|\^/| 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_y2 := proc(x) > return(sin(c(x))); > end; exact_soln_y2 := proc(x) return sin(c(x)) end proc > exact_soln_y2p := proc(x) > return( cos(c(x))); > end; exact_soln_y2p := proc(x) return cos(c(x)) end proc > exact_soln_y2pp := proc(x) > return( neg( sin(c(x)))); > end; exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc > exact_soln_y1 := proc(x) > return( cos(c(x))); > end; exact_soln_y1 := proc(x) return cos(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, 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0.001 + 0.003*I, 0. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[2,1] + array_given_rad_poles[2,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 4 > glob_least_given_sing := rad_given; > fi;# end if 4; > elif > (glob_type_given_pole = 3) then # if number 4 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > elif > (glob_type_given_pole = 5) then # if number 5 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 5; > if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," "); > if ((float_abs(array_rad_test_poles[2,1]) < glob_least_ratio_sing)) then # if number 6 > glob_least_ratio_sing := array_rad_test_poles[2,1]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," "); > if ((float_abs(array_rad_test_poles[2,2]) < glob_least_3_sing)) then # if number 6 > glob_least_3_sing := array_rad_test_poles[2,2]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," "); > if ((float_abs(array_rad_test_poles[2,3]) < glob_least_6_sing)) then # if number 6 > glob_least_6_sing := array_rad_test_poles[2,3]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 5 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[2, 1] - array_given_rad_poles[2, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_rad_test_poles[2, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles[2, 1], 4, " "); if float_abs(array_rad_test_poles[2, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[2, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[2, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 2] and array_rad_test_poles[2, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles[2, 2], 4, " "); if float_abs(array_rad_test_poles[2, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[2, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 3] and array_rad_test_poles[2, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles[2, 3], 4, " "); if float_abs(array_rad_test_poles[2, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[2, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[2, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 5 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 5; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_3, > array_const_0D0, > array_const_1, #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_g, > 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_3, array_const_0D0, array_const_1, 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_g, 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_3, > array_const_0D0, > array_const_1, #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_g, > 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_3, array_const_0D0, array_const_1, 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_g, 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_3, > array_const_0D0, > array_const_1, #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_g, > 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_3, array_const_0D0, array_const_1, 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_g, 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_3, > array_const_0D0, > array_const_1, #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_g, > 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_3, array_const_0D0, array_const_1, 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_g, 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_3, > array_const_0D0, > array_const_1, #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_g, > 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_3, array_const_0D0, array_const_1, 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_g, 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_3, > array_const_0D0, > array_const_1, #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_g, > 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_3, array_const_0D0, array_const_1, 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_g, 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_3, > array_const_0D0, > array_const_1, #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_g, > 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 - 3 - 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 - 3 - 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 - 3 - 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_3, array_const_0D0, array_const_1, 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_g, 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 - 13; 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 - 13; 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 - 13; 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_3, > array_const_0D0, > array_const_1, #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_g, > 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 cos 1 $eq_no = 1 > array_tmp1[1] := cos(array_x[1]); > array_tmp1_g[1] := sin(array_x[1]); > #emit pre neg FULL $eq_no = 1 > array_tmp2[1] := neg(array_tmp1[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[1]) * (expt((glob_h) , c(3))) * c(factorial_3(0,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[2,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[3,2] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(1); > array_y2_higher[4,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre neg FULL $eq_no = 2 > array_tmp5[1] := neg(array_y2[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 cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1); > array_tmp1_g[2] := array_tmp1[1] * array_x[2] / c(1); > #emit pre neg FULL $eq_no = 1 > array_tmp2[2] := neg(array_tmp1[2]); > #emit pre add CONST FULL $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[1,5]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[2]) * (expt((glob_h) , c(3))) * c(factorial_3(1,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[2,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[3,3] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[4,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre neg FULL $eq_no = 2 > array_tmp5[2] := neg(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 cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2); > array_tmp1_g[3] := array_tmp1[2] * array_x[2] / c(2); > #emit pre neg FULL $eq_no = 1 > array_tmp2[3] := neg(array_tmp1[3]); > #emit pre add CONST FULL $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[1,6]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[3]) * (expt((glob_h) , c(3))) * c(factorial_3(2,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[2,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[3,4] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[4,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre neg FULL $eq_no = 2 > array_tmp5[3] := neg(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 cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3); > array_tmp1_g[4] := array_tmp1[3] * array_x[2] / c(3); > #emit pre neg FULL $eq_no = 1 > array_tmp2[4] := neg(array_tmp1[4]); > #emit pre add CONST FULL $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[1,7]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[4]) * (expt((glob_h) , c(3))) * c(factorial_3(3,6)); > if (7 <= ATS_MAX_TERMS) then # if number 3 > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[2,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[3,5] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[4,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre neg FULL $eq_no = 2 > array_tmp5[4] := neg(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 cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4); > array_tmp1_g[5] := array_tmp1[4] * array_x[2] / c(4); > #emit pre neg FULL $eq_no = 1 > array_tmp2[5] := neg(array_tmp1[5]); > #emit pre add CONST FULL $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[1,8]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[5]) * (expt((glob_h) , c(3))) * c(factorial_3(4,7)); > if (8 <= ATS_MAX_TERMS) then # if number 3 > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(7); > array_y2_higher[2,7] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(6); > array_y2_higher[3,6] := c(temporary); > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[4,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre neg FULL $eq_no = 2 > array_tmp5[5] := neg(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 cos LINEAR $eq_no = 1 > array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1); > array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1); > #emit neg FULL $eq_no = 1 > array_tmp2[kkk] := neg(array_tmp1[kkk]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 3; > 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 neg FULL $eq_no = 2 > array_tmp5[kkk] := neg(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_3, array_const_0D0, array_const_1, 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_g, 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] := cos(array_x[1]); array_tmp1_g[1] := sin(array_x[1]); array_tmp2[1] := neg(array_tmp1[1]); array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y2_set_initial[1, 4] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp3[1])*expt(glob_h, c(3))*c(factorial_3(0, 3)); if 4 <= ATS_MAX_TERMS then array_y2[4] := temporary; array_y2_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[2, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[3, 2] := c(temporary); temporary := c(temporary)*c(1)/c(glob_h); array_y2_higher[4, 