0.003 y2[1] (numeric) = -0.0834673168061 -2.06277703198 y2[1] (closed_form) = -0.0834673168061 -2.06277703198 absolute error = 1.402e-14 relative error = 6.792e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.25098856187 -0.992875545377 y1[1] (closed_form) = 3.25098856187 -0.992875545377 absolute error = 1.001e-14 relative error = 2.944e-13 % Correct digits = 15 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=14147.2MB, alloc=44.3MB, time=184.44 x[1] = 0.4496 1.569 h = 0.0001 0.004 y2[1] (numeric) = -0.0887074669469 -2.06854212527 y2[1] (closed_form) = -0.0887074669469 -2.06854212527 absolute error = 1.401e-14 relative error = 6.765e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.25609945247 -0.998199461027 y1[1] (closed_form) = 3.25609945247 -0.998199461027 absolute error = 1.000e-14 relative error = 2.938e-13 % Correct digits = 15 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=14195.2MB, alloc=44.3MB, time=185.06 x[1] = 0.4497 1.573 h = 0.003 0.006 y2[1] (numeric) = -0.0929354188151 -2.07748282889 y2[1] (closed_form) = -0.0929354188151 -2.07748282889 absolute error = 1.501e-14 relative error = 7.218e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.26428240963 -1.00277004141 y1[1] (closed_form) = 3.26428240963 -1.00277004141 absolute error = 1.005e-14 relative error = 2.943e-13 % Correct digits = 15 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 x[1] = 0.4527 1.579 h = 0.0001 0.005 y2[1] (numeric) = -0.105797156861 -2.08806855701 y2[1] (closed_form) = -0.105797156861 -2.08806855701 absolute error = 1.502e-14 relative error = 7.185e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.27348098276 -1.01561450972 y1[1] (closed_form) = 3.27348098276 -1.01561450972 absolute error = 1.0e-14 relative error = 2.918e-13 % Correct digits = 15 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=14242.8MB, alloc=44.3MB, time=185.68 x[1] = 0.4528 1.584 h = 0.0001 0.003 y2[1] (numeric) = -0.111117462485 -2.09935998408 y2[1] (closed_form) = -0.111117462485 -2.09935998408 absolute error = 1.500e-14 relative error = 7.136e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.2838386873 -1.02136615485 y1[1] (closed_form) = 3.2838386873 -1.02136615485 absolute error = 1.005e-14 relative error = 2.922e-13 % Correct digits = 15 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=14290.7MB, alloc=44.3MB, time=186.31 x[1] = 0.4529 1.587 h = 0.001 0.001 y2[1] (numeric) = -0.114415574713 -2.1061184766 y2[1] (closed_form) = -0.114415574713 -2.1061184766 absolute error = 1.502e-14 relative error = 7.119e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.29003562387 -1.02491472537 y1[1] (closed_form) = 3.29003562387 -1.02491472537 absolute error = 1.005e-14 relative error = 2.916e-13 % Correct digits = 15 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=14338.8MB, alloc=44.3MB, time=186.94 x[1] = 0.4539 1.588 h = 0.0001 0.004 y2[1] (numeric) = -0.117732631602 -2.10738248198 y2[1] (closed_form) = -0.117732631602 -2.10738248198 absolute error = 1.602e-14 relative error = 7.588e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.29102630078 -1.02813754978 y1[1] (closed_form) = 3.29102630078 -1.02813754978 absolute error = 1.005e-14 relative error = 2.915e-13 % Correct digits = 15 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 x[1] = 0.454 1.592 h = 0.003 0.006 y2[1] (numeric) = -0.122084076449 -2.11646019845 y2[1] (closed_form) = -0.122084076449 -2.11646019845 absolute error = 1.600e-14 relative error = 7.549e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.29936198451 -1.03282836853 y1[1] (closed_form) = 3.29936198451 -1.03282836853 absolute error = 1.005e-14 relative error = 2.907e-13 % Correct digits = 15 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=14386.6MB, alloc=44.3MB, time=187.56 x[1] = 0.457 1.598 h = 0.0001 0.005 y2[1] (numeric) = -0.135232500291 -2.12716622938 y2[1] (closed_form) = -0.135232500291 -2.12716622938 absolute error = 1.6e-14 relative error = 7.507e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.30870690732 -1.0459657003 y1[1] (closed_form) = 3.30870690732 -1.0459657003 absolute error = 1.005e-14 relative error = 2.896e-13 % Correct digits = 15 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=14434.4MB, alloc=44.3MB, time=188.18 x[1] = 0.4571 1.603 h = 0.0001 0.003 y2[1] (numeric) = -0.140708472481 -2.13863122546 y2[1] (closed_form) = -0.140708472481 -2.13863122546 absolute error = 1.701e-14 relative error = 7.935e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.31925758243 -1.05186882944 y1[1] (closed_form) = 3.31925758243 -1.05186882944 absolute error = 1.105e-14 relative error = 3.172e-13 % Correct digits = 14 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=14482.3MB, alloc=44.3MB, time=188.80 x[1] = 0.4572 1.606 h = 0.001 0.001 y2[1] (numeric) = -0.144101779567 -2.14549309219 y2[1] (closed_form) = -0.144101779567 -2.14549309219 absolute error = 1.702e-14 relative error = 7.917e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.32556952384 -1.05551024799 y1[1] (closed_form) = 3.32556952384 -1.05551024799 absolute error = 1.105e-14 relative error = 3.166e-13 % Correct digits = 14 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 x[1] = 0.4582 1.607 h = 0.001 0.003 y2[1] (numeric) = -0.147485005255 -2.14676200624 y2[1] (closed_form) = -0.147485005255 -2.14676200624 absolute error = 1.603e-14 relative error = 7.447e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.32656985855 -1.05880216876 y1[1] (closed_form) = 3.32656985855 -1.05880216876 absolute error = 1.105e-14 relative error = 3.164e-13 % Correct digits = 14 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=14530.1MB, alloc=44.3MB, time=189.44 x[1] = 0.4592 1.61 h = 0.0001 0.004 y2[1] (numeric) = -0.152999025114 -2.15268806063 y2[1] (closed_form) = -0.152999025114 -2.15268806063 absolute error = 1.702e-14 relative error = 7.886e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.3318687909 -1.06440261346 y1[1] (closed_form) = 3.3318687909 -1.06440261346 absolute error = 1.1e-14 relative error = 3.145e-13 % Correct digits = 15 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=14578.0MB, alloc=44.3MB, time=190.06 x[1] = 0.4593 1.614 h = 0.003 0.006 y2[1] (numeric) = -0.157499914962 -2.16192586907 y2[1] (closed_form) = -0.157499914962 -2.16192586907 absolute error = 1.700e-14 relative error = 7.844e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.34038248279 -1.06923933502 y1[1] (closed_form) = 3.34038248279 -1.06923933502 absolute error = 1.1e-14 relative error = 3.136e-13 % Correct digits = 15 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=14626.0MB, alloc=44.3MB, time=190.68 x[1] = 0.4623 1.62 h = 0.0001 0.005 y2[1] (numeric) = -0.170991164955 -2.17276876495 y2[1] (closed_form) = -0.170991164955 -2.17276876495 absolute error = 1.702e-14 relative error = 7.809e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.34989384914 -1.08272679133 y1[1] (closed_form) = 3.34989384914 -1.08272679133 absolute error = 1.1e-14 relative error = 3.125e-13 % Correct digits = 15 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 x[1] = 0.4624 1.625 h = 0.0001 0.003 y2[1] (numeric) = -0.176655531717 -2.18443657237 y2[1] (closed_form) = -0.176655531717 -2.18443657237 absolute error = 1.701e-14 relative error = 7.760e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.36066945821 -1.08881375477 y1[1] (closed_form) = 3.36066945821 -1.08881375477 absolute error = 1.1e-14 relative error = 3.114e-13 % Correct digits = 15 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=14673.7MB, alloc=44.3MB, time=191.31 x[1] = 0.4625 1.628 h = 0.001 0.001 y2[1] (numeric) = -0.180163990275 -2.19141917551 y2[1] (closed_form) = -0.180163990275 -2.19141917551 absolute error = 1.700e-14 relative error = 7.733e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.36711539622 -1.0925677737 y1[1] (closed_form) = 3.36711539622 -1.0925677737 absolute error = 1.204e-14 relative error = 3.402e-13 % Correct digits = 14 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=14721.6MB, alloc=44.3MB, time=191.93 x[1] = 0.4635 1.629 h = 0.001 0.003 y2[1] (numeric) = -0.183625865289 -2.19269254182 y2[1] (closed_form) = -0.183625865289 -2.19269254182 absolute error = 1.7e-14 relative error = 7.726e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.36812555771 -1.09594172432 y1[1] (closed_form) = 3.36812555771 -1.09594172432 absolute error = 1.204e-14 relative error = 3.400e-13 % Correct digits = 14 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=14769.5MB, alloc=44.3MB, time=192.55 x[1] = 0.4645 1.632 h = 0.0001 0.004 y2[1] (numeric) = -0.18929314216 -2.19870619901 y2[1] (closed_form) = -0.18929314216 -2.19870619901 absolute error = 1.802e-14 relative error = 8.165e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.37352619559 -1.10169679566 y1[1] (closed_form) = 3.37352619559 -1.10169679566 absolute error = 1.3e-14 relative error = 3.663e-13 % Correct digits = 14 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 x[1] = 0.4646 1.636 h = 0.003 0.006 y2[1] (numeric) = -0.193947683486 -2.20810726147 y2[1] (closed_form) = -0.193947683486 -2.20810726147 absolute error = 1.802e-14 relative error = 8.131e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.38222064922 -1.10668361076 y1[1] (closed_form) = 3.38222064922 -1.10668361076 absolute error = 1.2e-14 relative error = 3.372e-13 % Correct digits = 14 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=14817.3MB, alloc=44.3MB, time=193.18 x[1] = 0.4676 1.642 h = 0.0001 0.005 y2[1] (numeric) = -0.207790439354 -2.21908881943 y2[1] (closed_form) = -0.207790439354 -2.21908881943 absolute error = 1.802e-14 relative error = 8.084e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.39189965004 -1.12052955906 y1[1] (closed_form) = 3.39189965004 -1.12052955906 absolute error = 1.3e-14 relative error = 3.639e-13 % Correct digits = 14 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=14865.1MB, alloc=44.3MB, time=193.80 x[1] = 0.4677 1.647 h = 0.0001 0.003 y2[1] (numeric) = -0.213648504342 -2.23096343677 y2[1] (closed_form) = -0.213648504342 -2.23096343677 absolute error = 1.801e-14 relative error = 8.035e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.40290368634 -1.12680564505 y1[1] (closed_form) = 3.40290368634 -1.12680564505 absolute error = 1.304e-14 relative error = 3.637e-13 % Correct digits = 14 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 x[1] = 0.4678 1.65 h = 0.001 0.001 y2[1] (numeric) = -0.217275342425 -2.23806914163 y2[1] (closed_form) = -0.217275342425 -2.23806914163 absolute error = 1.801e-14 relative error = 8.008e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.40948568428 -1.13067547922 y1[1] (closed_form) = 3.40948568428 -1.13067547922 absolute error = 1.404e-14 relative error = 3.907e-13 % Correct digits = 14 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=14913.0MB, alloc=44.3MB, time=194.42 x[1] = 0.4688 1.651 h = 0.001 0.003 y2[1] (numeric) = -0.220817742083 -2.23934673338 y2[1] (closed_form) = -0.220817742083 -2.23934673338 absolute error = 1.800e-14 relative error = 7.999e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.41050534625 -1.13413323353 y1[1] (closed_form) = 3.41050534625 -1.13413323353 absolute error = 1.304e-14 relative error = 3.628e-13 % Correct digits = 14 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=14960.9MB, alloc=44.3MB, time=195.05 x[1] = 0.4698 1.654 h = 0.0001 0.004 y2[1] (numeric) = -0.2266422623 -2.24544941343 y2[1] (closed_form) = -0.2266422623 -2.24544941343 absolute error = 1.800e-14 relative error = 7.978e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.41600880976 -1.14004681492 y1[1] (closed_form) = 3.41600880976 -1.14004681492 absolute error = 1.404e-14 relative error = 3.897e-13 % Correct digits = 14 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=15008.9MB, alloc=44.3MB, time=195.67 x[1] = 0.4699 1.658 h = 0.003 0.006 y2[1] (numeric) = -0.231454769711 -2.25501693053 y2[1] (closed_form) = -0.231454769711 -2.25501693053 absolute error = 1.800e-14 relative error = 7.942e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.4248868261 -1.14518802485 y1[1] (closed_form) = 3.4248868261 -1.14518802485 absolute error = 1.414e-14 relative error = 3.916e-13 % Correct digits = 14 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 x[1] = 0.4729 1.664 h = 0.0001 0.005 y2[1] (numeric) = -0.245657903774 -2.26613892894 y2[1] (closed_form) = -0.245657903774 -2.26613892894 absolute error = 1.800e-14 relative error = 7.897e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.43473464515 -1.15940103514 y1[1] (closed_form) = 3.43473464515 -1.15940103514 absolute error = 1.414e-14 relative error = 3.901e-13 % Correct digits = 14 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=15056.5MB, alloc=44.3MB, time=196.29 x[1] = 0.473 1.669 h = 0.0001 0.003 y2[1] (numeric) = -0.251715107185 -2.27822440391 y2[1] (closed_form) = -0.251715107185 -2.27822440391 absolute error = 1.800e-14 relative error = 7.854e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.44597066198 -1.16587167142 y1[1] (closed_form) = 3.44597066198 -1.16587167142 absolute error = 1.404e-14 relative error = 3.858e-13 % Correct digits = 14 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=15104.4MB, alloc=44.3MB, time=196.91 x[1] = 0.4731 1.672 h = 0.001 0.001 y2[1] (numeric) = -0.255463635527 -2.28545560429 y2[1] (closed_form) = -0.255463635527 -2.28545560429 absolute error = 1.803e-14 relative error = 7.839e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.45269081822 -1.16986062021 y1[1] (closed_form) = 3.45269081822 -1.16986062021 absolute error = 1.503e-14 relative error = 4.124e-13 % Correct digits = 14 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=15152.4MB, alloc=44.3MB, time=197.54 x[1] = 0.4741 1.673 h = 0.001 0.003 y2[1] (numeric) = -0.259088472848 -2.28673717781 y2[1] (closed_form) = -0.259088472848 -2.28673717781 absolute error = 1.802e-14 relative error = 7.831e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.45371963914 -1.17340399249 y1[1] (closed_form) = 3.45371963914 -1.17340399249 absolute error = 1.503e-14 relative error = 4.121e-13 % Correct digits = 14 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 x[1] = 0.4751 1.676 h = 0.0001 0.004 y2[1] (numeric) = -0.265074315194 -2.29293030469 y2[1] (closed_form) = -0.265074315194 -2.29293030469 absolute error = 1.802e-14 relative error = 7.806e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.45932705827 -1.17948006356 y1[1] (closed_form) = 3.45932705827 -1.17948006356 absolute error = 1.503e-14 relative error = 4.113e-13 % Correct digits = 14 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=15200.1MB, alloc=44.3MB, time=198.16 x[1] = 0.4752 1.68 h = 0.003 0.006 y2[1] (numeric) = -0.270049214135 -2.30266751613 y2[1] (closed_form) = -0.270049214135 -2.30266751613 absolute error = 1.800e-14 relative error = 7.764e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.46839148601 -1.18478008284 y1[1] (closed_form) = 3.46839148601 -1.18478008284 absolute error = 1.503e-14 relative error = 4.102e-13 % Correct digits = 14 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=15247.9MB, alloc=44.3MB, time=198.78 x[1] = 0.4782 1.686 h = 0.0001 0.005 y2[1] (numeric) = -0.284621795775 -2.31393171334 y2[1] (closed_form) = -0.284621795775 -2.31393171334 absolute error = 1.801e-14 relative error = 7.725e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.47840929841 -1.19936893184 y1[1] (closed_form) = 3.47840929841 -1.19936893184 absolute error = 1.503e-14 relative error = 4.086e-13 % Correct digits = 14 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=15295.8MB, alloc=44.3MB, time=199.40 x[1] = 0.4783 1.691 h = 0.0001 0.003 y2[1] (numeric) = -0.290883717772 -2.32623214333 y2[1] (closed_form) = -0.290883717772 -2.32623214333 absolute error = 1.803e-14 relative error = 7.692e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.48988090945 -1.20603968896 y1[1] (closed_form) = 3.48988090945 -1.20603968896 absolute error = 1.6e-14 relative error = 4.333e-13 % Correct digits = 14 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 x[1] = 0.4784 1.694 h = 0.001 0.001 y2[1] (numeric) = -0.294757331856 -2.33359126187 y2[1] (closed_form) = -0.294757331856 -2.33359126187 absolute error = 1.804e-14 relative error = 7.670e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.49674135757 -1.21015113829 y1[1] (closed_form) = 3.49674135757 -1.21015113829 absolute error = 1.6e-14 relative error = 4.324e-13 % Correct digits = 14 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=15343.5MB, alloc=44.3MB, time=200.04 x[1] = 0.4794 1.695 h = 0.0001 0.004 y2[1] (numeric) = -0.298466558372 -2.3348765561 y2[1] (closed_form) = -0.298466558372 -2.3348765561 absolute error = 1.802e-14 relative error = 7.657e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.49777898014 -1.21378198397 y1[1] (closed_form) = 3.49777898014 -1.21378198397 absolute error = 1.5e-14 relative error = 4.051e-13 % Correct digits = 14 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=15391.4MB, alloc=44.3MB, time=200.66 x[1] = 0.4795 1.699 h = 0.003 0.006 y2[1] (numeric) = -0.303582794334 -2.34476446742 y2[1] (closed_form) = -0.303582794334 -2.34476446742 absolute error = 1.801e-14 relative error = 7.619e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.50700814778 -1.21922005686 y1[1] (closed_form) = 3.50700814778 -1.21922005686 absolute error = 1.6e-14 relative error = 4.309e-13 % Correct digits = 14 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=15439.4MB, alloc=44.3MB, time=201.29 x[1] = 0.4825 1.705 h = 0.0001 0.005 y2[1] (numeric) = -0.318479078475 -2.35615700801 y2[1] (closed_form) = -0.318479078475 -2.35615700801 absolute error = 1.802e-14 relative error = 7.580e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.51717784127 -1.23413756062 y1[1] (closed_form) = 3.51717784127 -1.23413756062 absolute error = 1.5e-14 relative error = 4.024e-13 % Correct digits = 14 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 x[1] = 0.4826 1.71 h = 0.0001 0.003 y2[1] (numeric) = -0.324919165403 -2.3686483153 y2[1] (closed_form) = -0.324919165403 -2.3686483153 absolute error = 1.805e-14 relative error = 7.548e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.52885766091 -1.24098228127 y1[1] (closed_form) = 3.52885766091 -1.24098228127 absolute error = 1.6e-14 relative error = 4.277e-13 % Correct digits = 14 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=15487.2MB, alloc=44.3MB, time=201.91 x[1] = 0.4827 1.713 h = 0.001 0.001 y2[1] (numeric) = -0.328901670828 -2.37612105044 y2[1] (closed_form) = -0.328901670828 -2.37612105044 absolute error = 1.900e-14 relative error = 7.922e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.5358421189 -1.24520024748 y1[1] (closed_form) = 3.5358421189 -1.24520024748 absolute error = 1.6e-14 relative error = 4.268e-13 % Correct digits = 14 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=15535.2MB, alloc=44.3MB, time=202.53 x[1] = 0.4837 1.714 h = 0.001 0.003 y2[1] (numeric) = -0.332685089745 -2.37741036215 y2[1] (closed_form) = -0.332685089745 -2.37741036215 absolute error = 1.902e-14 relative error = 7.924e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.53688809184 -1.24890780639 y1[1] (closed_form) = 3.53688809184 -1.24890780639 absolute error = 1.603e-14 relative error = 4.274e-13 % Correct digits = 14 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=15583.1MB, alloc=44.3MB, time=203.16 x[1] = 0.4847 1.717 h = 0.0001 0.004 y2[1] (numeric) = -0.338981178979 -2.3837776324 y2[1] (closed_form) = -0.338981178979 -2.3837776324 absolute error = 1.904e-14 relative error = 7.910e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.54269404002 -1.25529589263 y1[1] (closed_form) = 3.54269404002 -1.25529589263 absolute error = 1.6e-14 relative error = 4.257e-13 % Correct digits = 14 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 x[1] = 0.4848 1.721 h = 0.003 0.006 y2[1] (numeric) = -0.344268306034 -2.39384142778 y2[1] (closed_form) = -0.344268306034 -2.39384142778 absolute error = 1.904e-14 relative error = 7.875e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.55211510349 -1.26090126446 y1[1] (closed_form) = 3.55211510349 -1.26090126446 absolute error = 1.6e-14 relative error = 4.245e-13 % Correct digits = 14 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=15631.0MB, alloc=44.3MB, time=203.78 x[1] = 0.4878 1.727 h = 0.0001 0.005 y2[1] (numeric) = -0.359551433539 -2.40537949502 y2[1] (closed_form) = -0.359551433539 -2.40537949502 absolute error = 2.001e-14 relative error = 8.228e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.56245705931 -1.27621148959 y1[1] (closed_form) = 3.56245705931 -1.27621148959 absolute error = 1.603e-14 relative error = 4.236e-13 % Correct digits = 14 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=15678.9MB, alloc=44.3MB, time=204.40 x[1] = 0.4879 1.732 h = 0.0001 0.003 y2[1] (numeric) = -0.366206956777 -2.4180935864 y2[1] (closed_form) = -0.366206956777 -2.4180935864 absolute error = 1.903e-14 relative error = 