1] := c(temporary) end if end if; kkk := 2; array_tmp5[1] := neg(array_y2[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_tmp1_g[1])*array_x[2]/c(1); array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1); array_tmp2[2] := neg(array_tmp1[2]); array_tmp3[2] := array_tmp2[2]; if not array_y2_set_initial[1, 5] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp3[2])*expt(glob_h, c(3))*c(factorial_3(1, 4)); if 5 <= ATS_MAX_TERMS then array_y2[5] := temporary; array_y2_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[2, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[3, 3] := c(temporary); temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[4, 2] := c(temporary) end if end if; kkk := 3; array_tmp5[2] := neg(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_tmp1_g[2])*array_x[2]/c(2); array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2); array_tmp2[3] := neg(array_tmp1[3]); array_tmp3[3] := array_tmp2[3]; if not array_y2_set_initial[1, 6] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp3[3])*expt(glob_h, c(3))*c(factorial_3(2, 5)); if 6 <= ATS_MAX_TERMS then array_y2[6] := temporary; array_y2_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[2, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[3, 4] := c(temporary); temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[4, 3] := c(temporary) end if end if; kkk := 4; array_tmp5[3] := neg(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_tmp1_g[3])*array_x[2]/c(3); array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3); array_tmp2[4] := neg(array_tmp1[4]); array_tmp3[4] := array_tmp2[4]; if not array_y2_set_initial[1, 7] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp3[4])*expt(glob_h, c(3))*c(factorial_3(3, 6)); if 7 <= ATS_MAX_TERMS then array_y2[7] := temporary; array_y2_higher[1, 7] := temporary end if; temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[2, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[3, 5] := c(temporary); temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[4, 4] := c(temporary) end if end if; kkk := 5; array_tmp5[4] := neg(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_tmp1_g[4])*array_x[2]/c(4); array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4); array_tmp2[5] := neg(array_tmp1[5]); array_tmp3[5] := array_tmp2[5]; if not array_y2_set_initial[1, 8] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp3[5])*expt(glob_h, c(3))*c(factorial_3(4, 7)); if 8 <= ATS_MAX_TERMS then array_y2[8] := temporary; array_y2_higher[1, 8] := temporary end if; temporary := c(temporary)*c(7)/c(glob_h); array_y2_higher[2, 7] := c(temporary); temporary := c(temporary)*c(6)/c(glob_h); array_y2_higher[3, 6] := c(temporary); temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[4, 5] := c(temporary) end if end if; kkk := 6; array_tmp5[5] := neg(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_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1) ; array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp2[kkk] := neg(array_tmp1[kkk]); array_tmp3[kkk] := array_tmp2[kkk]; order_d := 3; 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] := neg(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_3, > array_const_0D0, > array_const_1, > #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_g, > 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:=32; > 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_g:= 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..(4) ,(0..40+ 1),[]); > array_y2_higher_work := Array(0..(4) ,(0..40+ 1),[]); > array_y2_higher_work2 := Array(0..(4) ,(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_g[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 <=4) 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 <=4) 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 <=4) 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_g); > 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_3); > array_const_3[1] := c(3); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_m1); > array_m1[1] := glob__m1; > #END SYMBOLS INITIALIZATED > # before generate factorials init > #Initing Factorial Tables > iiif := 0; > while (iiif <= ATS_MAX_TERMS) do # do number 1 > jjjf := 0; > while (jjjf <= ATS_MAX_TERMS) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Table > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > glob_no_sing_tests := 4; > glob_ratio_test := 1; > glob_three_term_test := 2; > glob_six_term_test := 3; > glob_log_10 := log(c(10.0)); > MAX_UNCHANGED := 10; > glob__small := c(0.1e-50); > glob_small_float := c(0.1e-50); > glob_smallish_float := c(0.1e-60); > glob_large_float := c(1.0e100); > glob_larger_float := c(1.1e100); > glob__m2 := c(-2); > glob__m1 := c(-1); > glob__0 := c(0); > glob__1 := c(1); > glob__2 := c(2); > glob__3 := c(3); > glob__4 := c(4); > glob__5 := c(5); > glob__8 := c(8); > glob__10 := c(10); > glob__100 := c(100); > glob__pi := c(0.0); > glob__0_5 := c(0.5); > glob__0_8 := c(0.8); > glob__m0_8 := c(-0.8); > glob__0_25 := c(0.25); > glob__0_125 := c(0.125); > glob_h := 0.1; > glob_nxt := 1; > glob_prec := c(1.0e-16); > glob_check_sign := c(1.0); > glob_desired_digits_correct := c(8.0); > glob_max_estimated_step_error := c(0.0); > glob_ratio_of_radius := c(0.1); > glob_percent_done := c(0.0); > glob_total_exp_sec := c(0.1); > glob_optimal_expect_sec := c(0.1); > glob_estimated_size_answer := c(100.0); > glob_almost_1 := c(0.9990); > glob_clock_sec := c(0.0); > glob_clock_start_sec := c(0.0); > glob_disp_incr := c(0.1); > glob_diff_rc_fm := c(0.1); > glob_diff_rc_fmm1 := c(0.1); > glob_diff_rc_fmm2 := c(0.1); > glob_diff_ord_fm := c(0.1); > glob_diff_ord_fmm1 := c(0.1); > glob_diff_ord_fmm2 := c(0.1); > glob_six_term_ord_save := c(0.1); > glob_guess_error_rc := c(0.1); > glob_guess_error_ord := c(0.1); > glob_least_given_sing := c(9.9e200); > glob_least_ratio_sing := c(9.9e200); > glob_least_3_sing := c(9.9e100); > glob_least_6_sing := c(9.9e100); > glob_last_good_h := c(0.1); > glob_max_h := c(0.1); > glob_min_h := c(0.000001); > glob_display_interval := c(0.1); > glob_abserr := c(0.1e-10); > glob_relerr := c(0.1e-10); > glob_min_pole_est := c(0.1e+10); > glob_max_rel_trunc_err := c(0.1e-10); > glob_max_trunc_err := c(0.1e-10); > glob_max_hours := c(0.0); > glob_optimal_clock_start_sec := c(0.0); > glob_optimal_start := c(0.0); > glob_upper_ratio_limit := c(1.0001); > glob_lower_ratio_limit := c(0.9999); > glob_max_sec := c(10000.0); > glob_orig_start_sec := c(0.0); > glob_normmax := c(0.0); > glob_max_minutes := c(0.0); > glob_next_display := c(0.0); > glob_est_digits := 1; > glob_subiter_method := 3; > glob_html_log := true; > glob_min_good_digits := 99999; > glob_good_digits := 0; > glob_min_apfp_est_good_digits := 99999; > glob_apfp_est_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_h_reason := 0; > glob_sec_in_minute := 60 ; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_type_given_pole := 0; > glob_optimize := false; > glob_look_poles := false; > glob_dump_closed_form := false; > glob_max_iter := 10000; > glob_no_eqs := 0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_start := 0; > glob_iter := 0; > # before generate set diff initial > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := 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/mtest4postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; "); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > 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,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=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_y2 := proc(x)"); > omniout_str(ALWAYS,"return(sin(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return( cos(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return( neg( sin(c(x))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return( cos(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > glob_look_poles := true; > glob_type_given_pole := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=8; > glob_max_minutes:=(3.0); > glob_subiter_method:=3; > glob_max_iter:=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 := 3; > #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 <= 4) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 4 + 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 := 4; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 19 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 19; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 19 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 19; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; "); > omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; "); > 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,"2017-11-26T15:23:59-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest4") > ; > logitem_str(html_log_file,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ") > ; > 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,"mtest4 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest4 maple results") > ; > logitem_str(html_log_file,"Poor Accuracy - Not sure of algorithm for multiple equations") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ") > ; > 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_3, array_const_0D0, array_const_1, 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_g, 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 := 32; 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_g := 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 .. 4, 0 .. 41, []); array_y2_higher_work := Array(0 .. 4, 0 .. 41, []); array_y2_higher_work2 := Array(0 .. 