7.780e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.57437942985 -1.28326704353 y1[1] (closed_form) = 3.57437942985 -1.28326704353 absolute error = 1.7e-14 relative error = 4.476e-13 % Correct digits = 14 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 x[1] = 0.488 1.735 h = 0.001 0.001 y2[1] (numeric) = -0.370321069298 -2.42569886843 y2[1] (closed_form) = -0.370321069298 -2.42569886843 absolute error = 1.902e-14 relative error = 7.752e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.58150828701 -1.28761402158 y1[1] (closed_form) = 3.58150828701 -1.28761402158 absolute error = 1.7e-14 relative error = 4.467e-13 % Correct digits = 14 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=15726.8MB, alloc=44.3MB, time=205.02 x[1] = 0.489 1.736 h = 0.001 0.003 y2[1] (numeric) = -0.374192617736 -2.42699139108 y2[1] (closed_form) = -0.374192617736 -2.42699139108 absolute error = 1.903e-14 relative error = 7.748e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.58256237593 -1.29141262338 y1[1] (closed_form) = 3.58256237593 -1.29141262338 absolute error = 1.7e-14 relative error = 4.464e-13 % Correct digits = 14 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=15774.6MB, alloc=44.3MB, time=205.65 x[1] = 0.49 1.739 h = 0.0001 0.004 y2[1] (numeric) = -0.380662210804 -2.43345325312 y2[1] (closed_form) = -0.380662210804 -2.43345325312 absolute error = 1.901e-14 relative error = 7.717e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.58847561482 -1.29797512061 y1[1] (closed_form) = 3.58847561482 -1.29797512061 absolute error = 1.703e-14 relative error = 4.463e-13 % Correct digits = 14 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=15822.5MB, alloc=44.3MB, time=206.27 x[1] = 0.4901 1.743 h = 0.003 0.006 y2[1] (numeric) = -0.38612498653 -2.44369628781 y2[1] (closed_form) = -0.38612498653 -2.44369628781 absolute error = 1.904e-14 relative error = 7.695e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.59809156211 -1.30375254414 y1[1] (closed_form) = 3.59809156211 -1.30375254414 absolute error = 1.7e-14 relative error = 4.442e-13 % Correct digits = 14 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 x[1] = 0.4931 1.749 h = 0.0001 0.005 y2[1] (numeric) = -0.401804616206 -2.45538157787 y2[1] (closed_form) = -0.401804616206 -2.45538157787 absolute error = 2.005e-14 relative error = 8.058e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.60860692478 -1.31946488285 y1[1] (closed_form) = 3.60860692478 -1.31946488285 absolute error = 1.7e-14 relative error = 4.424e-13 % Correct digits = 14 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=15870.2MB, alloc=44.3MB, time=206.89 x[1] = 0.4932 1.754 h = 0.0001 0.003 y2[1] (numeric) = -0.40868157531 -2.46832269779 y2[1] (closed_form) = -0.40868157531 -2.46832269779 absolute error = 2.001e-14 relative error = 7.999e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.62077563643 -1.32673726738 y1[1] (closed_form) = 3.62077563643 -1.32673726738 absolute error = 1.7e-14 relative error = 4.408e-13 % Correct digits = 14 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=15918.0MB, alloc=44.3MB, time=207.52 x[1] = 0.4933 1.757 h = 0.001 0.001 y2[1] (numeric) = -0.412930944332 -2.47606303465 y2[1] (closed_form) = -0.412930944332 -2.47606303465 absolute error = 2.005e-14 relative error = 7.987e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.62805112917 -1.33121690173 y1[1] (closed_form) = 3.62805112917 -1.33121690173 absolute error = 1.703e-14 relative error = 4.407e-13 % Correct digits = 14 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=15966.1MB, alloc=44.3MB, time=208.15 x[1] = 0.4943 1.758 h = 0.001 0.003 y2[1] (numeric) = -0.416892688858 -2.47735845462 y2[1] (closed_form) = -0.416892688858 -2.47735845462 absolute error = 2.002e-14 relative error = 7.968e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.62911292875 -1.33510852412 y1[1] (closed_form) = 3.62911292875 -1.33510852412 absolute error = 1.603e-14 relative error = 4.146e-13 % Correct digits = 14 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 x[1] = 0.4953 1.761 h = 0.0001 0.004 y2[1] (numeric) = -0.423540242415 -2.48391634574 y2[1] (closed_form) = -0.423540242415 -2.48391634574 absolute error = 2.005e-14 relative error = 7.957e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.63513462384 -1.34184980341 y1[1] (closed_form) = 3.63513462384 -1.34184980341 absolute error = 1.703e-14 relative error = 4.395e-13 % Correct digits = 14 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=16013.7MB, alloc=44.3MB, time=208.77 x[1] = 0.4954 1.765 h = 0.003 0.006 y2[1] (numeric) = -0.429183546273 -2.49434201576 y2[1] (closed_form) = -0.429183546273 -2.49434201576 absolute error = 2.002e-14 relative error = 7.908e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.64494849169 -1.34780415531 y1[1] (closed_form) = 3.64494849169 -1.34780415531 absolute error = 1.703e-14 relative error = 4.382e-13 % Correct digits = 14 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=16061.7MB, alloc=44.3MB, time=209.39 x[1] = 0.4984 1.771 h = 0.0001 0.005 y2[1] (numeric) = -0.445269552038 -2.50617619947 y2[1] (closed_form) = -0.445269552038 -2.50617619947 absolute error = 2.101e-14 relative error = 8.255e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.65563839101 -1.36392822358 y1[1] (closed_form) = 3.65563839101 -1.36392822358 absolute error = 1.703e-14 relative error = 4.365e-13 % Correct digits = 14 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=16109.5MB, alloc=44.3MB, time=210.01 x[1] = 0.4985 1.776 h = 0.0001 0.003 y2[1] (numeric) = -0.452374100469 -2.51934864425 y2[1] (closed_form) = -0.452374100469 -2.51934864425 absolute error = 2.101e-14 relative error = 8.208e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.6680572957 -1.37142359231 y1[1] (closed_form) = 3.6680572957 -1.37142359231 absolute error = 1.703e-14 relative error = 4.349e-13 % Correct digits = 14 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 x[1] = 0.4986 1.779 h = 0.001 0.001 y2[1] (numeric) = -0.456762468559 -2.5272265739 y2[1] (closed_form) = -0.456762468559 -2.5272265739 absolute error = 2.002e-14 relative error = 7.796e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.67548169637 -1.3760396221 y1[1] (closed_form) = 3.67548169637 -1.3760396221 absolute error = 1.703e-14 relative error = 4.339e-13 % Correct digits = 14 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=16157.3MB, alloc=44.3MB, time=210.63 x[1] = 0.4996 1.78 h = 0.001 0.003 y2[1] (numeric) = -0.460816517537 -2.52852455786 y2[1] (closed_form) = -0.460816517537 -2.52852455786 absolute error = 2.003e-14 relative error = 7.793e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.67655078311 -1.38002628698 y1[1] (closed_form) = 3.67655078311 -1.38002628698 absolute error = 1.603e-14 relative error = 4.082e-13 % Correct digits = 14 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=16205.3MB, alloc=44.3MB, time=211.26 x[1] = 0.5006 1.783 h = 0.0001 0.004 y2[1] (numeric) = -0.467646591771 -2.53517991762 y2[1] (closed_form) = -0.467646591771 -2.53517991762 absolute error = 2.001e-14 relative error = 7.762e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.68268210764 -1.3869508262 y1[1] (closed_form) = 3.68268210764 -1.3869508262 absolute error = 1.603e-14 relative error = 4.074e-13 % Correct digits = 14 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=16253.4MB, alloc=44.3MB, time=211.88 x[1] = 0.5007 1.787 h = 0.003 0.006 y2[1] (numeric) = -0.473475428123 -2.54579166015 y2[1] (closed_form) = -0.473475428123 -2.54579166015 absolute error = 2.001e-14 relative error = 7.728e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.69269698176 -1.39308710997 y1[1] (closed_form) = 3.69269698176 -1.39308710997 absolute error = 1.603e-14 relative error = 4.062e-13 % Correct digits = 14 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 x[1] = 0.5037 1.793 h = 0.0001 0.005 y2[1] (numeric) = -0.489977903894 -2.55777638144 y2[1] (closed_form) = -0.489977903894 -2.55777638144 absolute error = 2.004e-14 relative error = 7.696e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.70356253107 -1.40963275221 y1[1] (closed_form) = 3.70356253107 -1.40963275221 absolute error = 1.703e-14 relative error = 4.297e-13 % Correct digits = 14 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=16300.9MB, alloc=44.3MB, time=212.50 x[1] = 0.5038 1.798 h = 0.0001 0.003 y2[1] (numeric) = -0.497316352826 -2.5711844998 y2[1] (closed_form) = -0.497316352826 -2.5711844998 absolute error = 2.006e-14 relative error = 7.661e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.71623554282 -1.41735741875 y1[1] (closed_form) = 3.71623554282 -1.41735741875 absolute error = 1.703e-14 relative error = 4.282e-13 % Correct digits = 14 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=16348.9MB, alloc=44.3MB, time=213.13 x[1] = 0.5039 1.801 h = 0.001 0.001 y2[1] (numeric) = -0.501847558013 -2.57920259052 y2[1] (closed_form) = -0.501847558013 -2.57920259052 absolute error = 1.905e-14 relative error = 7.251e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.72381115982 -1.42211368003 y1[1] (closed_form) = 3.72381115982 -1.42211368003 absolute error = 1.703e-14 relative error = 4.272e-13 % Correct digits = 14 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=16396.8MB, alloc=44.3MB, time=213.76 x[1] = 0.5049 1.802 h = 0.0001 0.004 y2[1] (numeric) = -0.50599606249 -2.58050278477 y2[1] (closed_form) = -0.50599606249 -2.58050278477 absolute error = 1.901e-14 relative error = 7.229e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.72488709138 -1.42619745435 y1[1] (closed_form) = 3.72488709138 -1.42619745435 absolute error = 1.703e-14 relative error = 4.270e-13 % Correct digits = 14 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 x[1] = 0.505 1.806 h = 0.003 0.006 y2[1] (numeric) = -0.511986431038 -2.59127977001 y2[1] (closed_form) = -0.511986431038 -2.59127977001 absolute error = 2.001e-14 relative error = 7.576e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.7350797442 -1.4324919994 y1[1] (closed_form) = 3.7350797442 -1.4324919994 absolute error = 1.703e-14 relative error = 4.257e-13 % Correct digits = 14 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=16444.6MB, alloc=44.3MB, time=214.38 x[1] = 0.508 1.812 h = 0.0001 0.005 y2[1] (numeric) = -0.528853825573 -2.60340049252 y2[1] (closed_form) = -0.528853825573 -2.60340049252 absolute error = 2.001e-14 relative error = 7.533e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.74610255054 -1.44940646943 y1[1] (closed_form) = 3.74610255054 -1.44940646943 absolute error = 1.811e-14 relative error = 4.509e-13 % Correct digits = 14 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=16492.4MB, alloc=44.3MB, time=215.00 x[1] = 0.5081 1.817 h = 0.0001 0.003 y2[1] (numeric) = -0.536395906541 -2.61701788508 y2[1] (closed_form) = -0.536395906541 -2.61701788508 absolute error = 2.001e-14 relative error = 7.490e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.7590003078 -1.45733059711 y1[1] (closed_form) = 3.7590003078 -1.45733059711 absolute error = 1.712e-14 relative error = 4.246e-13 % Correct digits = 14 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 x[1] = 0.5082 1.82 h = 0.001 0.001 y2[1] (numeric) = -0.541051497352 -2.62516046725 y2[1] (closed_form) = -0.541051497352 -2.62516046725 absolute error = 2.101e-14 relative error = 7.837e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.76670969743 -1.46220887309 y1[1] (closed_form) = 3.76670969743 -1.46220887309 absolute error = 1.712e-14 relative error = 4.236e-13 % Correct digits = 14 memory used=16540.3MB, alloc=44.3MB, time=215.63 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 x[1] = 0.5092 1.821 h = 0.001 0.003 y2[1] (numeric) = -0.545283041517 -2.62646342561 y2[1] (closed_form) = -0.545283041517 -2.62646342561 absolute error = 2.105e-14 relative error = 7.846e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.7677923428 -1.46637785212 y1[1] (closed_form) = 3.7677923428 -1.46637785212 absolute error = 1.712e-14 relative error = 4.234e-13 % Correct digits = 14 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=16588.1MB, alloc=44.3MB, time=216.25 x[1] = 0.5102 1.824 h = 0.0001 0.004 y2[1] (numeric) = -0.552464044344 -2.63330629674 y2[1] (closed_form) = -0.552464044344 -2.63330629674 absolute error = 2.101e-14 relative error = 7.807e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.77413312325 -1.47365434959 y1[1] (closed_form) = 3.77413312325 -1.47365434959 absolute error = 1.712e-14 relative error = 4.225e-13 % Correct digits = 14 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=16636.0MB, alloc=44.3MB, time=216.87 x[1] = 0.5103 1.828 h = 0.003 0.006 y2[1] (numeric) = -0.558649558255 -2.64427592448 y2[1] (closed_form) = -0.558649558255 -2.64427592448 absolute error = 2.101e-14 relative error = 7.772e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.78453271859 -1.48014044657 y1[1] (closed_form) = 3.78453271859 -1.48014044657 absolute error = 1.712e-14 relative error = 4.212e-13 % Correct digits = 14 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 x[1] = 0.5133 1.834 h = 0.0001 0.005 y2[1] (numeric) = -0.575952789159 -2.65655029309 y2[1] (closed_form) = -0.575952789159 -2.65655029309 absolute error = 2.001e-14 relative error = 7.361e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.79573332059 -1.49749542029 y1[1] (closed_form) = 3.79573332059 -1.49749542029 absolute error = 1.811e-14 relative error = 4.438e-13 % Correct digits = 14 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=16683.8MB, alloc=44.3MB, time=217.49 x[1] = 0.5134 1.839 h = 0.0001 0.003 y2[1] (numeric) = -0.583740894099 -2.67041167214 y2[1] (closed_form) = -0.583740894099 -2.67041167214 absolute error = 2.102e-14 relative error = 7.690e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.80889271409 -1.5056609845 y1[1] (closed_form) = 3.80889271409 -1.5056609845 absolute error = 1.726e-14 relative error = 4.215e-13 % Correct digits = 14 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=16731.6MB, alloc=44.3MB, time=218.12 x[1] = 0.5135 1.842 h = 0.001 0.001 y2[1] (numeric) = -0.588546694386 -2.67869932449 y2[1] (closed_form) = -0.588546694386 -2.67869932449 absolute error = 2.101e-14 relative error = 7.661e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.81675776056 -1.51068686727 y1[1] (closed_form) = 3.81675776056 -1.51068686727 absolute error = 1.726e-14 relative error = 4.205e-13 % Correct digits = 14 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=16779.6MB, alloc=44.3MB, time=218.74 x[1] = 0.5145 1.843 h = 0.001 0.003 y2[1] (numeric) = -0.592876818148 -2.68000380539 y2[1] (closed_form) = -0.592876818148 -2.68000380539 absolute error = 2.103e-14 relative error = 7.661e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.81784640109 -1.51495693041 y1[1] (closed_form) = 3.81784640109 -1.51495693041 absolute error = 1.726e-14 relative error = 4.203e-13 % Correct digits = 14 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 x[1] = 0.5155 1.846 h = 0.0001 0.004 y2[1] (numeric) = -0.600253963627 -2.68694833093 y2[1] (closed_form) = -0.600253963627 -2.68694833093 absolute error = 2.103e-14 relative error = 7.640e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.82430026333 -1.52243009444 y1[1] (closed_form) = 3.82430026333 -1.52243009444 absolute error = 1.712e-14 relative error = 4.159e-13 % Correct digits = 14 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=16827.3MB, alloc=44.3MB, time=219.36 x[1] = 0.5156 1.85 h = 0.003 0.006 y2[1] (numeric) = -0.606640001328 -2.69811415991 y2[1] (closed_form) = -0.606640001328 -2.69811415991 absolute error = 2.204e-14 relative error = 7.971e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.83491002992 -1.52911312588 y1[1] (closed_form) = 3.83491002992 -1.52911312588 absolute error = 1.726e-14 relative error = 4.181e-13 % Correct digits = 14 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=16875.3MB, alloc=44.3MB, time=219.98 x[1] = 0.5186 1.856 h = 0.0001 0.005 y2[1] (numeric) = -0.624389820139 -2.71054373536 y2[1] (closed_form) = -0.624389820139 -2.71054373536 absolute error = 2.101e-14 relative error = 7.554e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.84628948669 -1.54691912799 y1[1] (closed_form) = 3.84628948669 -1.54691912799 absolute error = 1.712e-14 relative error = 4.129e-13 % Correct digits = 14 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=16923.1MB, alloc=44.3MB, time=220.61 x[1] = 0.5187 1.861 h = 0.0001 0.003 y2[1] (numeric) = -0.632430732545 -2.72465360429 y2[1] (closed_form) = -0.632430732545 -2.72465360429 absolute error = 2.104e-14 relative error = 7.522e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.85971461176 -1.5553329206 y1[1] (closed_form) = 3.85971461176 -1.5553329206 absolute error = 1.726e-14 relative error = 4.148e-13 % Correct digits = 14 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 x[1] = 0.5188 1.864 h = 0.001 0.001 y2[1] (numeric) = -0.637390866209 -2.73308898455 y2[1] (closed_form) = -0.637390866209 -2.73308898455 absolute error = 2.201e-14 relative error = 7.844e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.86773772881 -1.56051053584 y1[1] (closed_form) = 3.86773772881 -1.56051053584 absolute error = 1.726e-14 relative error = 4.139e-13 % Correct digits = 14 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=16970.8MB, alloc=44.3MB, time=221.23 x[1] = 0.5198 1.865 h = 0.001 0.003 y2[1] (numeric) = -0.641821847998 -2.73439457288 y2[1] (closed_form) = -0.641821847998 -2.73439457288 absolute error = 2.102e-14 relative error = 7.482e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.86883186496 -1.5648838838 y1[1] (closed_form) = 3.86883186496 -1.5648838838 absolute error = 1.726e-14 relative error = 4.136e-13 % Correct digits = 14 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=17018.7MB, alloc=44.3MB, time=221.85 x[1] = 0.5208 1.868 h = 0.0001 0.004 y2[1] (numeric) = -0.649400119124 -2.74144219853 y2[1] (closed_form) = -0.649400119124 -2.74144219853 absolute error = 2.105e-14 relative error = 7.470e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.87540000859 -1.57255862673 y1[1] (closed_form) = 3.87540000859 -1.57255862673 absolute error = 1.726e-14 relative error = 4.128e-13 % Correct digits = 14 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=17066.8MB, alloc=44.3MB, time=222.48 x[1] = 0.5209 1.872 h = 0.003 0.006 y2[1] (numeric) = -0.655992196226 -2.75280783015 y2[1] (closed_form) = -0.655992196226 -2.75280783015 absolute error = 2.105e-14 relative error = 7.437e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.88622322507 -1.57944411397 y1[1] (closed_form) = 3.88622322507 -1.57944411397 absolute error = 1.726e-14 relative error = 4.115e-13 % Correct digits = 14 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 x[1] = 0.5239 1.878 h = 0.0001 0.005 y2[1] (numeric) = -0.674199594287 -2.7653941398 y2[1] (closed_form) = -0.674199594287 -2.7653941398 absolute error = 2.103e-14 relative error = 7.390e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.89778257209 -1.59771191652 y1[1] (closed_form) = 3.89778257209 -1.59771191652 absolute error = 1.712e-14 relative error = 4.063e-13 % Correct digits = 14 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=17114.4MB, alloc=44.3MB, time=223.10 x[1] = 0.524 1.883 h = 0.0001 0.003 y2[1] (numeric) = -0.682500270865 -2.77975705634 y2[1] (closed_form) = -0.682500270865 -2.77975705634 absolute error = 2.104e-14 relative error = 7.351e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.91147758729 -1.60638090454 y1[1] (closed_form) = 3.91147758729 -1.60638090454 absolute error = 1.712e-14 relative error = 4.048e-13 % Correct digits = 14 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=17162.3MB, alloc=44.3MB, time=223.72 x[1] = 0.5241 1.886 h = 0.001 0.001 y2[1] (numeric) = -0.687618966624 -2.78834285361 y2[1] (closed_form) = -0.687618966624 -2.78834285361 absolute error = 2.102e-14 relative error = 7.319e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.91966122533 -1.61171448399 y1[1] (closed_form) = 3.91966122533 -1.61171448399 absolute error = 1.712e-14 relative error = 4.039e-13 % Correct digits = 14 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=17210.3MB, alloc=44.3MB, time=224.35 x[1] = 0.5251 1.887 h = 0.001 0.003 y2[1] (numeric) = -0.692153131112 -2.78964911122 y2[1] (closed_form) = -0.692153131112 -2.78964911122 absolute error = 2.103e-14 relative error = 7.316e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 3.92076033601 -1.61619336584 y1[1] (closed_form) = 3.92076033601 -1.61619336584 absolute error = 1.712e-14 relative error = 4.036e-13 % Correct digits = 14 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 x[1] = 0.5261 1.89 h = 0.0001 0.004 y2[1] (numeric) = -0.699937626624 -2.79680128276 y2[1] (closed_form) = -0.699937626624 -2.79680128276 absolute error = 2.201e-14 relative error = 7.636e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.9274439657 -1.62407471858 y1[1] (closed_form) = 3.9274439657 -1.62407471858 absolute error = 1.712e-14 relative error = 4.028e-13 % Correct digits = 14 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=17258.1MB, alloc=44.3MB, time=224.97 x[1] = 0.5262 1.894 h = 0.003 0.006 y2[1] (numeric) = -0.70674139927 -2.8083703615 y2[1] (closed_form) = -0.70674139927 -2.8083703615 absolute error = 2.103e-14 relative error = 7.263e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.9384839608 -1.63116832502 y1[1] (closed_form) = 3.9384839608 -1.63116832502 absolute error = 1.712e-14 relative error = 4.015e-13 % Correct digits = 14 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=17305.9MB, alloc=44.3MB, time=225.60 x[1] = 0.5292 1.9 h = 0.0001 0.005 y2[1] (numeric) = -0.725417613101 -2.82111489744 y2[1] (closed_form) = -0.725417613101 -2.82111489744 absolute error = 2.203e-14 relative error = 7.562e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.95022420787 -1.64990895256 y1[1] (closed_form) = 3.95022420787 -1.64990895256 absolute error = 1.712e-14 relative error = 3.998e-13 % Correct digits = 14 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=17353.7MB, alloc=44.3MB, time=226.22 x[1] = 0.5293 1.905 h = 0.0001 0.003 y2[1] (numeric) = -0.733985188005 -2.8357354741 y2[1] (closed_form) = -0.733985188005 -2.8357354741 absolute error = 2.103e-14 relative error = 7.181e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 3.96419333531 -1.65884028232 y1[1] (closed_form) = 3.96419333531 -1.65884028232 absolute error = 1.811e-14 relative error = 4.214e-13 % Correct digits = 14 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 x[1] = 0.5294 1.908 h = 0.001 0.001 y2[1] (numeric) = -0.73926678195 -2.84447440907 y2[1] (closed_form) = -0.73926678195 -2.84447440907 absolute error = 2.205e-14 relative error = 7.503e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 3.97253998156 -1.66433416623 y1[1] (closed_form) = 3.97253998156 -1.66433416623 absolute error = 1.811e-14 relative error = 4.205e-13 % Correct digits = 14 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=17401.6MB, alloc=44.3MB, time=226.84 x[1] = 0.5304 1.909 h = 0.0001 0.004 y2[1] (numeric) = -0.743906501008 -2.84578087407 y2[1] (closed_form) = -0.743906501008 -2.84578087407 absolute error = 2.205e-14 relative error = 7.497e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 3.97364352332 -1.66892088033 y1[1] (closed_form) = 3.97364352332 -1.66892088033 absolute error = 1.712e-14 relative error = 3.972e-13 % Correct digits = 14 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=17449.5MB, alloc=44.3MB, time=227.47 x[1] = 0.5305 1.913 h = 0.003 0.006 y2[1] (numeric) = -0.750894649895 -2.85753064089 y2[1] (closed_form) = -0.750894649895 -2.85753064089 absolute error = 2.207e-14 relative error = 7.471e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 3.98487539181 -1.67619563777 y1[1] (closed_form) = 3.98487539181 -1.67619563777 absolute error = 1.712e-14 relative error = 3.960e-13 % Correct digits = 14 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 x[1] = 0.5335 1.919 h = 0.0001 0.005 y2[1] (numeric) = -0.769981685553 -2.87041831057 y2[1] (closed_form) = -0.769981685553 -2.87041831057 absolute error = 2.302e-14 relative error = 7.746e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 3.99677795485 -1.6953501114 y1[1] (closed_form) = 3.99677795485 -1.6953501114 absolute error = 1.811e-14 relative error = 4.172e-13 % Correct digits = 14 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=17497.2MB, alloc=44.3MB, time=228.08 x[1] = 0.5336 1.924 h = 0.0001 0.003 y2[1] (numeric) = -0.778781704111 -2.88526770653 y2[1] (closed_form) = -0.778781704111 -2.88526770653 absolute error = 2.203e-14 relative error = 7.371e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.01098970289 -1.70450978391 y1[1] (closed_form) = 4.01098970289 -1.70450978391 absolute error = 1.811e-14 relative error = 4.156e-13 % Correct digits = 14 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=17545.0MB, alloc=44.3MB, time=228.70 x[1] = 0.5337 1.927 h = 0.001 0.001 y2[1] (numeric) = -0.784205202643 -2.89414267305 y2[1] (closed_form) = -0.784205202643 -2.89414267305 absolute error = 2.203e-14 relative error = 7.348e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.01948066303 -1.71014323015 y1[1] (closed_form) = 4.01948066303 -1.71014323015 absolute error = 1.811e-14 relative error = 4.146e-13 % Correct digits = 14 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=17592.9MB, alloc=44.3MB, time=229.34 x[1] = 0.5347 1.928 h = 0.001 0.003 y2[1] (numeric) = -0.788937721115 -2.8954502247 y2[1] (closed_form) = -0.788937721115 -2.8954502247 absolute error = 2.207e-14 relative error = 7.355e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.0205888888 -1.71482459787 y1[1] (closed_form) = 4.0205888888 -1.71482459787 absolute error = 1.811e-14 relative error = 4.143e-13 % Correct digits = 14 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 x[1] = 0.5357 1.931 h = 0.0001 0.004 y2[1] (numeric) = -0.797118644147 -2.90280338338 y2[1] (closed_form) = -0.797118644147 -2.90280338338 absolute error = 2.207e-14 relative error = 7.333e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.02749324057 -1.72310280025 y1[1] (closed_form) = 4.02749324057 -1.72310280025 absolute error = 1.811e-14 relative error = 4.134e-13 % Correct digits = 14 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=17640.6MB, alloc=44.3MB, time=229.96 x[1] = 0.5358 1.935 h = 0.003 0.006 y2[1] (numeric) = -0.804329354546 -2.91476356601 y2[1] (closed_form) = -0.804329354546 -2.91476356601 absolute error = 2.303e-14 relative error = 7.615e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.0389482873 -1.73059656385 y1[1] (closed_form) = 4.0389482873 -1.73059656385 absolute error = 1.811e-14 relative error = 4.122e-13 % Correct digits = 14 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=17688.5MB, alloc=44.3MB, time=230.58 x[1] = 0.5388 1.941 h = 0.0001 0.005 y2[1] (numeric) = -0.823906769178 -2.9278122789 y2[1] (closed_form) = -0.823906769178 -2.9278122789 absolute error = 2.305e-14 relative error = 7.578e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.0510336924 -1.75024505552 y1[1] (closed_form) = 4.0510336924 -1.75024505552 absolute error = 1.910e-14 relative error = 4.329e-13 % Correct digits = 14 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=17736.5MB, alloc=44.3MB, time=231.20 x[1] = 0.5389 1.946 h = 0.0001 0.003 y2[1] (numeric) = -0.832987391733 -2.94292815528 y2[1] (closed_form) = -0.832987391733 -2.94292815528 absolute error = 2.304e-14 relative error = 7.532e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.06552766938 -1.75968080709 y1[1] (closed_form) = 4.06552766938 -1.75968080709 absolute error = 1.825e-14 relative error = 4.119e-13 % Correct digits = 14 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 x[1] = 0.539 1.949 h = 0.001 0.001 y2[1] (numeric) = -0.838582118356 -2.95196146174 y2[1] (closed_form) = -0.838582118356 -2.95196146174 absolute error = 2.304e-14 relative error = 7.507e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.07418641914 -1.76548290105 y1[1] (closed_form) = 4.07418641914 -1.76548290105 absolute error = 1.825e-14 relative error = 4.110e-13 % Correct digits = 14 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=17784.3MB, alloc=44.3MB, time=231.83 x[1] = 0.54 1.95 h = 0.001 0.003 y2[1] (numeric) = -0.843424740074 -2.95326832507 y2[1] (closed_form) = -0.843424740074 -2.95326832507 absolute error = 2.308e-14 relative error = 7.514e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.0752980314 -1.77027651919 y1[1] (closed_form) = 4.0752980314 -1.77027651919 absolute error = 1.811e-14 relative error = 4.076e-13 % Correct digits = 14 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=17832.2MB, alloc=44.3MB, time=232.45 x[1] = 0.541 1.953 h = 0.0001 0.004 y2[1] (numeric) = -0.851827119818 -2.96073022699 y2[1] (closed_form) = -0.851827119818 -2.96073022699 absolute error = 2.402e-14 relative error = 7.797e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.08232140286 -1.77877638708 y1[1] (closed_form) = 4.08232140286 -1.77877638708 absolute error = 1.811e-14 relative error = 4.067e-13 % Correct digits = 14 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=17880.1MB, alloc=44.3MB, time=233.08 x[1] = 0.5411 1.957 h = 0.003 0.006 y2[1] (numeric) = -0.859266468583 -2.97290459669 y2[1] (closed_form) = -0.859266468583 -2.97290459669 absolute error = 2.406e-14 relative error = 7.775e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.09400310278 -1.78649524493 y1[1] (closed_form) = 4.09400310278 -1.78649524493 absolute error = 1.903e-14 relative error = 4.259e-13 % Correct digits = 14 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 x[1] = 0.5441 1.963 h = 0.0001 0.005 y2[1] (numeric) = -0.879346231169 -2.98611573619 y2[1] (closed_form) = -0.879346231169 -2.98611573619 absolute error = 2.405e-14 relative error = 7.725e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.10627227759 -1.80664953138 y1[1] (closed_form) = 4.10627227759 -1.80664953138 absolute error = 1.910e-14 relative error = 4.259e-13 % Correct digits = 14 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=17927.8MB, alloc=44.3MB, time=233.70 x[1] = 0.5442 1.968 h = 0.0001 0.003 y2[1] (numeric) = -0.888715123074 -3.00150286692 y2[1] (closed_form) = -0.888715123074 -3.00150286692 absolute error = 2.506e-14 relative error = 8.005e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.12105289106 -1.81636904422 y1[1] (closed_form) = 4.12105289106 -1.81636904422 absolute error = 1.903e-14 relative error = 4.225e-13 % Correct digits = 14 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=17975.7MB, alloc=44.3MB, time=234.32 x[1] = 0.5443 1.971 h = 0.001 0.001 y2[1] (numeric) = -0.894485735279 -3.01069732701 y2[1] (closed_form) = -0.894485735279 -3.01069732701 absolute error = 2.506e-14 relative error = 7.978e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.12988202499 -1.8223444506 y1[1] (closed_form) = 4.12988202499 -1.8223444506 absolute error = 1.910e-14 relative error = 4.232e-13 % Correct digits = 14 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=18023.7MB, alloc=44.3MB, time=234.94 x[1] = 0.5453 1.972 h = 0.001 0.003 y2[1] (numeric) = -0.899440972887 -3.01200296845 y2[1] (closed_form) = -0.899440972887 -3.01200296845 absolute error = 2.409e-14 relative error = 7.664e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.1309964126 -1.82725276392 y1[1] (closed_form) = 4.1309964126 -1.82725276392 absolute error = 1.903e-14 relative error = 4.212e-13 % Correct digits = 14 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 x[1] = 0.5463 1.975 h = 0.0001 0.004 y2[1] (numeric) = -0.908070380428 -3.01957505609 y2[1] (closed_form) = -0.908070380428 -3.01957505609 absolute error = 2.507e-14 relative error = 7.951e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.13814002356 -1.83597981057 y1[1] (closed_form) = 4.13814002356 -1.83597981057 absolute error = 1.910e-14 relative error = 4.220e-13 % Correct digits = 14 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=18071.3MB, alloc=44.3MB, time=235.56 x[1] = 0.5464 1.979 h = 0.003 0.006 y2[1] (numeric) = -0.915744598606 -3.03196742845 y2[1] (closed_form) = -0.915744598606 -3.03196742845 absolute error = 2.503e-14 relative error = 7.904e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.15005190244 -1.84393000626 y1[1] (closed_form) = 4.15005190244 -1.84393000626 absolute error = 2.010e-14 relative error = 4.426e-13 % Correct digits = 14 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=18119.3MB, alloc=44.3MB, time=236.19 x[1] = 0.5494 1.985 h = 0.0001 0.005 y2[1] (numeric) = -0.93633894504 -3.04534233485 y2[1] (closed_form) = -0.93633894504 -3.04534233485 absolute error = 2.503e-14 relative error = 7.856e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.16250574041 -1.86460213767 y1[1] (closed_form) = 4.16250574041 -1.86460213767 absolute error = 2.010e-14 relative error = 4.407e-13 % Correct digits = 14 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=18167.1MB, alloc=44.3MB, time=236.81 x[1] = 0.5495 1.99 h = 0.0001 0.003 y2[1] (numeric) = -0.946003966337 -3.06100555027 y2[1] (closed_form) = -0.946003966337 -3.06100555027 absolute error = 2.503e-14 relative error = 7.814e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.17757746242 -1.87461329023 y1[1] (closed_form) = 4.17757746242 -1.87461329023 absolute error = 2.002e-14 relative error = 4.373e-13 % Correct digits = 14 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 x[1] = 0.5496 1.993 h = 0.001 0.001 y2[1] (numeric) = -0.951955239389 -3.07036401017 y2[1] (closed_form) = -0.951955239389 -3.07036401017 absolute error = 2.507e-14 relative error = 7.800e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.18657961237 -1.88076679246 y1[1] (closed_form) = 4.18657961237 -1.88076679246 absolute error = 2.002e-14 relative error = 4.363e-13 % Correct digits = 14 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=18214.9MB, alloc=44.3MB, time=237.43 x[1] = 0.5506 1.994 h = 0.001 0.003 y2[1] (numeric) = -0.957025656593 -3.07166786934 y2[1] (closed_form) = -0.957025656593 -3.07166786934 absolute error = 2.506e-14 relative error = 7.791e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.1876961387 -1.88579229866 y1[1] (closed_form) = 4.1876961387 -1.88579229866 absolute error = 1.9e-14 relative error = 4.137e-13 % Correct digits = 14 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=18262.7MB, alloc=44.3MB, time=238.06 x[1] = 0.5516 1.997 h = 0.0001 0.004 y2[1] (numeric) = -0.965887792219 -3.07935158244 y2[1] (closed_form) = -0.965887792219 -3.07935158244 absolute error = 2.408e-14 relative error = 7.460e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.19496121079 -1.89475216896 y1[1] (closed_form) = 4.19496121079 -1.89475216896 absolute error = 1.9e-14 relative error = 4.128e-13 % Correct digits = 14 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 x[1] = 0.5517 2.001 h = 0.003 0.006 y2[1] (numeric) = -0.973803268782 -3.09196581766 y2[1] (closed_form) = -0.973803268782 -3.09196581766 absolute error = 2.408e-14 relative error = 7.429e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.2071068454 -1.90294010523 y1[1] (closed_form) = 4.2071068454 -1.90294010523 absolute error = 2.0e-14 relative error = 4.331e-13 % Correct digits = 14 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=18310.6MB, alloc=44.3MB, time=238.68 x[1] = 0.5547 2.007 h = 0.0001 0.005 y2[1] (numeric) = -0.99492470776 -3.10550578593 y2[1] (closed_form) = -0.99492470776 -3.10550578593 absolute error = 2.406e-14 relative error = 7.378e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.21974620341 -1.92414241094 y1[1] (closed_form) = 4.21974620341 -1.92414241094 absolute error = 2.002e-14 relative error = 4.318e-13 % Correct digits = 14 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=18358.2MB, alloc=44.3MB, time=239.30 x[1] = 0.5548 2.012 h = 0.0001 0.003 y2[1] (numeric) = -1.00489391789 -3.12144997321 y2[1] (closed_form) = -1.00489391789 -3.12144997321 absolute error = 2.408e-14 relative error = 7.344e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.23511357073 -1.93445328254 y1[1] (closed_form) = 4.23511357073 -1.93445328254 absolute error = 2.002e-14 relative error = 4.301e-13 % Correct digits = 14 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=18406.3MB, alloc=44.3MB, time=239.92 x[1] = 0.5549 2.015 h = 0.001 0.001 y2[1] (numeric) = -1.01103074767 -3.13097531169 y2[1] (closed_form) = -1.01103074767 -3.13097531169 absolute error = 2.408e-14 relative error = 7.320e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.24429140587 -1.94078978559 y1[1] (closed_form) = 4.24429140587 -1.94078978559 absolute error = 2.102e-14 relative error = 4.505e-13 % Correct digits = 14 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 x[1] = 0.5559 2.016 h = 0.0001 0.004 y2[1] (numeric) = -1.01621896027 -3.13227680055 y2[1] (closed_form) = -1.01621896027 -3.13227680055 absolute error = 2.408e-14 relative error = 7.313e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.24540940793 -1.94593503632 y1[1] (closed_form) = 4.24540940793 -1.94593503632 absolute error = 2.102e-14 relative error = 4.502e-13 % Correct digits = 14 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=18454.0MB, alloc=44.3MB, time=240.54 x[1] = 0.556 2.02 h = 0.003 0.006 y2[1] (numeric) = -1.02434463728 -3.14508811377 y2[1] (closed_form) = -1.02434463728 -3.14508811377 absolute error = 2.402e-14 relative error = 7.262e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.25776209368 -1.95433001975 y1[1] (closed_form) = 4.25776209368 -1.95433001975 absolute error = 2.102e-14 relative error = 4.488e-13 % Correct digits = 14 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=18501.9MB, alloc=44.3MB, time=241.17 x[1] = 0.559 2.026 h = 0.0001 0.005 y2[1] (numeric) = -1.04592802297 -3.1587776491 y2[1] (closed_form) = -1.04592802297 -3.1587776491 absolute error = 2.402e-14 relative error = 7.219e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.27056831816 -1.97599654921 y1[1] (closed_form) = 4.27056831816 -1.97599654921 absolute error = 2.102e-14 relative error = 4.468e-13 % Correct digits = 14 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=18549.8MB, alloc=44.3MB, time=241.80 x[1] = 0.5591 2.031 h = 0.0001 0.003 y2[1] (numeric) = -1.05616225107 -3.17497140266 y2[1] (closed_form) = -1.05616225107 -3.17497140266 absolute error = 2.502e-14 relative error = 7.478e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.28619755461 -1.98656843903 y1[1] (closed_form) = 4.28619755461 -1.98656843903 absolute error = 2.102e-14 relative error = 4.450e-13 % Correct digits = 14 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 x[1] = 0.5592 2.034 h = 0.001 0.001 y2[1] (numeric) = -1.06246078148 -3.18464500699 y2[1] (closed_form) = -1.06246078148 -3.18464500699 absolute error = 2.502e-14 relative error = 7.453e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.2955310414 -1.99306434906 y1[1] (closed_form) = 4.2955310414 -1.99306434906 absolute error = 2.202e-14 relative error = 4.651e-13 % Correct digits = 14 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=18597.6MB, alloc=44.3MB, time=242.42 x[1] = 0.5602 2.035 h = 0.001 0.003 y2[1] (numeric) = -1.06775256195 -3.18594540945 y2[1] (closed_form) = -1.06775256195 -3.18594540945 absolute error = 2.402e-14 relative error = 7.149e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.29665123082 -1.99831475075 y1[1] (closed_form) = 4.29665123082 -1.99831475075 absolute error = 2.202e-14 relative error = 4.648e-13 % Correct digits = 14 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=18645.4MB, alloc=44.3MB, time=243.04 x[1] = 0.5612 2.038 h = 0.0001 0.004 y2[1] (numeric) = -1.07706200658 -3.19384359015 y2[1] (closed_form) = -1.07706200658 -3.19384359015 absolute error = 2.408e-14 relative error = 7.145e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.30414850674 -2.00772185709 y1[1] (closed_form) = 4.30414850674 -2.00772185709 absolute error = 2.2e-14 relative error = 4.632e-13 % Correct digits = 14 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=18693.3MB, alloc=44.3MB, time=243.66 x[1] = 0.5613 2.042 h = 0.003 0.006 y2[1] (numeric) = -1.08544121655 -3.20688414955 y2[1] (closed_form) = -1.08544121655 -3.20688414955 absolute error = 2.508e-14 relative error = 7.408e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.31674182085 -2.01636688756 y1[1] (closed_form) = 4.31674182085 -2.01636688756 absolute error = 2.2e-14 relative error = 4.618e-13 % Correct digits = 14 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 x[1] = 0.5643 2.048 h = 0.0001 0.005 y2[1] (numeric) = -1.10757570324 -3.2207411846 y2[1] (closed_form) = -1.10757570324 -3.2207411846 absolute error = 2.408e-14 relative error = 7.071e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.3297352089 -2.03858728735 y1[1] (closed_form) = 4.3297352089 -2.03858728735 absolute error = 2.202e-14 relative error = 4.602e-13 % Correct digits = 14 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=18741.0MB, alloc=44.3MB, time=244.28 x[1] = 0.5644 2.053 h = 0.0001 0.003 y2[1] (numeric) = -1.11812960437 -3.2372252581 y2[1] (closed_form) = -1.11812960437 -3.2372252581 absolute error = 2.408e-14 relative error = 7.032e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.34566880747 -2.04947442494 y1[1] (closed_form) = 4.34566880747 -2.04947442494 absolute error = 2.302e-14 relative error = 4.791e-13 % Correct digits = 14 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=18788.8MB, alloc=44.3MB, time=244.91 x[1] = 0.5645 2.056 h = 0.001 0.001 y2[1] (numeric) = -1.12462309739 -3.24707124707 y2[1] (closed_form) = -1.12462309739 -3.24707124707 absolute error = 2.508e-14 relative error = 7.298e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.3551831078 -2.05616276333 y1[1] (closed_form) = 4.3551831078 -2.05616276333 absolute error = 2.302e-14 relative error = 4.780e-13 % Correct digits = 14 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=18836.8MB, alloc=44.3MB, time=245.53 x[1] = 0.5655 2.057 h = 0.001 0.003 y2[1] (numeric) = -1.13003769077 -3.24836814098 y2[1] (closed_form) = -1.13003769077 -3.24836814098 absolute error = 2.408e-14 relative error = 7.002e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.35630349799 -2.06153781323 y1[1] (closed_form) = 4.35630349799 -2.06153781323 absolute error = 2.402e-14 relative error = 4.984e-13 % Correct digits = 14 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 x[1] = 0.5665 2.06 h = 0.0001 0.004 y2[1] (numeric) = -1.13959689371 -3.25638211815 y2[1] (closed_form) = -1.13959689371 -3.25638211815 absolute error = 2.408e-14 relative error = 6.981e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.36392580584 -2.07119462999 y1[1] (closed_form) = 4.36392580584 -2.07119462999 absolute error = 2.302e-14 relative error = 4.766e-13 % Correct digits = 14 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=18884.5MB, alloc=44.3MB, time=246.15 x[1] = 0.5666 2.064 h = 0.003 0.006 y2[1] (numeric) = -1.1482364982 -3.26965591504 y2[1] (closed_form) = -1.1482364982 -3.26965591504 absolute error = 2.408e-14 relative error = 6.950e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.37676347372 -2.08009658595 y1[1] (closed_form) = 4.37676347372 -2.08009658595 absolute error = 2.402e-14 relative error = 4.957e-13 % Correct digits = 14 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=18932.4MB, alloc=44.3MB, time=246.78 x[1] = 0.5696 2.07 h = 0.0001 0.005 y2[1] (numeric) = -1.17093540923 -3.2836816054 y2[1] (closed_form) = -1.17093540923 -3.2836816054 absolute error = 2.408e-14 relative error = 6.908e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.38994476712 -2.10288401714 y1[1] (closed_form) = 4.38994476712 -2.10288401714 absolute error = 2.408e-14 relative error = 4.948e-13 % Correct digits = 14 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=18980.2MB, alloc=44.3MB, time=247.40 x[1] = 0.5697 2.075 h = 0.0001 0.003 y2[1] (numeric) = -1.18181763952 -3.30046105296 y2[1] (closed_form) = -1.18181763952 -3.30046105296 absolute error = 2.508e-14 relative error = 7.154e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.40618745323 -2.1140950822 y1[1] (closed_form) = 4.40618745323 -2.1140950822 absolute error = 2.408e-14 relative error = 4.928e-13 % Correct digits = 14 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 x[1] = 0.5698 2.078 h = 0.001 0.001 y2[1] (numeric) = -1.18851135195 -3.31048240117 y2[1] (closed_form) = -1.18851135195 -3.31048240117 absolute error = 2.502e-14 relative error = 7.113e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.41588534504 -2.12098111721 y1[1] (closed_form) = 4.41588534504 -2.12098111721 absolute error = 2.408e-14 relative error = 4.916e-13 % Correct digits = 14 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=19028.1MB, alloc=44.3MB, time=248.02 x[1] = 0.5708 2.079 h = 0.001 0.003 y2[1] (numeric) = -1.19405152932 -3.31177511504 y2[1] (closed_form) = -1.19405152932 -3.31177511504 absolute error = 2.402e-14 relative error = 6.823e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.41700519327 -2.12648352722 y1[1] (closed_form) = 4.41700519327 -2.12648352722 absolute error = 2.408e-14 relative error = 4.913e-13 % Correct digits = 14 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=19075.9MB, alloc=44.3MB, time=248.64 x[1] = 0.5718 2.082 h = 0.0001 0.004 y2[1] (numeric) = -1.20386671783 -3.31990631307 y2[1] (closed_form) = -1.20386671783 -3.31990631307 absolute error = 2.408e-14 relative error = 6.820e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.42475375608 -2.13639623483 y1[1] (closed_form) = 4.42475375608 -2.13639623483 absolute error = 2.518e-14 relative error = 5.125e-13 % Correct digits = 14 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 x[1] = 0.5719 2.086 h = 0.003 0.006 y2[1] (numeric) = -1.21277375154 -3.33341738436 y2[1] (closed_form) = -1.21277375154 -3.33341738436 absolute error = 2.408e-14 relative error = 6.789e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.43783955463 -2.14556216886 y1[1] (closed_form) = 4.43783955463 -2.14556216886 absolute error = 2.518e-14 relative error = 5.108e-13 % Correct digits = 14 memory used=19124.0MB, alloc=44.3MB, time=249.27 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 x[1] = 0.5749 2.092 h = 0.0001 0.005 y2[1] (numeric) = -1.23605070687 -3.34761283087 y2[1] (closed_form) = -1.23605070687 -3.34761283087 absolute error = 2.402e-14 relative error = 6.731e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.45120944861 -2.16893009487 y1[1] (closed_form) = 4.45120944861 -2.16893009487 absolute error = 2.617e-14 relative error = 5.286e-13 % Correct digits = 14 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=19171.6MB, alloc=44.3MB, time=249.89 x[1] = 0.575 2.097 h = 0.0001 0.003 y2[1] (numeric) = -1.24727014106 -3.36469276468 y2[1] (closed_form) = -1.24727014106 -3.36469276468 absolute error = 2.309e-14 relative error = 6.434e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.46776601303 -2.18047398685 y1[1] (closed_form) = 4.46776601303 -2.18047398685 absolute error = 2.518e-14 relative error = 5.065e-13 % Correct digits = 14 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=19219.5MB, alloc=44.3MB, time=250.51 x[1] = 0.5751 2.1 h = 0.001 0.001 y2[1] (numeric) = -1.25416946186 -3.37489248002 y2[1] (closed_form) = -1.25416946186 -3.37489248002 absolute error = 2.309e-14 relative error = 6.412e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.47765031187 -2.18756311972 y1[1] (closed_form) = 4.47765031187 -2.18756311972 absolute error = 2.631e-14 relative error = 5.279e-13 % Correct digits = 14 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 x[1] = 0.5761 2.101 h = 0.001 0.003 y2[1] (numeric) = -1.25983805061 -3.37618031115 y2[1] (closed_form) = -1.25983805061 -3.37618031115 absolute error = 2.309e-14 relative error = 6.407e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.47876884545 -2.19319565968 y1[1] (closed_form) = 4.47876884545 -2.19319565968 absolute error = 2.631e-14 relative error = 5.275e-13 % Correct digits = 14 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=19267.3MB, alloc=44.3MB, time=251.13 x[1] = 0.5771 2.104 h = 0.0001 0.004 y2[1] (numeric) = -1.269915596 -3.38443014816 y2[1] (closed_form) = -1.269915596 -3.38443014816 absolute error = 2.319e-14 relative error = 6.417e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.48664488415 -2.20337058466 y1[1] (closed_form) = 4.48664488415 -2.20337058466 absolute error = 2.631e-14 relative error = 5.263e-13 % Correct digits = 14 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=19315.1MB, alloc=44.3MB, time=251.75 x[1] = 0.5772 2.108 h = 0.003 0.006 y2[1] (numeric) = -1.27909727085 -3.39818257659 y2[1] (closed_form) = -1.27909727085 -3.39818257659 absolute error = 2.319e-14 relative error = 6.388e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.49998264181 -2.21280772757 y1[1] (closed_form) = 4.49998264181 -2.21280772757 absolute error = 2.648e-14 relative error = 5.280e-13 % Correct digits = 14 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=19363.1MB, alloc=44.3MB, time=252.38 x[1] = 0.5802 2.114 h = 0.0001 0.005 y2[1] (numeric) = -1.30296619363 -3.41254882267 y2[1] (closed_form) = -1.30296619363 -3.41254882267 absolute error = 2.319e-14 relative error = 6.350e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.51354178219 -2.23676992047 y1[1] (closed_form) = 4.51354178219 -2.23676992047 absolute error = 2.648e-14 relative error = 5.256e-13 % Correct digits = 14 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 x[1] = 0.5803 2.119 h = 0.0001 0.003 y2[1] (numeric) = -1.31453193025 -3.4299344133 y2[1] (closed_form) = -1.31453193025 -3.4299344133 absolute error = 2.319e-14 relative error = 6.315e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.53041708123 -2.24865576378 y1[1] (closed_form) = 4.53041708123 -2.24865576378 absolute error = 2.648e-14 relative error = 5.235e-13 % Correct digits = 14 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=19410.8MB, alloc=44.3MB, time=253.00 x[1] = 0.5804 2.122 h = 0.001 0.001 y2[1] (numeric) = -1.32164238373 -3.440315537 y2[1] (closed_form) = -1.32164238373 -3.440315537 absolute error = 2.408e-14 relative error = 6.535e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.54049064025 -2.25595353178 y1[1] (closed_form) = 4.54049064025 -2.25595353178 absolute error = 2.746e-14 relative error = 5.416e-13 % Correct digits = 14 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=19458.8MB, alloc=44.3MB, time=253.62 x[1] = 0.5814 2.123 h = 0.0001 0.004 y2[1] (numeric) = -1.32744226864 -3.44159775053 y2[1] (closed_form) = -1.32744226864 -3.44159775053 absolute error = 2.309e-14 relative error = 6.259e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.54160705553 -2.26171903056 y1[1] (closed_form) = 4.54160705553 -2.26171903056 absolute error = 2.648e-14 relative error = 5.218e-13 % Correct digits = 14 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=19506.8MB, alloc=44.3MB, time=254.25 x[1] = 0.5815 2.127 h = 0.003 0.006 y2[1] (numeric) = -1.33686331695 -3.45556462738 y2[1] (closed_form) = -1.33686331695 -3.45556462738 absolute error = 2.408e-14 relative error = 6.500e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.55516814758 -2.27139248606 y1[1] (closed_form) = 4.55516814758 -2.27139248606 absolute error = 2.746e-14 relative error = 5.395e-13 % Correct digits = 14 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 x[1] = 0.5845 2.133 h = 0.0001 0.005 y2[1] (numeric) = -1.36125112078 -3.47008596468 y2[1] (closed_form) = -1.36125112078 -3.47008596468 absolute error = 2.408e-14 relative error = 6.461e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.56889797026 -2.29587520898 y1[1] (closed_form) = 4.56889797026 -2.29587520898 absolute error = 2.746e-14 relative error = 5.370e-13 % Correct digits = 14 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=19554.4MB, alloc=44.3MB, time=254.87 x[1] = 0.5846 2.138 h = 0.0001 0.003 y2[1] (numeric) = -1.3731186778 -3.48774311659 y2[1] (closed_form) = -1.3731186778 -3.48774311659 absolute error = 2.408e-14 relative error = 6.425e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.58605578976 -2.30805899813 y1[1] (closed_form) = 4.58605578976 -2.30805899813 absolute error = 2.746e-14 relative error = 5.348e-13 % Correct digits = 14 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=19602.3MB, alloc=44.3MB, time=255.49 x[1] = 0.5847 2.141 h = 0.001 0.001 y2[1] (numeric) = -1.38041318584 -3.49828545858 y2[1] (closed_form) = -1.38041318584 -3.49828545858 absolute error = 2.419e-14 relative error = 6.431e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.59629714873 -2.31553859124 y1[1] (closed_form) = 4.59629714873 -2.31553859124 absolute error = 2.746e-14 relative error = 5.335e-13 % Correct digits = 14 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=19650.3MB, alloc=44.3MB, time=256.12 x[1] = 0.5857 2.142 h = 0.001 0.003 y2[1] (numeric) = -1.38632852029 -3.49956383476 y2[1] (closed_form) = -1.38632852029 -3.49956383476 absolute error = 2.419e-14 relative error = 6.426e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.5974127035 -2.32142088655 y1[1] (closed_form) = 4.5974127035 -2.32142088655 absolute error = 2.729e-14 relative error = 5.300e-13 % Correct digits = 14 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 x[1] = 0.5867 2.145 h = 0.0001 0.004 y2[1] (numeric) = -1.39691026223 -3.50804149198 y2[1] (closed_form) = -1.39691026223 -3.50804149198 absolute error = 2.518e-14 relative error = 6.668e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.60553249203 -2.33209953621 y1[1] (closed_form) = 4.60553249203 -2.33209953621 absolute error = 2.746e-14 relative error = 5.319e-13 % Correct digits = 14 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=19697.9MB, alloc=44.3MB, time=256.74 x[1] = 0.5868 2.149 h = 0.003 0.006 y2[1] (numeric) = -1.40661980788 -3.52225753658 y2[1] (closed_form) = -1.40661980788 -3.52225753658 absolute error = 2.518e-14 relative error = 6.639e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.61935289583 -2.34205809711 y1[1] (closed_form) = 4.61935289583 -2.34205809711 absolute error = 2.746e-14 relative error = 5.302e-13 % Correct digits = 14 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=19745.7MB, alloc=44.3MB, time=257.36 x[1] = 0.5898 2.155 h = 0.0001 0.005 y2[1] (numeric) = -1.43162630562 -3.53695162734 y2[1] (closed_form) = -1.43162630562 -3.53695162734 absolute error = 2.518e-14 relative error = 6.599e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.63327319814 -2.36716155095 y1[1] (closed_form) = 4.63327319814 -2.36716155095 absolute error = 2.746e-14 relative error = 5.278e-13 % Correct digits = 14 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=19793.6MB, alloc=44.3MB, time=257.98 x[1] = 0.5899 2.16 h = 0.0001 0.003 y2[1] (numeric) = -1.44385764621 -3.55492432831 y2[1] (closed_form) = -1.44385764621 -3.55492432831 absolute error = 2.518e-14 relative error = 6.562e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.65075907846 -2.37970482705 y1[1] (closed_form) = 4.65075907846 -2.37970482705 absolute error = 2.844e-14 relative error = 5.444e-13 % Correct digits = 14 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 x[1] = 0.59 2.163 h = 0.001 0.001 y2[1] (numeric) = -1.45137390054 -3.5656538966 y2[1] (closed_form) = -1.45137390054 -3.5656538966 absolute error = 2.508e-14 relative error = 6.515e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.66119517679 -2.38740369699 y1[1] (closed_form) = 4.66119517679 -2.38740369699 absolute error = 2.844e-14 relative error = 5.431e-13 % Correct digits = 14 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=19841.4MB, alloc=44.3MB, time=258.61 x[1] = 0.591 2.164 h = 0.001 0.003 y2[1] (numeric) = -1.45742606549 -3.56692523469 y2[1] (closed_form) = -1.45742606549 -3.56692523469 absolute error = 2.508e-14 relative error = 6.509e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.66230706737 -2.39342438636 y1[1] (closed_form) = 4.66230706737 -2.39342438636 absolute error = 2.844e-14 relative error = 5.427e-13 % Correct digits = 14 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=19889.4MB, alloc=44.3MB, time=259.23 x[1] = 0.592 2.167 h = 0.0001 0.004 y2[1] (numeric) = -1.46828919926 -3.57552562754 y2[1] (closed_form) = -1.46828919926 -3.57552562754 absolute error = 2.508e-14 relative error = 6.489e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.67055788601 -2.40438417325 y1[1] (closed_form) = 4.67055788601 -2.40438417325 absolute error = 2.828e-14 relative error = 5.384e-13 % Correct digits = 14 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=19937.3MB, alloc=44.3MB, time=259.86 x[1] = 0.5921 2.171 h = 0.003 0.006 y2[1] (numeric) = -1.47829498449 -3.58999505687 y2[1] (closed_form) = -1.47829498449 -3.58999505687 absolute error = 2.508e-14 relative error = 6.460e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.68464158009 -2.41463560306 y1[1] (closed_form) = 4.68464158009 -2.41463560306 absolute error = 2.844e-14 relative error = 5.397e-13 % Correct digits = 14 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 x[1] = 0.5951 2.177 h = 0.0001 0.005 y2[1] (numeric) = -1.5039350041 -3.60486276852 y2[1] (closed_form) = -1.5039350041 -3.60486276852 absolute error = 2.508e-14 relative error = 6.421e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.69875285405 -2.44037447951 y1[1] (closed_form) = 4.69875285405 -2.44037447951 absolute error = 2.844e-14 relative error = 5.372e-13 % Correct digits = 14 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=19985.0MB, alloc=44.3MB, time=260.48 x[1] = 0.5952 2.182 h = 0.0001 0.003 y2[1] (numeric) = -1.51653989636 -3.62315636013 y2[1] (closed_form) = -1.51653989636 -3.62315636013 absolute error = 2.518e-14 relative error = 6.411e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.7165718421 -2.45328703935 y1[1] (closed_form) = 4.7165718421 -2.45328703935 absolute error = 2.844e-14 relative error = 5.350e-13 % Correct digits = 14 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=20032.9MB, alloc=44.3MB, time=261.10 x[1] = 0.5953 2.185 h = 0.001 0.001 y2[1] (numeric) = -1.52428382614 -3.63407629366 y2[1] (closed_form) = -1.52428382614 -3.63407629366 absolute error = 2.617e-14 relative error = 6.641e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.72720564232 -2.46121113009 y1[1] (closed_form) = 4.72720564232 -2.46121113009 absolute error = 2.844e-14 relative error = 5.337e-13 % Correct digits = 14 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 x[1] = 0.5963 2.186 h = 0.001 0.003 y2[1] (numeric) = -1.53047587741 -3.63533976182 y2[1] (closed_form) = -1.53047587741 -3.63533976182 absolute error = 2.518e-14 relative error = 6.384e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.72831297152 -2.46737321779 y1[1] (closed_form) = 4.72831297152 -2.46737321779 absolute error = 2.844e-14 relative error = 5.333e-13 % Correct digits = 14 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=20080.8MB, alloc=44.3MB, time=261.72 x[1] = 0.5973 2.189 h = 0.0001 0.004 y2[1] (numeric) = -1.54162736153 -3.64406427794 y2[1] (closed_form) = -1.54162736153 -3.64406427794 absolute error = 2.518e-14 relative error = 6.364e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.736696026 -2.47862106298 y1[1] (closed_form) = 4.736696026 -2.47862106298 absolute error = 2.844e-14 relative error = 5.320e-13 % Correct digits = 14 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=20128.6MB, alloc=44.3MB, time=262.34 x[1] = 0.5974 2.193 h = 0.003 0.006 y2[1] (numeric) = -1.55193732273 -3.65879135542 y2[1] (closed_form) = -1.55193732273 -3.65879135542 absolute error = 2.617e-14 relative error = 6.585e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.75104704061 -2.48917332011 y1[1] (closed_form) = 4.75104704061 -2.48917332011 absolute error = 2.844e-14 relative error = 5.303e-13 % Correct digits = 14 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=20176.5MB, alloc=44.3MB, time=262.97 x[1] = 0.6004 2.199 h = 0.0001 0.005 y2[1] (numeric) = -1.57822602149 -3.67383348676 y2[1] (closed_form) = -1.57822602149 -3.67383348676 absolute error = 2.617e-14 relative error = 6.546e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.76534971711 -2.51556264512 y1[1] (closed_form) = 4.76534971711 -2.51556264512 absolute error = 2.844e-14 relative error = 5.278e-13 % Correct digits = 14 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 x[1] = 0.6005 2.204 h = 0.0001 0.003 y2[1] (numeric) = -1.59121447866 -3.69245336982 y2[1] (closed_form) = -1.59121447866 -3.69245336982 absolute error = 2.617e-14 relative error = 6.509e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.78350692552 -2.52885453152 y1[1] (closed_form) = 4.78350692552 -2.52885453152 absolute error = 2.927e-14 relative error = 5.410e-13 % Correct digits = 14 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=20224.2MB, alloc=44.3MB, time=263.59 x[1] = 0.6006 2.207 h = 0.001 0.001 y2[1] (numeric) = -1.59919216125 -3.7035668412 y2[1] (closed_form) = -1.59919216125 -3.7035668412 absolute error = 2.617e-14 relative error = 6.488e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.7943414278 -2.53700993584 y1[1] (closed_form) = 4.7943414278 -2.53700993584 absolute error = 2.927e-14 relative error = 5.397e-13 % Correct digits = 14 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=20272.2MB, alloc=44.3MB, time=264.21 x[1] = 0.6016 2.208 h = 0.001 0.003 y2[1] (numeric) = -1.6055272166 -3.70482157139 y2[1] (closed_form) = -1.6055272166 -3.70482157139 absolute error = 2.617e-14 relative error = 6.482e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.79544326336 -2.54331648955 y1[1] (closed_form) = 4.79544326336 -2.54331648955 absolute error = 2.915e-14 relative error = 5.371e-13 % Correct digits = 14 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=20320.2MB, alloc=44.3MB, time=264.84 x[1] = 0.6026 2.211 h = 0.0001 0.004 y2[1] (numeric) = -1.61697417 -3.71367158775 y2[1] (closed_form) = -1.61697417 -3.71367158775 absolute error = 2.617e-14 relative error = 6.462e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.8039597525 -2.55485947626 y1[1] (closed_form) = 4.8039597525 -2.55485947626 absolute error = 2.915e-14 relative error = 5.358e-13 % Correct digits = 14 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 x[1] = 0.6027 2.215 h = 0.003 0.006 y2[1] (numeric) = -1.62759644233 -3.72866062332 y2[1] (closed_form) = -1.62759644233 -3.72866062332 absolute error = 2.617e-14 relative error = 6.433e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.81858216963 -2.56572071865 y1[1] (closed_form) = 4.81858216963 -2.56572071865 absolute error = 2.927e-14 relative error = 5.363e-13 % Correct digits = 14 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=20368.0MB, alloc=44.3MB, time=265.46 x[1] = 0.6057 2.221 h = 0.0001 0.005 y2[1] (numeric) = -1.65454931394 -3.74387790143 y2[1] (closed_form) = -1.65454931394 -3.74387790143 absolute error = 2.532e-14 relative error = 6.185e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.83307661513 -2.59277585934 y1[1] (closed_form) = 4.83307661513 -2.59277585934 absolute error = 2.915e-14 