4, 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_g[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 <= 4 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 <= 4 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 <= 4 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_g); 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_3); array_const_3[1] := c(3); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_m1); array_m1[1] := glob__m1; iiif := 0; while iiif <= ATS_MAX_TERMS do jjjf := 0; while jjjf <= ATS_MAX_TERMS do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; glob_no_sing_tests := 4; glob_ratio_test := 1; glob_three_term_test := 2; glob_six_term_test := 3; glob_log_10 := log(c(10.0)); MAX_UNCHANGED := 10; glob__small := c(0.1*10^(-50)); glob_small_float := c(0.1*10^(-50)); glob_smallish_float := c(0.1*10^(-60)); glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob__m2 := c(-2); glob__m1 := c(-1); glob__0 := c(0); glob__1 := c(1); glob__2 := c(2); glob__3 := c(3); glob__4 := c(4); glob__5 := c(5); glob__8 := c(8); glob__10 := c(10); glob__100 := c(100); glob__pi := c(0.); glob__0_5 := c(0.5); glob__0_8 := c(0.8); glob__m0_8 := c(-0.8); glob__0_25 := c(0.25); glob__0_125 := c(0.125); glob_h := 0.1; glob_nxt := 1; glob_prec := c(0.10*10^(-15)); glob_check_sign := c(1.0); glob_desired_digits_correct := c(8.0); glob_max_estimated_step_error := c(0.); glob_ratio_of_radius := c(0.1); glob_percent_done := c(0.); glob_total_exp_sec := c(0.1); glob_optimal_expect_sec := c(0.1); glob_estimated_size_answer := c(100.0); glob_almost_1 := c(0.9990); glob_clock_sec := c(0.); glob_clock_start_sec := c(0.); glob_disp_incr := c(0.1); glob_diff_rc_fm := c(0.1); glob_diff_rc_fmm1 := c(0.1); glob_diff_rc_fmm2 := c(0.1); glob_diff_ord_fm := c(0.1); glob_diff_ord_fmm1 := c(0.1); glob_diff_ord_fmm2 := c(0.1); glob_six_term_ord_save := c(0.1); glob_guess_error_rc := c(0.1); glob_guess_error_ord := c(0.1); glob_least_given_sing := c(0.99*10^201); glob_least_ratio_sing := c(0.99*10^201); glob_least_3_sing := c(0.99*10^101); glob_least_6_sing := c(0.99*10^101); glob_last_good_h := c(0.1); glob_max_h := c(0.1); glob_min_h := c(0.1*10^(-5)); glob_display_interval := c(0.1); glob_abserr := c(0.1*10^(-10)); glob_relerr := c(0.1*10^(-10)); glob_min_pole_est := c(0.1*10^10); glob_max_rel_trunc_err := c(0.1*10^(-10)); glob_max_trunc_err := c(0.1*10^(-10)); glob_max_hours := c(0.); glob_optimal_clock_start_sec := c(0.); glob_optimal_start := c(0.); glob_upper_ratio_limit := c(1.0001); glob_lower_ratio_limit := c(0.9999); glob_max_sec := c(10000.0); glob_orig_start_sec := c(0.); glob_normmax := c(0.); glob_max_minutes := c(0.); glob_next_display := c(0.); glob_est_digits := 1; glob_subiter_method := 3; glob_html_log := true; glob_min_good_digits := 99999; glob_good_digits := 0; glob_min_apfp_est_good_digits := 99999; glob_apfp_est_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_h_reason := 0; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_type_given_pole := 0; glob_optimize := false; glob_look_poles := false; glob_dump_closed_form := false; glob_max_iter := 10000; glob_no_eqs := 0; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_start := 0; glob_iter := 0; array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := 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/mtest4postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; "); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); 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, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=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_y2 := proc(x)"); omniout_str(ALWAYS, "return(sin(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return( cos(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return( neg( sin(c(x))));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return( cos(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 * 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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, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * 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(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); glob_look_poles := true; glob_type_given_pole := 3; glob_desired_digits_correct := 8; glob_max_minutes := 3.0; glob_subiter_method := 3; glob_max_iter := 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 := 3; 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 <= 4 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 4 + 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 := 4; ord := 4; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 4; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 3; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 3; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 3; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 4; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 3; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; "); omniout_str(INFO, "diff ( y1 , x , 1 ) = neg ( y2 ) ; "); 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, "2017-11-26T15:23:59-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest4"); logitem_str(html_log_file, "diff ( y2 , x , 3 ) = n\ eg ( cos ( x ) ) ; "); 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, "mtest4 diffeq.mxt"); logitem_str(html_log_file, "mtest4 maple results"); logitem_str(html_log_file, "Poor