relative error = 5.316e-13 % Correct digits = 14 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=20415.7MB, alloc=44.3MB, time=266.08 x[1] = 0.6058 2.226 h = 0.0001 0.003 y2[1] (numeric) = -1.66793160025 -3.76282953601 y2[1] (closed_form) = -1.66793160025 -3.76282953601 absolute error = 2.631e-14 relative error = 6.391e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.85157722229 -2.60645736697 y1[1] (closed_form) = 4.85157722229 -2.60645736697 absolute error = 2.915e-14 relative error = 5.294e-13 % Correct digits = 14 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=20463.7MB, alloc=44.3MB, time=266.71 x[1] = 0.6059 2.229 h = 0.001 0.001 y2[1] (numeric) = -1.67614926471 -3.77413975159 y2[1] (closed_form) = -1.67614926471 -3.77413975159 absolute error = 2.532e-14 relative error = 6.131e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.86261546433 -2.61485032989 y1[1] (closed_form) = 4.86261546433 -2.61485032989 absolute error = 2.915e-14 relative error = 5.281e-13 % Correct digits = 14 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 x[1] = 0.6069 2.23 h = 0.0001 0.004 y2[1] (numeric) = -1.68263050506 -3.77538483842 y2[1] (closed_form) = -1.68263050506 -3.77538483842 absolute error = 2.631e-14 relative error = 6.364e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.86371083781 -2.62130448189 y1[1] (closed_form) = 4.86371083781 -2.62130448189 absolute error = 2.915e-14 relative error = 5.277e-13 % Correct digits = 14 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=20511.3MB, alloc=44.3MB, time=267.34 x[1] = 0.607 2.234 h = 0.003 0.006 y2[1] (numeric) = -1.69352508289 -3.79060670154 y2[1] (closed_form) = -1.69352508289 -3.79060670154 absolute error = 2.617e-14 relative error = 6.304e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.87857399405 -2.63243507682 y1[1] (closed_form) = 4.87857399405 -2.63243507682 absolute error = 2.915e-14 relative error = 5.259e-13 % Correct digits = 14 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=20559.2MB, alloc=44.3MB, time=267.96 x[1] = 0.61 2.24 h = 0.0001 0.005 y2[1] (numeric) = -1.72106022476 -3.80598343431 y2[1] (closed_form) = -1.72106022476 -3.80598343431 absolute error = 2.631e-14 relative error = 6.298e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.89324193641 -2.66007361175 y1[1] (closed_form) = 4.89324193641 -2.66007361175 absolute error = 2.915e-14 relative error = 5.235e-13 % Correct digits = 14 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=20607.1MB, alloc=44.3MB, time=268.58 x[1] = 0.6101 2.245 h = 0.0001 0.003 y2[1] (numeric) = -1.73478587995 -3.82522990964 y2[1] (closed_form) = -1.73478587995 -3.82522990964 absolute error = 2.617e-14 relative error = 6.231e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.91204713947 -2.67409475692 y1[1] (closed_form) = 4.91204713947 -2.67409475692 absolute error = 3.015e-14 relative error = 5.391e-13 % Correct digits = 14 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 x[1] = 0.6102 2.248 h = 0.001 0.001 y2[1] (numeric) = -1.74321282313 -3.83671503191 y2[1] (closed_form) = -1.74321282313 -3.83671503191 absolute error = 2.617e-14 relative error = 6.211e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.92326614897 -2.68269484522 y1[1] (closed_form) = 4.92326614897 -2.68269484522 absolute error = 2.907e-14 relative error = 5.185e-13 % Correct digits = 14 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=20654.8MB, alloc=44.3MB, time=269.20 x[1] = 0.6112 2.249 h = 0.001 0.003 y2[1] (numeric) = -1.74982262126 -3.8379528578 y2[1] (closed_form) = -1.74982262126 -3.8379528578 absolute error = 2.617e-14 relative error = 6.205e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.92435696629 -2.6892786967 y1[1] (closed_form) = 4.92435696629 -2.6892786967 absolute error = 2.907e-14 relative error = 5.181e-13 % Correct digits = 14 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=20702.6MB, alloc=44.3MB, time=269.83 x[1] = 0.6122 2.252 h = 0.0001 0.004 y2[1] (numeric) = -1.76183735255 -3.84704375246 y2[1] (closed_form) = -1.76183735255 -3.84704375246 absolute error = 2.617e-14 relative error = 6.185e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 4.93312863143 -2.70138867251 y1[1] (closed_form) = 4.93312863143 -2.70138867251 absolute error = 3.007e-14 relative error = 5.346e-13 % Correct digits = 14 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=20750.7MB, alloc=44.3MB, time=270.45 x[1] = 0.6123 2.256 h = 0.003 0.006 y2[1] (numeric) = -1.77305987175 -3.86253582025 y2[1] (closed_form) = -1.77305987175 -3.86253582025 absolute error = 2.617e-14 relative error = 6.158e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 4.9482710263 -2.71284392966 y1[1] (closed_form) = 4.9482710263 -2.71284392966 absolute error = 3.007e-14 relative error = 5.328e-13 % Correct digits = 14 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 x[1] = 0.6153 2.262 h = 0.0001 0.005 y2[1] (numeric) = -1.80128893047 -3.87808904471 y2[1] (closed_form) = -1.80128893047 -3.87808904471 absolute error = 2.617e-14 relative error = 6.121e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 4.96313142925 -2.74117780503 y1[1] (closed_form) = 4.96313142925 -2.74117780503 absolute error = 3.007e-14 relative error = 5.303e-13 % Correct digits = 14 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=20798.3MB, alloc=44.3MB, time=271.07 x[1] = 0.6154 2.267 h = 0.0001 0.003 y2[1] (numeric) = -1.81542813586 -3.89767771929 y2[1] (closed_form) = -1.81542813586 -3.89767771929 absolute error = 2.729e-14 relative error = 6.348e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 4.98228997162 -2.75560835439 y1[1] (closed_form) = 4.98228997162 -2.75560835439 absolute error = 3.007e-14 relative error = 5.281e-13 % Correct digits = 14 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=20846.3MB, alloc=44.3MB, time=271.70 x[1] = 0.6155 2.27 h = 0.001 0.001 y2[1] (numeric) = -1.82410702873 -3.90936572043 y2[1] (closed_form) = -1.82410702873 -3.90936572043 absolute error = 2.717e-14 relative error = 6.297e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 4.9937185519 -2.76445800211 y1[1] (closed_form) = 4.9937185519 -2.76445800211 absolute error = 3.007e-14 relative error = 5.268e-13 % Correct digits = 14 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 x[1] = 0.6165 2.271 h = 0.001 0.003 y2[1] (numeric) = -1.83086911506 -3.91059215462 y2[1] (closed_form) = -1.83086911506 -3.91059215462 absolute error = 2.729e-14 relative error = 6.321e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 4.99480104389 -2.77119546894 y1[1] (closed_form) = 4.99480104389 -2.77119546894 absolute error = 3.007e-14 relative error = 5.264e-13 % Correct digits = 14 memory used=20894.3MB, alloc=44.3MB, time=272.32 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 x[1] = 0.6175 2.274 h = 0.0001 0.004 y2[1] (numeric) = -1.84320058341 -3.91981251202 y2[1] (closed_form) = -1.84320058341 -3.91981251202 absolute error = 2.717e-14 relative error = 6.272e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.00370961631 -2.78362176308 y1[1] (closed_form) = 5.00370961631 -2.78362176308 absolute error = 3.007e-14 relative error = 5.251e-13 % Correct digits = 14 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=20942.0MB, alloc=44.3MB, time=272.94 x[1] = 0.6176 2.278 h = 0.003 0.006 y2[1] (numeric) = -1.85475977361 -3.93557923036 y2[1] (closed_form) = -1.85475977361 -3.93557923036 absolute error = 2.631e-14 relative error = 6.046e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.01913548201 -2.79541043664 y1[1] (closed_form) = 5.01913548201 -2.79541043664 absolute error = 3.007e-14 relative error = 5.233e-13 % Correct digits = 14 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=20990.0MB, alloc=44.3MB, time=273.56 x[1] = 0.6206 2.284 h = 0.0001 0.005 y2[1] (numeric) = -1.88369924671 -3.95130945406 y2[1] (closed_form) = -1.88369924671 -3.95130945406 absolute error = 2.631e-14 relative error = 6.010e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.0341885128 -2.82445603622 y1[1] (closed_form) = 5.0341885128 -2.82445603622 absolute error = 3.102e-14 relative error = 5.373e-13 % Correct digits = 14 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 x[1] = 0.6207 2.289 h = 0.0001 0.003 y2[1] (numeric) = -1.89826301712 -3.9712459613 y2[1] (closed_form) = -1.89826301712 -3.9712459613 absolute error = 2.631e-14 relative error = 5.976e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.05370576382 -2.83930703709 y1[1] (closed_form) = 5.05370576382 -2.83930703709 absolute error = 3.007e-14 relative error = 5.187e-13 % Correct digits = 14 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=21037.7MB, alloc=44.3MB, time=274.18 x[1] = 0.6208 2.292 h = 0.001 0.001 y2[1] (numeric) = -1.90720054244 -3.98314014607 y2[1] (closed_form) = -1.90720054244 -3.98314014607 absolute error = 2.631e-14 relative error = 5.957e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.06534706154 -2.84841294434 y1[1] (closed_form) = 5.06534706154 -2.84841294434 absolute error = 3.106e-14 relative error = 5.346e-13 % Correct digits = 14 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=21085.7MB, alloc=44.3MB, time=274.80 x[1] = 0.6218 2.293 h = 0.001 0.003 y2[1] (numeric) = -1.914118286 -3.98435417068 y2[1] (closed_form) = -1.914118286 -3.98435417068 absolute error = 2.631e-14 relative error = 5.951e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.06642015043 -2.85530735073 y1[1] (closed_form) = 5.06642015043 -2.85530735073 absolute error = 3.106e-14 relative error = 5.342e-13 % Correct digits = 14 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=21133.5MB, alloc=44.3MB, time=275.43 x[1] = 0.6228 2.296 h = 0.0001 0.004 y2[1] (numeric) = -1.92677426394 -3.99370531867 y2[1] (closed_form) = -1.92677426394 -3.99370531867 absolute error = 2.631e-14 relative error = 5.932e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.07546679373 -2.86805770628 y1[1] (closed_form) = 5.07546679373 -2.86805770628 absolute error = 3.102e-14 relative error = 5.320e-13 % Correct digits = 14 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 x[1] = 0.6229 2.3 h = 0.003 0.006 y2[1] (numeric) = -1.93867907232 -4.00975118017 y2[1] (closed_form) = -1.93867907232 -4.00975118017 absolute error = 2.631e-14 relative error = 5.906e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.09118041393 -2.88018876856 y1[1] (closed_form) = 5.09118041393 -2.88018876856 absolute error = 3.007e-14 relative error = 5.140e-13 % Correct digits = 14 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=21181.3MB, alloc=44.3MB, time=276.05 x[1] = 0.6259 2.306 h = 0.0001 0.005 y2[1] (numeric) = -1.96834582255 -4.02565882568 y2[1] (closed_form) = -1.96834582255 -4.02565882568 absolute error = 2.729e-14 relative error = 6.091e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.10642616163 -2.90996284553 y1[1] (closed_form) = 5.10642616163 -2.90996284553 absolute error = 3.002e-14 relative error = 5.107e-13 % Correct digits = 14 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=21229.1MB, alloc=44.3MB, time=276.67 x[1] = 0.626 2.311 h = 0.0001 0.003 y2[1] (numeric) = -1.98334544747 -4.04594885855 y2[1] (closed_form) = -1.98334544747 -4.04594885855 absolute error = 2.729e-14 relative error = 6.058e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.12630755614 -2.9252456206 y1[1] (closed_form) = 5.12630755614 -2.9252456206 absolute error = 3.102e-14 relative error = 5.255e-13 % Correct digits = 14 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=21277.0MB, alloc=44.3MB, time=277.30 x[1] = 0.6261 2.314 h = 0.001 0.001 y2[1] (numeric) = -1.992548454 -4.0580525654 y2[1] (closed_form) = -1.992548454 -4.0580525654 absolute error = 2.717e-14 relative error = 6.009e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.13816475517 -2.93461465391 y1[1] (closed_form) = 5.13816475517 -2.93461465391 absolute error = 3.102e-14 relative error = 5.242e-13 % Correct digits = 14 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 x[1] = 0.6271 2.315 h = 0.001 0.003 y2[1] (numeric) = -1.99962529186 -4.05925312059 y2[1] (closed_form) = -1.99962529186 -4.05925312059 absolute error = 2.729e-14 relative error = 6.032e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.13922732232 -2.94166939345 y1[1] (closed_form) = 5.13922732232 -2.94166939345 absolute error = 3.102e-14 relative error = 5.238e-13 % Correct digits = 14 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=21324.7MB, alloc=44.3MB, time=277.92 x[1] = 0.6281 2.318 h = 0.0001 0.004 y2[1] (numeric) = -2.01261373041 -4.06873637096 y2[1] (closed_form) = -2.01261373041 -4.06873637096 absolute error = 2.828e-14 relative error = 6.231e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.14841318746 -2.95475173342 y1[1] (closed_form) = 5.14841318746 -2.95475173342 absolute error = 3.102e-14 relative error = 5.225e-13 % Correct digits = 14 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=21372.6MB, alloc=44.3MB, time=278.54 x[1] = 0.6282 2.322 h = 0.003 0.006 y2[1] (numeric) = -2.02487332681 -4.08506591489 y2[1] (closed_form) = -2.02487332681 -4.08506591489 absolute error = 2.844e-14 relative error = 6.238e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.16441889718 -2.96723437995 y1[1] (closed_form) = 5.16441889718 -2.96723437995 absolute error = 3.102e-14 relative error = 5.207e-13 % Correct digits = 14 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=21420.5MB, alloc=44.3MB, time=279.16 x[1] = 0.6312 2.328 h = 0.0001 0.005 y2[1] (numeric) = -2.05528458987 -4.10115131606 y2[1] (closed_form) = -2.05528458987 -4.10115131606 absolute error = 2.828e-14 relative error = 6.166e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.17985736882 -2.99775406456 y1[1] (closed_form) = 5.17985736882 -2.99775406456 absolute error = 3.102e-14 relative error = 5.183e-13 % Correct digits = 14 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 x[1] = 0.6313 2.333 h = 0.0001 0.003 y2[1] (numeric) = -2.07073163997 -4.12180062707 y2[1] (closed_form) = -2.07073163997 -4.12180062707 absolute error = 2.943e-14 relative error = 6.380e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.20010840701 -3.01348021829 y1[1] (closed_form) = 5.20010840701 -3.01348021829 absolute error = 3.202e-14 relative error = 5.327e-13 % Correct digits = 14 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=21468.2MB, alloc=44.3MB, time=279.78 x[1] = 0.6314 2.336 h = 0.001 0.001 y2[1] (numeric) = -2.08020714636 -4.13411722804 y2[1] (closed_form) = -2.08020714636 -4.13411722804 absolute error = 2.943e-14 relative error = 6.359e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.21218472829 -3.02311941454 y1[1] (closed_form) = 5.21218472829 -3.02311941454 absolute error = 3.106e-14 relative error = 5.156e-13 % Correct digits = 14 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=21516.2MB, alloc=44.3MB, time=280.41 x[1] = 0.6324 2.337 h = 0.0001 0.004 y2[1] (numeric) = -2.08744658502 -4.13530321073 y2[1] (closed_form) = -2.08744658502 -4.13530321073 absolute error = 2.943e-14 relative error = 6.353e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.21323561284 -3.03033795145 y1[1] (closed_form) = 5.21323561284 -3.03033795145 absolute error = 3.206e-14 relative error = 5.317e-13 % Correct digits = 14 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=21564.2MB, alloc=44.3MB, time=281.03 x[1] = 0.6325 2.341 h = 0.003 0.006 y2[1] (numeric) = -2.10001563431 -4.15188498863 y2[1] (closed_form) = -2.10001563431 -4.15188498863 absolute error = 2.943e-14 relative error = 6.325e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.22950059531 -3.04312721717 y1[1] (closed_form) = 5.22950059531 -3.04312721717 absolute error = 3.202e-14 relative error = 5.291e-13 % Correct digits = 14 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 x[1] = 0.6355 2.347 h = 0.0001 0.005 y2[1] (numeric) = -2.13107972055 -4.1681327478 y2[1] (closed_form) = -2.13107972055 -4.1681327478 absolute error = 3.041e-14 relative error = 6.497e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.24511406388 -3.07430041286 y1[1] (closed_form) = 5.24511406388 -3.07430041286 absolute error = 3.302e-14 relative error = 5.430e-13 % Correct digits = 14 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=21611.9MB, alloc=44.3MB, time=281.65 x[1] = 0.6356 2.352 h = 0.0001 0.003 y2[1] (numeric) = -2.1469170103 -4.18910148795 y2[1] (closed_form) = -2.1469170103 -4.18910148795 absolute error = 3.059e-14 relative error = 6.499e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.26569320812 -3.09041323113 y1[1] (closed_form) = 5.26569320812 -3.09041323113 absolute error = 3.302e-14 relative error = 5.407e-13 % Correct digits = 14 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=21659.7MB, alloc=44.3MB, time=282.28 x[1] = 0.6357 2.355 h = 0.001 0.001 y2[1] (numeric) = -2.15663023723 -4.20160742994 y2[1] (closed_form) = -2.15663023723 -4.20160742994 absolute error = 2.961e-14 relative error = 6.271e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.27796408543 -3.10028807943 y1[1] (closed_form) = 5.27796408543 -3.10028807943 absolute error = 3.302e-14 relative error = 5.394e-13 % Correct digits = 14 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=21707.6MB, alloc=44.3MB, time=282.90 x[1] = 0.6367 2.356 h = 0.001 0.003 y2[1] (numeric) = -2.16401269139 -4.20278194686 y2[1] (closed_form) = -2.16401269139 -4.20278194686 absolute error = 2.961e-14 relative error = 6.265e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.27900595988 -3.10765059541 y1[1] (closed_form) = 5.27900595988 -3.10765059541 absolute error = 3.401e-14 relative error = 5.553e-13 % Correct digits = 14 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 x[1] = 0.6377 2.359 h = 0.0001 0.004 y2[1] (numeric) = -2.17763994142 -4.21251863259 y2[1] (closed_form) = -2.17763994142 -4.21251863259 absolute error = 2.961e-14 relative error = 6.245e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.28845808499 -3.12137071078 y1[1] (closed_form) = 5.28845808499 -3.12137071078 absolute error = 3.401e-14 relative error = 5.539e-13 % Correct digits = 14 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=21755.3MB, alloc=44.3MB, time=283.52 x[1] = 0.6378 2.363 h = 0.003 0.006 y2[1] (numeric) = -2.19058139701 -4.2293927791 y2[1] (closed_form) = -2.19058139701 -4.2293927791 absolute error = 2.961e-14 relative error = 6.218e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.30502347555 -3.13452923039 y1[1] (closed_form) = 5.30502347555 -3.13452923039 absolute error = 3.401e-14 relative error = 5.520e-13 % Correct digits = 14 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=21803.2MB, alloc=44.3MB, time=284.14 x[1] = 0.6408 2.369 h = 0.0001 0.005 y2[1] (numeric) = -2.22242308632 -4.24581888182 y2[1] (closed_form) = -2.22242308632 -4.24581888182 absolute error = 2.983e-14 relative error = 6.225e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.3208296641 -3.16648094202 y1[1] (closed_form) = 5.3208296641 -3.16648094202 absolute error = 3.4e-14 relative error = 5.491e-13 % Correct digits = 14 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 x[1] = 0.6409 2.374 h = 0.0001 0.003 y2[1] (numeric) = -2.23873003246 -4.2671579084 y2[1] (closed_form) = -2.23873003246 -4.2671579084 absolute error = 3.059e-14 relative error = 6.349e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.34178900616 -3.18305943739 y1[1] (closed_form) = 5.34178900616 -3.18305943739 absolute error = 3.401e-14 relative error = 5.470e-13 % Correct digits = 14 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=21851.0MB, alloc=44.3MB, time=284.76 x[1] = 0.641 2.377 h = 0.001 0.001 y2[1] (numeric) = -2.24872924415 -4.27988319678 y2[1] (closed_form) = -2.24872924415 -4.27988319678 absolute error = 3.059e-14 relative error = 6.328e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.354285186 -3.19321797012 y1[1] (closed_form) = 5.354285186 -3.19321797012 absolute error = 3.401e-14 relative error = 5.456e-13 % Correct digits = 14 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=21898.9MB, alloc=44.3MB, time=285.39 x[1] = 0.642 2.378 h = 0.001 0.003 y2[1] (numeric) = -2.25628102758 -4.28104101275 y2[1] (closed_form) = -2.25628102758 -4.28104101275 absolute error = 3.081e-14 relative error = 6.366e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.35531314422 -3.20075093719 y1[1] (closed_form) = 5.35531314422 -3.20075093719 absolute error = 3.401e-14 relative error = 5.452e-13 % Correct digits = 14 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=21946.8MB, alloc=44.3MB, time=286.01 x[1] = 0.643 2.381 h = 0.0001 0.004 y2[1] (numeric) = -2.27026449028 -4.29091355576 y2[1] (closed_form) = -2.27026449028 -4.29091355576 absolute error = 3.178e-14 relative error = 6.547e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.36490780396 -3.21482671857 y1[1] (closed_form) = 5.36490780396 -3.21482671857 absolute error = 3.501e-14 relative error = 5.598e-13 % Correct digits = 14 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 x[1] = 0.6431 2.385 h = 0.003 0.006 y2[1] (numeric) = -2.28358818782 -4.30808474599 y2[1] (closed_form) = -2.28358818782 -4.30808474599 absolute error = 3.081e-14 relative error = 6.318e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.38177808635 -3.22836435468 y1[1] (closed_form) = 5.38177808635 -3.22836435468 absolute error = 3.501e-14 relative error = 5.579e-13 % Correct digits = 14 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=21994.5MB, alloc=44.3MB, time=286.63 x[1] = 0.6461 2.391 h = 0.0001 0.005 y2[1] (numeric) = -2.3162258284 -4.32468925527 y2[1] (closed_form) = -2.3162258284 -4.32468925527 absolute error = 3.178e-14 relative error = 6.478e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.39777674958 -3.26111283605 y1[1] (closed_form) = 5.39777674958 -3.26111283605 absolute error = 3.501e-14 relative error = 5.552e-13 % Correct digits = 14 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=22042.4MB, alloc=44.3MB, time=287.26 x[1] = 0.6462 2.396 h = 0.0001 0.003 y2[1] (numeric) = -2.33301484229 -4.34640449415 y2[1] (closed_form) = -2.33301484229 -4.34640449415 absolute error = 3.178e-14 relative error = 6.442e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.41912197889 -3.27816945511 y1[1] (closed_form) = 5.41912197889 -3.27816945511 absolute error = 3.501e-14 relative error = 5.528e-13 % Correct digits = 14 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=22090.4MB, alloc=44.3MB, time=287.88 x[1] = 0.6463 2.399 h = 0.001 0.001 y2[1] (numeric) = -2.34330756538 -4.35935259868 y2[1] (closed_form) = -2.34330756538 -4.35935259868 absolute error = 3.178e-14 relative error = 6.421e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.43184678939 -3.28861921811 y1[1] (closed_form) = 5.43184678939 -3.28861921811 absolute error = 3.501e-14 relative error = 5.514e-13 % Correct digits = 14 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 x[1] = 0.6473 2.4 h = 0.001 0.003 y2[1] (numeric) = -2.35103239112 -4.36049248037 y2[1] (closed_form) = -2.35103239112 -4.36049248037 absolute error = 3.081e-14 relative error = 6.218e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.43285954324 -3.29632631046 y1[1] (closed_form) = 5.43285954324 -3.29632631046 absolute error = 3.401e-14 relative error = 5.353e-13 % Correct digits = 14 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=22138.1MB, alloc=44.3MB, time=288.50 x[1] = 0.6483 2.403 h = 0.0001 0.004 y2[1] (numeric) = -2.36538074432 -4.37050212057 y2[1] (closed_form) = -2.36538074432 -4.37050212057 absolute error = 3.081e-14 relative error = 6.199e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.4425978293 -3.31076641297 y1[1] (closed_form) = 5.4425978293 -3.31076641297 absolute error = 3.501e-14 relative error = 5.496e-13 % Correct digits = 14 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=22185.9MB, alloc=44.3MB, time=289.13 x[1] = 0.6484 2.407 h = 0.003 0.006 y2[1] (numeric) = -2.37909676302 -4.38797507595 y2[1] (closed_form) = -2.37909676302 -4.38797507595 absolute error = 3.178e-14 relative error = 6.367e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.45977753786 -3.32469327214 y1[1] (closed_form) = 5.45977753786 -3.32469327214 absolute error = 3.5e-14 relative error = 5.475e-13 % Correct digits = 14 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=22233.8MB, alloc=44.3MB, time=289.76 x[1] = 0.6514 2.413 h = 0.0001 0.005 y2[1] (numeric) = -2.41254910758 -4.40475795047 y2[1] (closed_form) = -2.41254910758 -4.40475795047 absolute error = 3.178e-14 relative error = 6.328e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.47596833239 -3.3582571852 y1[1] (closed_form) = 5.47596833239 -3.3582571852 absolute error = 3.5e-14 relative error = 5.449e-13 % Correct digits = 14 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 x[1] = 0.6515 2.418 h = 0.0001 0.003 y2[1] (numeric) = -2.42983290809 -4.42685538664 y2[1] (closed_form) = -2.42983290809 -4.42685538664 absolute error = 3.178e-14 relative error = 6.293e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.49770520283 -3.37580468256 y1[1] (closed_form) = 5.49770520283 -3.37580468256 absolute error = 3.501e-14 relative error = 5.427e-13 % Correct digits = 14 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=22281.5MB, alloc=44.3MB, time=290.38 x[1] = 0.6516 2.421 h = 0.001 0.001 y2[1] (numeric) = -2.44042685499 -4.44002981021 y2[1] (closed_form) = -2.44042685499 -4.44002981021 absolute error = 3.178e-14 relative error = 6.273e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.51066200847 -3.38655340776 y1[1] (closed_form) = 5.51066200847 -3.38655340776 absolute error = 3.501e-14 relative error = 5.413e-13 % Correct digits = 14 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=22329.3MB, alloc=44.3MB, time=291.01 x[1] = 0.6526 2.422 h = 0.001 0.003 y2[1] (numeric) = -2.44832851081 -4.44115047575 y2[1] (closed_form) = -2.44832851081 -4.44115047575 absolute error = 3.178e-14 relative error = 6.267e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.51165822224 -3.39443837542 y1[1] (closed_form) = 5.51165822224 -3.39443837542 absolute error = 3.501e-14 relative error = 5.409e-13 % Correct digits = 14 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=22377.3MB, alloc=44.3MB, time=291.64 x[1] = 0.6536 2.425 h = 0.0001 0.004 y2[1] (numeric) = -2.46305063068 -4.45129843048 y2[1] (closed_form) = -2.46305063068 -4.45129843048 absolute error = 3.202e-14 relative error = 6.293e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.52154120685 -3.40925165377 y1[1] (closed_form) = 5.52154120685 -3.40925165377 absolute error = 3.501e-14 relative error = 5.396e-13 % Correct digits = 14 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 x[1] = 0.6537 2.429 h = 0.003 0.006 y2[1] (numeric) = -2.47716929898 -4.46907791851 y2[1] (closed_form) = -2.47716929898 -4.46907791851 absolute error = 3.276e-14 relative error = 6.411e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.53903492619 -3.42357809219 y1[1] (closed_form) = 5.53903492619 -3.42357809219 absolute error = 3.501e-14 relative error = 5.377e-13 % Correct digits = 14 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=22425.1MB, alloc=44.3MB, time=292.25 x[1] = 0.6567 2.435 h = 0.0001 0.005 y2[1] (numeric) = -2.51145551328 -4.48603900829 y2[1] (closed_form) = -2.51145551328 -4.48603900829 absolute error = 3.298e-14 relative error = 6.416e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.55541740609 -3.45797651547 y1[1] (closed_form) = 5.55541740609 -3.45797651547 absolute error = 3.501e-14 relative error = 5.351e-13 % Correct digits = 14 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=22472.9MB, alloc=44.3MB, time=292.88 x[1] = 0.6568 2.44 h = 0.0001 0.003 y2[1] (numeric) = -2.529247134 -4.50852468558 y2[1] (closed_form) = -2.529247134 -4.50852468558 absolute error = 3.298e-14 relative error = 6.381e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.5775517356 -3.47602796084 y1[1] (closed_form) = 5.5775517356 -3.47602796084 absolute error = 3.501e-14 relative error = 5.328e-13 % Correct digits = 14 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=22521.0MB, alloc=44.3MB, time=293.50 x[1] = 0.6569 2.443 h = 0.001 0.001 y2[1] (numeric) = -2.54015020724 -4.52192896401 y2[1] (closed_form) = -2.54015020724 -4.52192896401 absolute error = 3.298e-14 relative error = 6.360e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.59074393688 -3.48708357059 y1[1] (closed_form) = 5.59074393688 -3.48708357059 absolute error = 3.601e-14 relative error = 5.466e-13 % Correct digits = 14 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 x[1] = 0.6579 2.444 h = 0.0001 0.004 y2[1] (numeric) = -2.54823255705 -4.52302908153 y2[1] (closed_form) = -2.54823255705 -4.52302908153 absolute error = 3.396e-14 relative error = 6.541e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.59172222586 -3.49515024083 y1[1] (closed_form) = 5.59172222586 -3.49515024083 absolute error = 3.601e-14 relative error = 5.461e-13 % Correct digits = 14 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=22568.8MB, alloc=44.3MB, time=294.12 x[1] = 0.658 2.448 h = 0.003 0.006 y2[1] (numeric) = -2.56270254849 -4.54108124387 y2[1] (closed_form) = -2.56270254849 -4.54108124387 absolute error = 3.396e-14 relative error = 6.512e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.60949487706 -3.50982529582 y1[1] (closed_form) = 5.60949487706 -3.50982529582 absolute error = 3.6e-14 relative error = 5.440e-13 % Correct digits = 14 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=22616.7MB, alloc=44.3MB, time=294.75 x[1] = 0.661 2.454 h = 0.0001 0.005 y2[1] (numeric) = -2.59772008088 -4.55820578055 y2[1] (closed_form) = -2.59772008088 -4.55820578055 absolute error = 3.493e-14 relative error = 6.658e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.62605217232 -3.54495536553 y1[1] (closed_form) = 5.62605217232 -3.54495536553 absolute error = 3.6e-14 relative error = 5.414e-13 % Correct digits = 14 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 x[1] = 0.6611 2.459 h = 0.0001 0.003 y2[1] (numeric) = -2.61595477519 -4.58103679374 y2[1] (closed_form) = -2.61595477519 -4.58103679374 absolute error = 3.396e-14 relative error = 6.437e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.64853954973 -3.56344647442 y1[1] (closed_form) = 5.64853954973 -3.56344647442 absolute error = 3.6e-14 relative error = 5.390e-13 % Correct digits = 14 memory used=22664.5MB, alloc=44.3MB, time=295.37 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 x[1] = 0.6612 2.462 h = 0.001 0.001 y2[1] (numeric) = -2.62712761469 -4.59464559397 y2[1] (closed_form) = -2.62712761469 -4.59464559397 absolute error = 3.396e-14 relative error = 6.416e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.66194090971 -3.57476987297 y1[1] (closed_form) = 5.66194090971 -3.57476987297 absolute error = 3.6e-14 relative error = 5.376e-13 % Correct digits = 14 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=22712.5MB, alloc=44.3MB, time=295.99 x[1] = 0.6622 2.463 h = 0.001 0.003 y2[1] (numeric) = -2.63536892048 -4.59572913514 y2[1] (closed_form) = -2.63536892048 -4.59572913514 absolute error = 3.396e-14 relative error = 6.410e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.66290485018 -3.58299630844 y1[1] (closed_form) = 5.66290485018 -3.58299630844 absolute error = 3.6e-14 relative error = 5.372e-13 % Correct digits = 14 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=22760.4MB, alloc=44.3MB, time=296.62 x[1] = 0.6632 2.466 h = 0.0001 0.004 y2[1] (numeric) = -2.65080917389 -4.60614232864 y2[1] (closed_form) = -2.65080917389 -4.60614232864 absolute error = 3.396e-14 relative error = 6.389e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.67306456932 -3.59852649588 y1[1] (closed_form) = 5.67306456932 -3.59852649588 absolute error = 3.6e-14 relative error = 5.359e-13 % Correct digits = 14 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 x[1] = 0.6633 2.47 h = 0.003 0.006 y2[1] (numeric) = -2.6657016591 -4.62451014697 y2[1] (closed_form) = -2.6657016591 -4.62451014697 absolute error = 3.396e-14 relative error = 6.361e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.69116002563 -3.61362102885 y1[1] (closed_form) = 5.69116002563 -3.61362102885 absolute error = 3.6e-14 relative error = 5.340e-13 % Correct digits = 14 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=22808.3MB, alloc=44.3MB, time=297.24 x[1] = 0.6663 2.476 h = 0.0001 0.005 y2[1] (numeric) = -2.70158985853 -4.64181255524 y2[1] (closed_form) = -2.70158985853 -4.64181255524 absolute error = 3.396e-14 relative error = 6.322e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.70790812678 -3.64962225621 y1[1] (closed_form) = 5.70790812678 -3.64962225621 absolute error = 3.6e-14 relative error = 5.314e-13 % Correct digits = 14 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=22856.1MB, alloc=44.3MB, time=297.86 x[1] = 0.6664 2.481 h = 0.0001 0.003 y2[1] (numeric) = -2.72035741483 -4.66504337581 y2[1] (closed_form) = -2.72035741483 -4.66504337581 absolute error = 3.517e-14 relative error = 6.513e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.73080412314 -3.66864242567 y1[1] (closed_form) = 5.73080412314 -3.66864242567 absolute error = 3.601e-14 relative error = 5.293e-13 % Correct digits = 14 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=22904.1MB, alloc=44.3MB, time=298.49 x[1] = 0.6665 2.484 h = 0.001 0.001 y2[1] (numeric) = -2.73185456364 -4.67888879678 y2[1] (closed_form) = -2.73185456364 -4.67888879678 absolute error = 3.517e-14 relative error = 6.491e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.74444740117 -3.68028793084 y1[1] (closed_form) = 5.74444740117 -3.68028793084 absolute error = 3.6e-14 relative error = 5.277e-13 % Correct digits = 14 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 x[1] = 0.6675 2.485 h = 0.001 0.003 y2[1] (numeric) = -2.74028397821 -4.67994922159 y2[1] (closed_form) = -2.74028397821 -4.67994922159 absolute error = 3.396e-14 relative error = 6.261e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.74539075231 -3.68870341896 y1[1] (closed_form) = 5.74539075231 -3.68870341896 absolute error = 3.6e-14 relative error = 5.273e-13 % Correct digits = 14 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=22951.8MB, alloc=44.3MB, time=299.11 x[1] = 0.6685 2.488 h = 0.0001 0.004 y2[1] (numeric) = -2.75612451186 -4.69050418762 y2[1] (closed_form) = -2.75612451186 -4.69050418762 absolute error = 3.421e-14 relative error = 6.287e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.75569822927 -3.70463324263 y1[1] (closed_form) = 5.75569822927 -3.70463324263 absolute error = 3.7e-14 relative error = 5.406e-13 % Correct digits = 14 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=22999.7MB, alloc=44.3MB, time=299.73 x[1] = 0.6686 2.492 h = 0.003 0.006 y2[1] (numeric) = -2.77145056436 -4.70919256305 y2[1] (closed_form) = -2.77145056436 -4.70919256305 absolute error = 3.396e-14 relative error = 6.214e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.7741212205 -3.7201583557 y1[1] (closed_form) = 5.7741212205 -3.7201583557 absolute error = 3.701e-14 relative error = 5.389e-13 % Correct digits = 14 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=23047.6MB, alloc=44.3MB, time=300.36 x[1] = 0.6716 2.498 h = 0.0001 0.005 y2[1] (numeric) = -2.80822982829 -4.7266723617 y2[1] (closed_form) = -2.80822982829 -4.7266723617 absolute error = 3.493e-14 relative error = 6.353e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.79105936726 -3.75705106045 y1[1] (closed_form) = 5.79105936726 -3.75705106045 absolute error = 3.7e-14 relative error = 5.360e-13 % Correct digits = 14 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 x[1] = 0.6717 2.503 h = 0.0001 0.003 y2[1] (numeric) = -2.82754422098 -4.7503092042 y2[1] (closed_form) = -2.82754422098 -4.7503092042 absolute error = 3.517e-14 relative error = 6.362e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.81436998555 -3.77661430197 y1[1] (closed_form) = 5.81436998555 -3.77661430197 absolute error = 3.7e-14 relative error = 5.337e-13 % Correct digits = 14 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=23095.3MB, alloc=44.3MB, time=300.98 x[1] = 0.6718 2.506 h = 0.001 0.001 y2[1] (numeric) = -2.8393741499 -4.76439487701 y2[1] (closed_form) = -2.8393741499 -4.76439487701 absolute error = 3.517e-14 relative error = 6.341e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.82825868595 -3.78859040506 y1[1] (closed_form) = 5.82825868595 -3.78859040506 absolute error = 3.701e-14 relative error = 5.325e-13 % Correct digits = 14 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=23143.1MB, alloc=44.3MB, time=301.60 x[1] = 0.6728 2.507 h = 0.001 0.003 y2[1] (numeric) = -2.84799576374 -4.76543070305 y2[1] (closed_form) = -2.84799576374 -4.76543070305 absolute error = 3.493e-14 relative error = 6.292e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.82917991522 -3.79719900265 y1[1] (closed_form) = 5.82917991522 -3.79719900265 absolute error = 3.7e-14 relative error = 5.318e-13 % Correct digits = 14 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=23191.1MB, alloc=44.3MB, time=302.23 x[1] = 0.6738 2.51 h = 0.0001 0.004 y2[1] (numeric) = -2.86424626128 -4.77612855955 y2[1] (closed_form) = -2.86424626128 -4.77612855955 absolute error = 3.493e-14 relative error = 6.272e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.8396361343 -3.8135381292 y1[1] (closed_form) = 5.8396361343 -3.8135381292 absolute error = 3.8e-14 relative error = 5.448e-13 % Correct digits = 14 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 x[1] = 0.6739 2.514 h = 0.003 0.006 y2[1] (numeric) = -2.88001722702 -4.79514243824 y2[1] (closed_form) = -2.88001722702 -4.79514243824 absolute error = 3.396e-14 relative error = 6.071e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.85839143919 -3.8295051972 y1[1] (closed_form) = 5.85839143919 -3.8295051972 absolute error = 3.8e-14 relative error = 5.429e-13 % Correct digits = 14 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=23238.7MB, alloc=44.3MB, time=302.85 x[1] = 0.6769 2.52 h = 0.0001 0.005 y2[1] (numeric) = -2.91770840057 -4.81279901914 y2[1] (closed_form) = -2.91770840057 -4.81279901914 absolute error = 3.396e-14 relative error = 6.033e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.87551875 -3.86731014983 y1[1] (closed_form) = 5.87551875 -3.86731014983 absolute error = 3.8e-14 relative error = 5.402e-13 % Correct digits = 14 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=23286.6MB, alloc=44.3MB, time=303.48 x[1] = 0.677 2.525 h = 0.0001 0.003 y2[1] (numeric) = -2.93758394804 -4.83684815568 y2[1] (closed_form) = -2.93758394804 -4.83684815568 absolute error = 3.421e-14 relative error = 6.044e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.89925005558 -3.88743081918 y1[1] (closed_form) = 5.89925005558 -3.88743081918 absolute error = 3.9e-14 relative error = 5.520e-13 % Correct digits = 14 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=23334.6MB, alloc=44.3MB, time=304.10 x[1] = 0.6771 2.528 h = 0.001 0.001 y2[1] (numeric) = -2.94975533565 -4.85117774336 y2[1] (closed_form) = -2.94975533565 -4.85117774336 absolute error = 3.517e-14 relative error = 6.195e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.91338771749 -3.89974621946 y1[1] (closed_form) = 5.91338771749 -3.89974621946 absolute error = 3.9e-14 relative error = 5.506e-13 % Correct digits = 14 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 x[1] = 0.6781 2.529 h = 0.001 0.003 y2[1] (numeric) = -2.95857332111 -4.85218743216 y2[1] (closed_form) = -2.95857332111 -4.85218743216 absolute error = 3.517e-14 relative error = 6.189e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 5.91428523721 -3.90855206623 y1[1] (closed_form) = 5.91428523721 -3.90855206623 absolute error = 3.8e-14 relative error = 5.360e-13 % Correct digits = 14 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=23382.5MB, alloc=44.3MB, time=304.72 x[1] = 0.6791 2.532 h = 0.0001 0.004 y2[1] (numeric) = -2.97524368644 -4.86302926663 y2[1] (closed_form) = -2.97524368644 -4.86302926663 absolute error = 3.517e-14 relative error = 6.169e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 5.92489115507 -3.92531038362 y1[1] (closed_form) = 5.92489115507 -3.92531038362 absolute error = 3.801e-14 relative error = 5.349e-13 % Correct digits = 14 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=23430.4MB, alloc=44.3MB, time=305.35 x[1] = 0.6792 2.536 h = 0.003 0.006 y2[1] (numeric) = -2.99147119016 -4.88237363938 y2[1] (closed_form) = -2.99147119016 -4.88237363938 absolute error = 3.517e-14 relative error = 6.142e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 5.94398360079 -3.94173106036 y1[1] (closed_form) = 5.94398360079 -3.94173106036 absolute error = 3.801e-14 relative error = 5.330e-13 % Correct digits = 14 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 x[1] = 0.6822 2.542 h = 0.0001 0.005 y2[1] (numeric) = -3.03009557541 -4.9002062623 y2[1] (closed_form) = -3.03009557541 -4.9002062623 absolute error = 3.544e-14 relative error = 6.151e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 5.9612990676 -3.9804694914 y1[1] (closed_form) = 5.9612990676 -3.9804694914 absolute error = 3.801e-14 relative error = 5.303e-13 % Correct digits = 14 memory used=23478.2MB, alloc=44.3MB, time=305.97 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 x[1] = 0.6823 2.547 h = 0.0001 0.003 y2[1] (numeric) = -3.05054694806 -4.9246740221 y2[1] (closed_form) = -3.05054694806 -4.9246740221 absolute error = 3.544e-14 relative error = 6.118e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 5.9854571876 -4.00116229662 y1[1] (closed_form) = 5.9854571876 -4.00116229662 absolute error = 3.801e-14 relative error = 5.280e-13 % Correct digits = 14 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=23525.9MB, alloc=44.3MB, time=306.59 x[1] = 0.6824 2.55 h = 0.001 0.001 y2[1] (numeric) = -3.06306868549 -4.93925121926 y2[1] (closed_form) = -3.06306868549 -4.93925121926 absolute error = 3.544e-14 relative error = 6.098e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 5.99984738453 -4.01382590613 y1[1] (closed_form) = 5.99984738453 -4.01382590613 absolute error = 3.801e-14 relative error = 5.266e-13 % Correct digits = 14 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=23573.9MB, alloc=44.3MB, time=307.21 x[1] = 0.6834 2.551 h = 0.0001 0.004 y2[1] (numeric) = -3.07208729836 -4.94023317466 y2[1] (closed_form) = -3.07208729836 -4.94023317466 absolute error = 3.544e-14 relative error = 6.092e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.00071955024 -4.02283322617 y1[1] (closed_form) = 6.00071955024 -4.02283322617 absolute error = 3.801e-14 relative error = 5.262e-13 % Correct digits = 14 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 x[1] = 0.6835 2.555 h = 0.003 0.006 y2[1] (numeric) = -3.08871328253 -4.95987168794 y2[1] (closed_form) = -3.08871328253 -4.95987168794 absolute error = 3.544e-14 relative error = 6.065e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.02011169522 -4.03964980887 y1[1] (closed_form) = 6.02011169522 -4.03964980887 absolute error = 3.801e-14 relative error = 5.243e-13 % Correct digits = 14 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=23621.7MB, alloc=44.3MB, time=307.83 x[1] = 0.6865 2.561 h = 0.0001 0.005 y2[1] (numeric) = -3.12815627694 -4.97786661488 y2[1] (closed_form) = -3.12815627694 -4.97786661488 absolute error = 3.640e-14 relative error = 6.191e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.03759968511 -4.07920688354 y1[1] (closed_form) = 6.03759968511 -4.07920688354 absolute error = 3.805e-14 relative error = 5.222e-13 % Correct digits = 14 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=23669.5MB, alloc=44.3MB, time=308.45 x[1] = 0.6866 2.566 h = 0.0001 0.003 y2[1] (numeric) = -3.14911023287 -5.00270692683 y2[1] (closed_form) = -3.14911023287 -5.00270692683 absolute error = 3.669e-14 relative error = 6.206e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.0621372063 -4.10039903231 y1[1] (closed_form) = 6.0621372063 -4.10039903231 absolute error = 3.805e-14 relative error = 5.199e-13 % Correct digits = 14 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=23717.5MB, alloc=44.3MB, time=309.08 x[1] = 0.6867 2.569 h = 0.001 0.001 y2[1] (numeric) = -3.16193781543 -5.01750456186 y2[1] (closed_form) = -3.16193781543 -5.01750456186 absolute error = 3.669e-14 relative error = 6.186e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.07675196084 -4.11336660451 y1[1] (closed_form) = 6.07675196083 -4.11336660451 absolute error = 3.805e-14 relative error = 5.186e-13 % Correct digits = 14 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 x[1] = 0.6877 2.57 h = 0.001 0.003 y2[1] (numeric) = -3.17113295182 -5.01846378221 y2[1] (closed_form) = -3.17113295182 -5.01846378221 absolute error = 3.669e-14 relative error = 6.180e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.07760341115 -4.12255112393 y1[1] (closed_form) = 6.07760341115 -4.12255112393 absolute error = 3.805e-14 relative error = 5.182e-13 % Correct digits = 14 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=23765.3MB, alloc=44.3MB, time=309.70 x[1] = 0.6887 2.573 h = 0.0001 0.004 y2[1] (numeric) = -3.18860998293 -5.02958159913 y2[1] (closed_form) = -3.18860998293 -5.02958159913 absolute error = 3.669e-14 relative error = 6.161e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.08849560928 -4.14011474387 y1[1] (closed_form) = 6.08849560928 -4.14011474387 absolute error = 3.805e-14 relative error = 5.168e-13 % Correct digits = 14 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=23813.1MB, alloc=44.3MB, time=310.32 x[1] = 0.6888 2.577 h = 0.003 0.006 y2[1] (numeric) = -3.20571483943 -5.04956015707 y2[1] (closed_form) = -3.20571483943 -5.04956015707 absolute error = 3.669e-14 relative error = 6.134e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.1082341514 -4.15740732624 y1[1] (closed_form) = 6.1082341514 -4.15740732624 absolute error = 3.812e-14 relative error = 5.159e-13 % Correct digits = 14 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=23861.1MB, alloc=44.3MB, time=310.95 x[1] = 0.6918 2.583 h = 0.0001 0.005 y2[1] (numeric) = -3.24613194566 -5.06772964592 y2[1] (closed_form) = -3.24613194566 -5.06772964592 absolute error = 3.764e-14 relative error = 6.255e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.12590833246 -4.19793865708 y1[1] (closed_form) = 6.12590833246 -4.19793865708 absolute error = 3.912e-14 relative error = 5.267e-13 % Correct digits = 14 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 x[1] = 0.6919 2.588 h = 0.0001 0.003 y2[1] (numeric) = -3.26768991294 -5.09300069347 y2[1] (closed_form) = -3.26768991294 -5.09300069347 absolute error = 3.764e-14 relative error = 6.221e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.15088441702 -4.21973120078 y1[1] (closed_form) = 6.15088441702 -4.21973120078 absolute error = 3.912e-14 relative error = 5.244e-13 % Correct digits = 14 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=23908.9MB, alloc=44.3MB, time=311.57 x[1] = 0.692 2.591 h = 0.001 0.001 y2[1] (numeric) = -3.28088492741 -5.10805300755 y2[1] (closed_form) = -3.28088492741 -5.10805300755 absolute error = 3.764e-14 relative error = 6.201e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.16575855835 -4.23306410499 y1[1] (closed_form) = 6.16575855835 -4.23306410499 absolute error = 4.011e-14 relative error = 5.363e-13 % Correct digits = 14 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=23956.9MB, alloc=44.3MB, time=312.19 x[1] = 0.693 2.592 h = 0.001 0.003 y2[1] (numeric) = -3.29028885844 -5.10898141798 y2[1] (closed_form) = -3.29028885844 -5.10898141798 absolute error = 3.860e-14 relative error = 6.352e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.16658149024 -4.24245820896 y1[1] (closed_form) = 6.16658149024 -4.24245820896 absolute error = 4.011e-14 relative error = 5.359e-13 % Correct digits = 14 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=24004.8MB, alloc=44.3MB, time=312.82 x[1] = 0.694 2.595 h = 0.0001 0.004 y2[1] (numeric) = -3.30821533779 -5.12024626641 y2[1] (closed_form) = -3.30821533779 -5.12024626641 absolute error = 3.764e-14 relative error = 6.175e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.17762608131 -4.26047056157 y1[1] (closed_form) = 6.17762608131 -4.26047056157 absolute error = 3.920e-14 relative error = 5.224e-13 % Correct digits = 14 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 x[1] = 0.6941 2.599 h = 0.003 0.006 y2[1] (numeric) = -3.32581152448 -5.14056998853 y2[1] (closed_form) = -3.32581152448 -5.14056998853 absolute error = 3.764e-14 relative error = 6.148e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.19771598689 -4.27825163107 y1[1] (closed_form) = 6.19771598689 -4.27825163107 absolute error = 3.912e-14 relative error = 5.194e-13 % Correct digits = 14 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=24052.6MB, alloc=44.3MB, time=313.44 x[1] = 0.6971 2.605 h = 0.0001 0.005 y2[1] (numeric) = -3.36722540705 -5.15891289718 y2[1] (closed_form) = -3.36722540705 -5.15891289718 absolute error = 3.764e-14 relative error = 6.110e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.21557496455 -4.31977981918 y1[1] (closed_form) = 6.21557496455 -4.31977981918 absolute error = 3.920e-14 relative error = 5.179e-13 % Correct digits = 14 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=24100.4MB, alloc=44.3MB, time=314.06 x[1] = 0.6972 2.61 h = 0.0001 0.003 y2[1] (numeric) = -3.38940310811 -5.18462117427 y2[1] (closed_form) = -3.38940310811 -5.18462117427 absolute error = 3.764e-14 relative error = 6.077e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.24099591723 -4.34218851839 y1[1] (closed_form) = 6.24099591723 -4.34218851839 absolute error = 3.920e-14 relative error = 5.157e-13 % Correct digits = 14 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=24148.4MB, alloc=44.3MB, time=314.69 x[1] = 0.6973 2.613 h = 0.001 0.001 y2[1] (numeric) = -3.40297508086 -5.19993195279 y2[1] (closed_form) = -3.40297508086 -5.19993195279 absolute error = 3.764e-14 relative error = 6.057e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.25613311736 -4.3558963023 y1[1] (closed_form) = 6.25613311736 -4.3558963023 absolute error = 3.920e-14 relative error = 5.143e-13 % Correct digits = 14 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 x[1] = 0.6983 2.614 h = 0.001 0.003 y2[1] (numeric) = -3.41259231051 -5.20082778343 y2[1] (closed_form) = -3.41259231051 -5.20082778343 absolute error = 3.764e-14 relative error = 6.051e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.25692571513 -4.36550446573 y1[1] (closed_form) = 6.25692571513 -4.36550446573 absolute error = 4.020e-14 relative error = 5.269e-13 % Correct digits = 14 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=24196.2MB, alloc=44.3MB, time=315.31 x[1] = 0.6993 2.617 h = 0.0001 0.004 y2[1] (numeric) = -3.43097903838 -5.21224061848 y2[1] (closed_form) = -3.43097903838 -5.21224061848 absolute error = 3.764e-14 relative error = 6.032e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.26812353383 -4.38397633904 y1[1] (closed_form) = 6.26812353383 -4.38397633904 absolute error = 4.020e-14 relative error = 5.255e-13 % Correct digits = 14 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=24244.0MB, alloc=44.3MB, time=315.93 x[1] = 0.6994 2.621 h = 0.003 0.006 y2[1] (numeric) = -3.4490793176 -5.23291466709 y2[1] (closed_form) = -3.4490793176 -5.23291466709 absolute error = 3.860e-14 relative error = 6.159e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.28856981546 -4.4022586878 y1[1] (closed_form) = 6.28856981546 -4.4022586878 absolute error = 4.020e-14 relative error = 5.237e-13 % Correct digits = 14 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=24291.8MB, alloc=44.3MB, time=316.55 x[1] = 0.7024 2.627 h = 0.0001 0.005 y2[1] (numeric) = -3.49151313593 -5.25142970004 y2[1] (closed_form) = -3.49151313593 -5.25142970004 absolute error = 3.736e-14 relative error = 5.925e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.30661204693 -4.44480683185 y1[1] (closed_form) = 6.30661204693 -4.44480683185 absolute error = 4.020e-14 relative error = 5.210e-13 % Correct digits = 14 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 x[1] = 0.7025 2.632 h = 0.0001 0.003 y2[1] (numeric) = -3.51432667772 -5.27758175544 y2[1] (closed_form) = -3.51432667772 -5.27758175544 absolute error = 3.833e-14 relative error = 6.045e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.33248423162 -4.46784783182 y1[1] (closed_form) = 6.33248423162 -4.46784783182 absolute error = 4.020e-14 relative error = 5.187e-13 % Correct digits = 14 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=24339.5MB, alloc=44.3MB, time=317.17 x[1] = 0.7026 2.635 h = 0.001 0.001 y2[1] (numeric) = -3.52828536726 -5.29315481371 y2[1] (closed_form) = -3.52828536726 -5.29315481371 absolute error = 3.833e-14 relative error = 6.025e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.34788819504 -4.48194027538 y1[1] (closed_form) = 6.34788819504 -4.48194027538 absolute error = 4.020e-14 relative error = 5.173e-13 % Correct digits = 14 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=24387.5MB, alloc=44.3MB, time=317.80 x[1] = 0.7036 2.636 h = 0.001 0.003 y2[1] (numeric) = -3.53812048918 -5.29401623007 y2[1] (closed_form) = -3.53812048918 -5.29401623007 absolute error = 3.956e-14 relative error = 6.213e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.34864857927 -4.49176706371 y1[1] (closed_form) = 6.34864857927 -4.49176706371 absolute error = 4.020e-14 relative error = 5.169e-13 % Correct digits = 14 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 x[1] = 0.7046 2.639 h = 0.0001 0.004 y2[1] (numeric) = -3.55697851016 -5.30557796701 y2[1] (closed_form) = -3.55697851016 -5.30557796701 absolute error = 3.956e-14 relative error = 6.193e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.36000042297 -4.510709491 y1[1] (closed_form) = 6.36000042297 -4.510709491 absolute error = 4.020e-14 relative error = 5.156e-13 % Correct digits = 14 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=24435.3MB, alloc=44.3MB, time=318.42 x[1] = 0.7047 2.643 h = 0.003 0.006 y2[1] (numeric) = -3.5755959558 -5.32660754657 y2[1] (closed_form) = -3.5755959558 -5.32660754657 absolute error = 3.956e-14 relative error = 6.166e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.3808081388 -4.52950622277 y1[1] (closed_form) = 6.3808081388 -4.52950622277 absolute error = 4.011e-14 relative error = 5.126e-13 % Correct digits = 14 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=24483.2MB, alloc=44.3MB, time=319.04 x[1] = 0.7077 2.649 h = 0.0001 0.005 y2[1] (numeric) = -3.61907337448 -5.34529324893 y2[1] (closed_form) = -3.61907337448 -5.34529324893 absolute error = 3.985e-14 relative error = 6.173e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.39903192696 -4.57309792921 y1[1] (closed_form) = 6.39903192696 -4.57309792921 absolute error = 4.111e-14 relative error = 5.227e-13 % Correct digits = 14 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=24531.0MB, alloc=44.3MB, time=319.67 x[1] = 0.7078 2.654 h = 0.0001 0.003 y2[1] (numeric) = -3.64253925732 -5.37189568543 y2[1] (closed_form) = -3.64253925732 -5.37189568543 absolute error = 3.985e-14 relative error = 6.140e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.42536176581 -4.5967877687 y1[1] (closed_form) = 6.42536176581 -4.5967877687 absolute error = 4.111e-14 relative error = 5.204e-13 % Correct digits = 14 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 x[1] = 0.7079 2.657 h = 0.001 0.001 y2[1] (numeric) = -3.65689465966 -5.38773486814 y2[1] (closed_form) = -3.65689465966 -5.38773486814 absolute error = 3.985e-14 relative error = 6.120e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.44103622892 -4.61127488947 y1[1] (closed_form) = 6.44103622892 -4.61127488947 absolute error = 4.119e-14 relative error = 5.200e-13 % Correct digits = 14 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=24578.7MB, alloc=44.3MB, time=320.30 x[1] = 0.7089 2.658 h = 0.0001 0.004 y2[1] (numeric) = -3.66695235879 -5.38855996923 y2[1] (closed_form) = -3.66695235879 -5.38855996923 absolute error = 3.985e-14 relative error = 6.114e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.44176245451 -4.62132496028 y1[1] (closed_form) = 6.44176245451 -4.62132496028 absolute error = 4.119e-14 relative error = 5.196e-13 % Correct digits = 14 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=24626.7MB, alloc=44.3MB, time=320.92 x[1] = 0.709 2.662 h = 0.003 0.006 y2[1] (numeric) = -3.6860213562 -5.40990615561 y2[1] (closed_form) = -3.6860213562 -5.40990615561 absolute error = 4.080e-14 relative error = 6.233e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.4628917112 -4.64057080396 y1[1] (closed_form) = 6.4628917112 -4.64057080396 absolute error = 4.119e-14 relative error = 5.178e-13 % Correct digits = 14 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=24674.5MB, alloc=44.3MB, time=321.54 x[1] = 0.712 2.668 h = 0.0001 0.005 y2[1] (numeric) = -3.73041440826 -5.42875029776 y2[1] (closed_form) = -3.73041440826 -5.42875029776 absolute error = 4.080e-14 relative error = 6.195e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.48128311905 -4.68507794062 y1[1] (closed_form) = 6.48128311905 -4.68507794062 absolute error = 4.130e-14 relative error = 5.165e-13 % Correct digits = 14 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 x[1] = 0.7121 2.673 h = 0.0001 0.003 y2[1] (numeric) = -3.75444985165 -5.45575378092 y2[1] (closed_form) = -3.75444985165 -5.45575378092 absolute error = 4.052e-14 relative error = 6.119e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.50802008238 -4.70933427373 y1[1] (closed_form) = 6.50802008238 -4.70933427373 absolute error = 4.130e-14 relative error = 5.142e-13 % Correct digits = 14 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=24722.2MB, alloc=44.3MB, time=322.16 x[1] = 0.7122 2.676 h = 0.001 0.001 y2[1] (numeric) = -3.76915168808 -5.47183002762 y2[1] (closed_form) = -3.76915168808 -5.47183002762 absolute error = 3.956e-14 relative error = 5.954e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.52393526683 -4.72416604332 y1[1] (closed_form) = 6.52393526683 -4.72416604332 absolute error = 4.130e-14 relative error = 5.128e-13 % Correct digits = 14 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=24770.1MB, alloc=44.3MB, time=322.79 x[1] = 0.7132 2.677 h = 0.001 0.003 y2[1] (numeric) = -3.77940526148 -5.47262502427 y2[1] (closed_form) = -3.77940526148 -5.47262502427 absolute error = 4.052e-14 relative error = 6.093e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.52463321759 -4.73441254921 y1[1] (closed_form) = 6.52463321759 -4.73441254921 absolute error = 4.130e-14 relative error = 5.124e-13 % Correct digits = 14 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=24818.0MB, alloc=44.3MB, time=323.41 x[1] = 0.7142 2.68 h = 0.0001 0.004 y2[1] (numeric) = -3.79916870601 -5.48447205971 y2[1] (closed_form) = -3.79916870601 -5.48447205971 absolute error = 4.052e-14 relative error = 6.074e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.53627957839 -4.75425893965 y1[1] (closed_form) = 6.53627957839 -4.75425893965 absolute error = 4.230e-14 relative error = 5.233e-13 % Correct digits = 14 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 x[1] = 0.7143 2.684 h = 0.003 0.006 y2[1] (numeric) = -3.81877998797 -5.50618373601 y2[1] (closed_form) = -3.81877998797 -5.50618373601 absolute error = 3.985e-14 relative error = 5.947e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.55777996522 -4.77404434203 y1[1] (closed_form) = 6.55777996522 -4.77404434203 absolute error = 4.130e-14 relative error = 5.092e-13 % Correct digits = 14 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=24865.7MB, alloc=44.3MB, time=324.03 x[1] = 0.7173 2.69 h = 0.0001 0.005 y2[1] (numeric) = -3.86426207717 -5.5251956914 y2[1] (closed_form) = -3.86426207717 -5.5251956914 absolute error = 4.080e-14 relative error = 6.052e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.57634963541 -4.81964037906 y1[1] (closed_form) = 6.57634963541 -4.81964037906 absolute error = 4.130e-14 relative error = 5.066e-13 % Correct digits = 14 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=24913.5MB, alloc=44.3MB, time=324.66 x[1] = 0.7174 2.695 h = 0.0001 0.003 y2[1] (numeric) = -3.88898156298 -5.55266219087 y2[1] (closed_form) = -3.88898156298 -5.55266219087 absolute error = 4.080e-14 relative error = 6.019e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.60355656335 -4.84457732686 y1[1] (closed_form) = 6.60355656335 -4.84457732686 absolute error = 4.119e-14 relative error = 5.030e-13 % Correct digits = 14 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=24961.4MB, alloc=44.3MB, time=325.28 x[1] = 0.7175 2.698 h = 0.001 0.001 y2[1] (numeric) = -3.90409931665 -5.56901191832 y2[1] (closed_form) = -3.90409931665 -5.56901191832 absolute error = 4.080e-14 relative error = 6.000e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.6197494091 -4.85982301965 y1[1] (closed_form) = 6.6197494091 -4.85982301965 absolute error = 4.130e-14 relative error = 5.030e-13 % Correct digits = 14 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 x[1] = 0.7185 2.699 h = 0.001 0.003 y2[1] (numeric) = -3.91458445834 -5.56976693711 y2[1] (closed_form) = -3.91458445834 -5.56976693711 absolute error = 4.052e-14 relative error = 5.952e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.62040945839 -4.87030175086 y1[1] (closed_form) = 6.62040945839 -4.87030175086 absolute error = 4.130e-14 relative error = 5.025e-13 % Correct digits = 14 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=25009.3MB, alloc=44.3MB, time=325.90 x[1] = 0.7195 2.702 h = 0.0001 0.004 y2[1] (numeric) = -3.93485217969 -5.5817653948 y2[1] (closed_form) = -3.93485217969 -5.5817653948 absolute error = 4.052e-14 relative error = 5.934e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.63221204088 -4.89065165251 y1[1] (closed_form) = 6.63221204088 -4.89065165251 absolute error = 4.130e-14 relative error = 5.012e-13 % Correct digits = 14 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=25057.2MB, alloc=44.3MB, time=326.53 x[1] = 0.7196 2.706 h = 0.003 0.006 y2[1] (numeric) = -3.95501975098 -5.60384788617 y2[1] (closed_form) = -3.95501975098 -5.60384788617 absolute error = 4.052e-14 relative error = 5.908e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.65408874605 -4.91099064848 y1[1] (closed_form) = 6.65408874605 -4.91099064848 absolute error = 4.144e-14 relative error = 5.010e-13 % Correct digits = 14 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=25105.0MB, alloc=44.3MB, time=327.16 x[1] = 0.7226 2.712 h = 0.0001 0.005 y2[1] (numeric) = -4.00161604755 -5.62302571555 y2[1] (closed_form) = -4.00161604755 -5.62302571555 absolute error = 4.052e-14 relative error = 5.871e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.67283451111 -4.95770070494 y1[1] (closed_form) = 6.67283451111 -4.95770070494 absolute error = 4.243e-14 relative error = 5.104e-13 % Correct digits = 14 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 x[1] = 0.7227 2.717 h = 0.0001 0.003 y2[1] (numeric) = -4.02703725163 -5.65096198892 y2[1] (closed_form) = -4.02703725163 -5.65096198892 absolute error = 3.956e-14 relative error = 5.701e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.70051799219 -4.98333598188 y1[1] (closed_form) = 6.70051799219 -4.98333598188 absolute error = 4.243e-14 relative error = 5.081e-13 % Correct digits = 14 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=25152.6MB, alloc=44.3MB, time=327.78 x[1] = 0.7228 2.72 h = 0.001 0.001 y2[1] (numeric) = -4.04258162813 -5.6675891256 y2[1] (closed_form) = -4.04258162813 -5.6675891256 absolute error = 3.956e-14 relative error = 5.683e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.71699232636 -4.99900632519 y1[1] (closed_form) = 6.71699232636 -4.99900632519 absolute error = 4.243e-14 relative error = 5.067e-13 % Correct digits = 14 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=25200.6MB, alloc=44.3MB, time=328.40 x[1] = 0.7238 2.721 h = 0.001 0.003 y2[1] (numeric) = -4.05330329461 -5.66830206545 y2[1] (closed_form) = -4.05330329461 -5.66830206545 absolute error = 3.956e-14 relative error = 5.677e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.71761233128 -5.00972221315 y1[1] (closed_form) = 6.71761233128 -5.00972221315 absolute error = 4.243e-14 relative error = 5.063e-13 % Correct digits = 14 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 x[1] = 0.7248 2.724 h = 0.0001 0.004 y2[1] (numeric) = -4.07408733153 -5.68045268896 y2[1] (closed_form) = -4.07408733153 -5.68045268896 absolute error = 3.985e-14 relative error = 5.701e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.72957177056 -5.03058765657 y1[1] (closed_form) = 6.72957177056 -5.03058765657 absolute error = 4.230e-14 relative error = 5.034e-13 % Correct digits = 14 memory used=25248.5MB, alloc=44.3MB, time=329.03 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 x[1] = 0.7249 2.728 h = 0.003 0.006 y2[1] (numeric) = -4.09482553705 -5.70291135989 y2[1] (closed_form) = -4.09482553705 -5.70291135989 absolute error = 3.956e-14 relative error = 5.635e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.75183002475 -5.05149462117 y1[1] (closed_form) = 6.75183002475 -5.05149462117 absolute error = 4.243e-14 relative error = 5.031e-13 % Correct digits = 14 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=25296.3MB, alloc=44.3MB, time=329.65 x[1] = 0.7279 2.734 h = 0.0001 0.005 y2[1] (numeric) = -4.14256175792 -5.72225293979 y2[1] (closed_form) = -4.14256175792 -5.72225293979 absolute error = 4.052e-14 relative error = 5.736e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.77074953768 -5.09934436508 y1[1] (closed_form) = 6.77074953768 -5.09934436508 absolute error = 4.342e-14 relative error = 5.122e-13 % Correct digits = 14 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=25344.1MB, alloc=44.3MB, time=330.27 x[1] = 0.728 2.739 h = 0.0001 0.003 y2[1] (numeric) = -4.1687027856 -5.75066579516 y2[1] (closed_form) = -4.1687027856 -5.75066579516 absolute error = 4.052e-14 relative error = 5.705e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.79891621483 -5.12569611516 y1[1] (closed_form) = 6.79891621483 -5.12569611516 absolute error = 4.243e-14 relative error = 4.983e-13 % Correct digits = 14 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 x[1] = 0.7281 2.742 h = 0.001 0.001 y2[1] (numeric) = -4.1846847497 -5.76757429654 y2[1] (closed_form) = -4.1846847497 -5.76757429654 absolute error = 4.052e-14 relative error = 5.687e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.81567589384 -5.14180209556 y1[1] (closed_form) = 6.81567589384 -5.14180209556 absolute error = 4.243e-14 relative error = 4.969e-13 % Correct digits = 14 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=25391.9MB, alloc=44.3MB, time=330.89 x[1] = 0.7291 2.743 h = 0.001 0.003 y2[1] (numeric) = -4.19564799549 -5.768242982 y2[1] (closed_form) = -4.19564799549 -5.768242982 absolute error = 4.052e-14 relative error = 5.681e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 6.81625363793 -5.15276017047 y1[1] (closed_form) = 6.81625363793 -5.15276017047 absolute error = 4.342e-14 relative error = 5.081e-13 % Correct digits = 14 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=25439.8MB, alloc=44.3MB, time=331.52 x[1] = 0.7301 2.746 h = 0.0001 0.004 y2[1] (numeric) = -4.21696065765 -5.78054646388 y2[1] (closed_form) = -4.21696065765 -5.78054646388 absolute error = 4.052e-14 relative error = 5.663e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.8283705204 -5.17415345786 y1[1] (closed_form) = 6.8283705204 -5.17415345786 absolute error = 4.342e-14 relative error = 5.068e-13 % Correct digits = 14 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=25487.8MB, alloc=44.3MB, time=332.14 x[1] = 0.7302 2.75 h = 0.003 0.006 y2[1] (numeric) = -4.23828419016 -5.80338671727 y2[1] (closed_form) = -4.23828419016 -5.80338671727 absolute error = 4.148e-14 relative error = 5.773e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.85101559577 -5.19564311407 y1[1] (closed_form) = 6.85101559577 -5.19564311407 absolute error = 4.342e-14 relative error = 5.049e-13 % Correct digits = 14 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 x[1] = 0.7332 2.756 h = 0.0001 0.005 y2[1] (numeric) = -4.28718661017 -5.82288973302 y2[1] (closed_form) = -4.28718661017 -5.82288973302 absolute error = 4.148e-14 relative error = 5.737e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.87010632302 -5.24465877359 y1[1] (closed_form) = 6.87010632302 -5.24465877359 absolute error = 4.357e-14 relative error = 5.041e-13 % Correct digits = 14 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=25535.4MB, alloc=44.3MB, time=332.76 x[1] = 0.7333 2.761 h = 0.0001 0.003 y2[1] (numeric) = -4.31406600613 -5.8517860279 y2[1] (closed_form) = -4.31406600613 -5.8517860279 absolute error = 4.148e-14 relative error = 5.706e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.89876289237 -5.27174558012 y1[1] (closed_form) = 6.89876289237 -5.27174558012 absolute error = 4.455e-14 relative error = 5.131e-13 % Correct digits = 14 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=25583.2MB, alloc=44.3MB, time=333.38 x[1] = 0.7334 2.764 h = 0.001 0.001 y2[1] (numeric) = -4.33049678774 -5.86897987568 y2[1] (closed_form) = -4.33049678774 -5.86897987568 absolute error = 4.176e-14 relative error = 5.726e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 6.91581180114 -5.28829844935 y1[1] (closed_form) = 6.91581180114 -5.28829844935 absolute error = 4.455e-14 relative error = 5.118e-13 % Correct digits = 14 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=25631.1MB, alloc=44.3MB, time=334.03 x[1] = 0.7344 2.765 h = 0.0001 0.004 y2[1] (numeric) = -4.34170676718 -5.8696020548 y2[1] (closed_form) = -4.34170676718 -5.8696020548 absolute error = 4.176e-14 relative error = 5.720e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 6.91634499219 -5.299503842 y1[1] (closed_form) = 6.91634499219 -5.299503842 absolute error = 4.455e-14 relative error = 5.113e-13 % Correct digits = 14 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 x[1] = 0.7345 2.769 h = 0.003 0.006 y2[1] (numeric) = -4.36354153305 -5.89278233398 y2[1] (closed_form) = -4.36354153305 -5.89278233398 absolute error = 4.272e-14 relative error = 5.826e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 6.93933446939 -5.32150242698 y1[1] (closed_form) = 6.93933446939 -5.32150242698 absolute error = 4.455e-14 relative error = 5.095e-13 % Correct digits = 14 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=25678.8MB, alloc=44.3MB, time=334.66 x[1] = 0.7375 2.775 h = 0.0001 0.005 y2[1] (numeric) = -4.41346737115 -5.91243663179 y2[1] (closed_form) = -4.41346737115 -5.91243663179 absolute error = 4.272e-14 relative error = 5.790e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 6.95858471973 -5.3715411118 y1[1] (closed_form) = 6.95858471973 -5.3715411118 absolute error = 4.455e-14 relative error = 5.068e-13 % Correct digits = 14 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=25726.7MB, alloc=44.3MB, time=335.28 x[1] = 0.7376 2.78 h = 0.0001 0.003 y2[1] (numeric) = -4.44099165205 -5.94176368786 y2[1] (closed_form) = -4.44099165205 -5.94176368786 absolute error = 4.368e-14 relative error = 5.888e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 6.98767743931 -5.39926990921 y1[1] (closed_form) = 6.98767743931 -5.39926990921 absolute error = 4.571e-14 relative error = 5.176e-13 % Correct digits = 14 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=25774.6MB, alloc=44.3MB, time=335.90 x[1] = 0.7377 2.783 h = 0.001 0.001 y2[1] (numeric) = -4.45781449624 -5.95921189356 y2[1] (closed_form) = -4.45781449624 -5.95921189356 absolute error = 4.368e-14 relative error = 5.869e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 7.00498395025 -5.41621315365 y1[1] (closed_form) = 7.00498395025 -5.41621315365 absolute error = 4.571e-14 relative error = 5.162e-13 % Correct digits = 14 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 x[1] = 0.7387 2.784 h = 0.001 0.003 y2[1] (numeric) = -4.46924165275 -5.95979520273 y2[1] (closed_form) = -4.46924165275 -5.95979520273 absolute error = 4.438e-14 relative error = 5.958e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 7.00547992763 -5.42763618519 y1[1] (closed_form) = 7.00547992763 -5.42763618519 absolute error = 4.554e-14 relative error = 5.139e-13 % Correct digits = 14 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=25822.4MB, alloc=44.3MB, time=336.53 x[1] = 0.7397 2.787 h = 0.0001 0.004 y2[1] (numeric) = -4.49156983992 -5.97239143227 y2[1] (closed_form) = -4.49156983992 -5.97239143227 absolute error = 4.438e-14 relative error = 5.939e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 7.01789780476 -5.4500434746 y1[1] (closed_form) = 7.01789780476 -5.4500434746 absolute error = 4.669e-14 relative error = 5.255e-13 % Correct digits = 14 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=25870.3MB, alloc=44.3MB, time=337.15 x[1] = 0.7398 2.791 h = 0.003 0.006 y2[1] (numeric) = -4.51401816056 -5.99596363155 y2[1] (closed_form) = -4.51401816056 -5.99596363155 absolute error = 4.464e-14 relative error = 5.948e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 7.04128420583 -5.47265303667 y1[1] (closed_form) = 7.04128420583 -5.47265303667 absolute error = 4.669e-14 relative error = 5.236e-13 % Correct digits = 14 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=25918.2MB, alloc=44.3MB, time=337.78 x[1] = 0.7428 2.797 h = 0.0001 0.005 y2[1] (numeric) = -4.56516064664 -6.01577485375 y2[1] (closed_form) = -4.56516064664 -6.01577485375 absolute error = 4.464e-14 relative error = 5.912e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 7.06070076316 -5.52390800724 y1[1] (closed_form) = 7.06070076316 -5.52390800724 absolute error = 4.669e-14 relative error = 5.208e-13 % Correct digits = 14 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 x[1] = 0.7429 2.802 h = 0.0001 0.003 y2[1] (numeric) = -4.593458924 -6.04559847064 y2[1] (closed_form) = -4.593458924 -6.04559847064 absolute error = 4.438e-14 relative error = 5.846e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 7.09029620623 -5.55240756302 y1[1] (closed_form) = 7.09029620623 -5.55240756302 absolute error = 4.669e-14 relative error = 5.185e-13 % Correct digits = 14 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=25965.9MB, alloc=44.3MB, time=338.40 x[1] = 0.743 2.805 h = 0.001 0.001 y2[1] (numeric) = -4.61075216025 -6.06333964027 y2[1] (closed_form) = -4.61075216025 -6.06333964027 absolute error = 4.438e-14 relative error = 5.827e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 7.10789939053 -5.56981931263 y1[1] (closed_form) = 7.10789939053 -5.56981931263 absolute error = 4.768e-14 relative error = 5.280e-13 % Correct digits = 14 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=26013.8MB, alloc=44.3MB, time=339.02 x[1] = 0.744 2.806 h = 0.001 0.003 y2[1] (numeric) = -4.62243594247 -6.0638721057 y2[1] (closed_form) = -4.62243594247 -6.0638721057 absolute error = 4.438e-14 relative error = 5.821e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 7.1083464043 -5.58149951248 y1[1] (closed_form) = 7.1083464043 -5.58149951248 absolute error = 4.768e-14 relative error = 5.275e-13 % Correct digits = 14 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=26061.7MB, alloc=44.3MB, time=339.65 x[1] = 0.745 2.809 h = 0.0001 0.004 y2[1] (numeric) = -4.64532951202 -6.0766230277 y2[1] (closed_form) = -4.64532951202 -6.0766230277 absolute error = 4.438e-14 relative error = 5.803e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 7.12092326737 -5.60447138662 y1[1] (closed_form) = 7.12092326737 -5.60447138662 absolute error = 4.687e-14 relative error = 5.172e-13 % Correct digits = 14 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 x[1] = 0.7451 2.813 h = 0.003 0.006 y2[1] (numeric) = -4.66840711958 -6.10059265885 y2[1] (closed_form) = -4.66840711958 -6.10059265885 absolute error = 4.438e-14 relative error = 5.778e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 7.14471198176 -5.62770768812 y1[1] (closed_form) = 7.14471198176 -5.62770768812 absolute error = 4.785e-14 relative error = 5.262e-13 % Correct digits = 14 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=26109.4MB, alloc=44.3MB, time=340.27 x[1] = 0.7481 2.819 h = 0.0001 0.005 y2[1] (numeric) = -4.72079419099 -6.12055791047 y2[1] (closed_form) = -4.72079419099 -6.12055791047 absolute error = 4.438e-14 relative error = 5.742e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 7.16429174495 -5.68020684104 y1[1] (closed_form) = 7.16429174495 -5.68020684104 absolute error = 4.785e-14 relative error = 5.234e-13 % Correct digits = 14 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=26157.3MB, alloc=44.3MB, time=340.89 x[1] = 0.7482 2.824 h = 0.0001 0.003 y2[1] (numeric) = -4.74988632203 -6.1508850858 y2[1] (closed_form) = -4.74988632203 -6.1508850858 absolute error = 4.535e-14 relative error = 5.836e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 7.19439675816 -5.70949705097 y1[1] (closed_form) = 7.19439675816 -5.70949705097 absolute error = 4.785e-14 relative error = 5.210e-13 % Correct digits = 14 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 x[1] = 0.7483 2.827 h = 0.001 0.001 y2[1] (numeric) = -4.76766197228 -6.16892327487 y2[1] (closed_form) = -4.76766197228 -6.16892327487 absolute error = 4.535e-14 relative error = 5.817e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 7.21230058077 -5.72738934953 y1[1] (closed_form) = 7.21230058077 -5.72738934953 absolute error = 4.884e-14 relative error = 5.303e-13 % Correct digits = 14 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=26205.0MB, alloc=44.3MB, time=341.51 x[1] = 0.7493 2.828 h = 0.001 0.003 y2[1] (numeric) = -4.7796078313 -6.16940241445 y2[1] (closed_form) = -4.7796078313 -6.16940241445 absolute error = 4.561e-14 relative error = 5.844e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 7.2126961107 -5.73933214721 y1[1] (closed_form) = 7.2126961107 -5.73933214721 absolute error = 4.785e-14 relative error = 5.192e-13 % Correct digits = 14 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=26252.9MB, alloc=44.3MB, time=342.14 x[1] = 0.7503 2.831 h = 0.0001 0.004 y2[1] (numeric) = -4.80308019466 -6.18230850318 y2[1] (closed_form) = -4.80308019466 -6.18230850318 absolute error = 4.657e-14 relative error = 5.949e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 7.22543233635 -5.76288201264 y1[1] (closed_form) = 7.22543233635 -5.76288201264 absolute error = 4.903e-14 relative error = 5.305e-13 % Correct digits = 14 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=26300.9MB, alloc=44.3MB, time=342.76 x[1] = 0.7504 2.835 h = 0.003 0.006 y2[1] (numeric) = -4.8268032009 -6.20668111238 y2[1] (closed_form) = -4.8268032009 -6.20668111238 absolute error = 4.561e-14 relative error = 5.800e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 7.24962879076 -5.78676119548 y1[1] (closed_form) = 7.24962879076 -5.78676119548 absolute error = 4.805e-14 relative error = 5.180e-13 % Correct digits = 14 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 x[1] = 0.7534 2.841 h = 0.0001 0.005 y2[1] (numeric) = -4.88046339835 -6.22679727845 y2[1] (closed_form) = -4.88046339835 -6.22679727845 absolute error = 4.561e-14 relative error = 5.765e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 7.26936844293 -5.84053303266 y1[1] (closed_form) = 7.26936844293 -5.84053303266 absolute error = 4.924e-14 relative error = 5.281e-13 % Correct digits = 14 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=26348.7MB, alloc=44.3MB, time=343.38 x[1] = 0.7535 2.846 h = 0.0001 0.003 y2[1] (numeric) = -4.91036971968 -6.25763505427 y2[1] (closed_form) = -4.91036971968 -6.25763505427 absolute error = 4.561e-14 relative error = 5.734e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 7.29998992085 -5.87063427183 y1[1] (closed_form) = 7.29998992085 -5.87063427183 absolute error = 4.903e-14 relative error = 5.234e-13 % Correct digits = 14 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=26396.7MB, alloc=44.3MB, time=344.00 x[1] = 0.7536 2.849 h = 0.001 0.001 y2[1] (numeric) = -4.92864009507 -6.2759743412 y2[1] (closed_form) = -4.92864009507 -6.2759743412 absolute error = 4.561e-14 relative error = 5.715e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 7.31819837173 -5.88901945234 y1[1] (closed_form) = 7.31819837173 -5.88901945234 absolute error = 5.022e-14 relative error = 5.346e-13 % Correct digits = 14 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=26444.7MB, alloc=44.3MB, time=344.63 x[1] = 0.7546 2.85 h = 0.001 0.003 y2[1] (numeric) = -4.94085358901 -6.27639758741 y2[1] (closed_form) = -4.94085358901 -6.27639758741 absolute error = 4.657e-14 relative error = 5.830e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 7.31853981289 -5.90123038509 y1[1] (closed_form) = 7.31853981289 -5.90123038509 absolute error = 5.022e-14 relative error = 5.342e-13 % Correct digits = 14 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 x[1] = 0.7556 2.853 h = 0.0001 0.004 y2[1] (numeric) = -4.9649184577 -6.28945925286 y2[1] (closed_form) = -4.9649184577 -6.28945925286 absolute error = 4.684e-14 relative error = 5.846e-13 % Correct digits = 14 h = 0.0001 0.004 y1[1] (numeric) = 7.3314357156 -5.92537194904 y1[1] (closed_form) = 7.3314357156 -5.92537194904 absolute error = 4.903e-14 relative error = 5.201e-13 % Correct digits = 14 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=26492.4MB, alloc=44.3MB, time=345.25 x[1] = 0.7557 2.857 h = 0.003 0.006 y2[1] (numeric) = -4.9893033626 -6.31424041951 y2[1] (closed_form) = -4.9893033626 -6.31424041951 absolute error = 4.561e-14 relative error = 5.667e-13 % Correct digits = 14 h = 0.003 0.006 y1[1] (numeric) = 7.3560453727 -5.94991054332 y1[1] (closed_form) = 7.3560453727 -5.94991054332 absolute error = 4.903e-14 relative error = 5.182e-13 % Correct digits = 14 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=26540.3MB, alloc=44.3MB, time=345.87 x[1] = 0.7587 2.863 h = 0.0001 0.005 y2[1] (numeric) = -5.04426584244 -6.33450415695 y2[1] (closed_form) = -5.04426584244 -6.33450415695 absolute error = 4.684e-14 relative error = 5.784e-13 % Correct digits = 14 h = 0.0001 0.005 y1[1] (numeric) = 7.37594137307 -6.0049841842 y1[1] (closed_form) = 7.37594137307 -6.0049841842 absolute error = 5.001e-14 relative error = 5.258e-13 % Correct digits = 14 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=26588.2MB, alloc=44.3MB, time=346.50 x[1] = 0.7588 2.868 h = 0.0001 0.003 y2[1] (numeric) = -5.07500718095 -6.36585961822 y2[1] (closed_form) = -5.07500718095 -6.36585961822 absolute error = 4.684e-14 relative error = 5.753e-13 % Correct digits = 14 h = 0.0001 0.003 y1[1] (numeric) = 7.40708625658 -6.03591731793 y1[1] (closed_form) = 7.40708625658 -6.03591731793 absolute error = 5.001e-14 relative error = 5.234e-13 % Correct digits = 14 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 x[1] = 0.7589 2.871 h = 0.001 0.001 y2[1] (numeric) = -5.09378488842 -6.38450410333 y2[1] (closed_form) = -5.09378488842 -6.38450410333 absolute error = 4.684e-14 relative error = 5.735e-13 % Correct digits = 14 h = 0.001 0.001 y1[1] (numeric) = 7.42560334963 -6.05480800915 y1[1] (closed_form) = 7.42560334963 -6.05480800915 absolute error = 5.022e-14 relative error = 5.241e-13 % Correct digits = 14 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=26635.9MB, alloc=44.3MB, time=347.12 x[1] = 0.7599 2.872 h = 0.001 0.003 y2[1] (numeric) = -5.1062716844 -6.38486880073 y2[1] (closed_form) = -5.1062716844 -6.38486880073 absolute error = 4.657e-14 relative error = 5.697e-13 % Correct digits = 14 h = 0.001 0.003 y1[1] (numeric) = 7.42588800987 -6.06729272384 y1[1] (closed_form) = 7.42588800987 -6.06729272384 absolute error = 5.001e-14 relative error = 5.215e-13 % Correct digits = 14 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=26684.5MB, alloc=44.3MB, time=347.76 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 1 ) = neg ( y1 ) + 1.0 ; diff ( y1 , x , 1 ) = y2 - 1.0 ; Iterations = 754 Total Elapsed Time = 5 Minutes 47 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 5 Minutes 47 Seconds > quit memory used=26697.4MB, alloc=44.3MB, time=347.92