Accuracy - Not sure of algor\ ithm for multiple equations"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = neg ( y2 ) ; "); 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=3.6MB, alloc=40.3MB, time=0.07 ##############ECHO OF PROBLEM################# ##############temp/mtest4postcpx.cpx################# diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; diff ( y1 , x , 1 ) = neg ( y2 ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); glob_look_poles := true; glob_type_given_pole := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=8; glob_max_minutes:=(3.0); glob_subiter_method:=3; glob_max_iter:=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_y2 := proc(x) return(sin(c(x))); end; exact_soln_y2p := proc(x) return( cos(c(x))); end; exact_soln_y2pp := proc(x) return( neg( sin(c(x)))); end; exact_soln_y1 := proc(x) return( cos(c(x))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion memory used=53.1MB, alloc=40.3MB, time=0.67 x[1] = 0.1 0.1 h = 0.0001 0.005 y2[1] (numeric) = 0.100332999841 0.0996663334921 y2[1] (closed_form) = 0.100332999841 0.0996663334921 absolute error = 0 relative error = 0 % Correct digits = 30 h = 0.0001 0.005 y1[1] (numeric) = 0.999983333337 -0.00999998888889 y1[1] (closed_form) = 0.999983333337 -0.00999998888889 absolute error = 0 relative error = 0 % Correct digits = 30 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1768 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 = 0.1768 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=98.8MB, alloc=40.3MB, time=1.22 memory used=144.9MB, alloc=40.3MB, time=1.79 x[1] = 0.1001 0.105 h = 0.0001 0.003 y2[1] (numeric) = 0.100473841619 0.103666044323 y2[1] (closed_form) = 0.100484303074 0.104666466122 absolute error = 0.001 relative error = 0.6895 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.0004816233 -0.0105121718948 y1[1] (closed_form) = 1.00048412347 -0.0105122476776 absolute error = 2.501e-06 relative error = 0.00025 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08713 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 = 0.08713 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=190.6MB, alloc=40.3MB, time=2.36 memory used=236.8MB, alloc=40.3MB, time=2.93 x[1] = 0.1002 0.108 h = 0.001 0.001 y2[1] (numeric) = 0.100616375263 0.10766737703 y2[1] (closed_form) = 0.100616371804 0.107667312081 absolute error = 6.504e-08 relative error = 4.414e-05 % Correct digits = 6 h = 0.001 0.001 y1[1] (numeric) = 1.00078856852 -0.0108243734538 y1[1] (closed_form) = 1.00079256889 -0.0108245151295 absolute error = 4.003e-06 relative error = 0.0003999 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06949 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 = 0.06949 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=282.6MB, alloc=40.3MB, time=3.50 x[1] = 0.1012 0.109 h = 0.001 0.003 y2[1] (numeric) = 0.10076060456 0.111670370011 y2[1] (closed_form) = 0.101628096885 0.108657179181 absolute error = 0.003136 relative error = 2.108 % Correct digits = 2 h = 0.001 0.003 y1[1] (numeric) = 1.00079754891 -0.0110347305372 y1[1] (closed_form) = 1.00079960894 -0.0110337996083 absolute error = 2.261e-06 relative error = 0.0002259 % Correct digits = 6 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.333 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 = 0.333 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=328.5MB, alloc=40.3MB, time=4.05 memory used=374.6MB, alloc=40.3MB, time=4.62 x[1] = 0.1022 0.112 h = 0.0001 0.004 y2[1] (numeric) = 0.1009065357 0.115675029355 y2[1] (closed_form) = 0.102662734747 0.111648676907 absolute error = 0.004393 relative error = 2.896 % Correct digits = 2 h = 0.0001 0.004 y1[1] (numeric) = 1.00103773316 -0.0114509033802 y1[1] (closed_form) = 1.00102792236 -0.0114503883919 absolute error = 9.824e-06 relative error = 0.0009814 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1921 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 = 0.1921 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=420.2MB, alloc=40.3MB, time=5.18 memory used=466.2MB, alloc=40.3MB, time=5.74 x[1] = 0.1023 0.116 h = 0.003 0.006 y2[1] (numeric) = 0.101054187418 0.11968137719 y2[1] (closed_form) = 0.102809505465 0.115652505773 absolute error = 0.004395 relative error = 2.84 % Correct digits = 2 h = 0.003 0.006 y1[1] (numeric) = 1.00149834738 -0.0118665920569 y1[1] (closed_form) = 1.00147225055 -0.0118726973391 absolute error = 2.680e-05 relative error = 0.002676 % Correct digits = 5 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2598 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 = 0.2598 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=511.9MB, alloc=40.3MB, time=6.30 memory used=558.0MB, alloc=40.3MB, time=6.86 x[1] = 0.1053 0.122 h = 0.0001 0.005 y2[1] (numeric) = 0.101203617471 0.12368946749 y2[1] (closed_form) = 0.105888677761 0.121625440337 absolute error = 0.00512 relative error = 3.175 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.00192507279 -0.0128384203568 y1[1] (closed_form) = 1.00187103916 -0.0128547054021 absolute error = 5.643e-05 relative error = 0.005632 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1205 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 = 0.1205 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=603.6MB, alloc=40.3MB, time=7.42 x[1] = 0.1054 0.127 h = 0.0001 0.003 y2[1] (numeric) = 0.10135502708 0.127699365406 y2[1] (closed_form) = 0.106054523806 0.126634997662 absolute error = 0.004819 relative error = 2.917 % Correct digits = 2 h = 0.0001 0.003 y1[1] (numeric) = 1.00254341618 -0.0133573855475 y1[1] (closed_form) = 1.00248109187 -0.0133969752478 absolute error = 7.384e-05 relative error = 0.007365 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0994 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 = 0.0994 Order of pole (three term test) = 32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=649.4MB, alloc=40.3MB, time=7.98 memory used=695.7MB, alloc=40.3MB, time=8.55 x[1] = 0.1055 0.13 h = 0.001 0.001 y2[1] (numeric) = 0.101508472579 0.131711167183 y2[1] (closed_form) = 0.106195478058 0.129641643138 absolute error = 0.005124 relative error = 3.057 % Correct digits = 2 h = 0.001 0.001 y1[1] (numeric) = 1.00292238834 -0.0136746507979 y1[1] (closed_form) = 1.00285489407 -0.0137281638158 absolute error = 8.613e-05 relative error = 0.008588 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07919 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 = 0.07919 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=741.5MB, alloc=40.3MB, time=9.12 memory used=787.7MB, alloc=40.3MB, time=9.68 x[1] = 0.1065 0.131 h = 0.001 0.003 y2[1] (numeric) = 0.101663957884 0.135724911282 y2[1] (closed_form) = 0.107212191087 0.130630663334 absolute error = 0.007532 relative error = 4.457 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.00295452017 -0.0139099547201 y1[1] (closed_form) = 1.00287832643 -0.0139650037997 absolute error = 9.400e-05 relative error = 0.009372 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.379 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 = 0.379 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=833.4MB, alloc=40.3MB, time=10.25 memory used=879.5MB, alloc=40.3MB, time=10.81 x[1] = 0.1075 0.134 h = 0.0001 0.004 y2[1] (numeric) = 0.101821489214 0.139740603789 y2[1] (closed_form) = 0.108257789554 0.133625537144 absolute error = 0.008878 relative error = 5.162 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.00326597541 -0.0143529149717 y1[1] (closed_form) = 1.00316697577 -0.014420336423 absolute error = 0.0001198 relative error = 0.01194 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2183 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 = 0.2183 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=925.1MB, alloc=40.3MB, time=11.37 x[1] = 0.1076 0.138 h = 0.003 0.006 y2[1] (numeric) = 0.101981085408 0.143758266824 y2[1] (closed_form) = 0.108416707526 0.137637798716 absolute error = 0.008881 relative error = 5.069 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.00382278237 -0.0147746943574 y1[1] (closed_form) = 1.00369866804 -0.014867247953 absolute error = 0.0001548 relative error = 0.01542 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2949 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 = 0.2949 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=970.7MB, alloc=40.3MB, time=11.92 memory used=1016.7MB, alloc=40.3MB, time=12.48 x[1] = 0.1106 0.144 h = 0.0001 0.005 y2[1] (numeric) = 0.102142804514 0.147777954309 y2[1] (closed_form) = 0.111520997949 0.143615303875 absolute error = 0.01026 relative error = 5.643 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.00439120473 -0.0158243687342 y1[1] (closed_form) = 1.00421252288 -0.015948936748 absolute error = 0.0002178 relative error = 0.02169 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1361 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 = 0.1361 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1062.3MB, alloc=40.3MB, time=13.04 memory used=1108.4MB, alloc=40.3MB, time=13.61 x[1] = 0.1107 0.149 h = 0.0001 0.003 y2[1] (numeric) = 0.102306848413 0.151799730948 y2[1] (closed_form) = 0.111702630738 0.148636531188 absolute error = 0.009914 relative error = 5.332 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.00512992559 -0.0163504707422 y1[1] (closed_form) = 1.00493198983 -0.0165216071589 absolute error = 0.0002617 relative error = 0.02603 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1122 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 = 0.1122 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1154.2MB, alloc=40.3MB, time=14.17 memory used=1200.3MB, alloc=40.3MB, time=14.75 x[1] = 0.1108 0.152 h = 0.001 0.001 y2[1] (numeric) = 0.102473273868 0.15582369305 y2[1] (closed_form) = 0.111853235979 0.151650314108 absolute error = 0.01027 relative error = 5.448 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.00558112118 -0.0166730214823 y1[1] (closed_form) = 1.005371242 -0.0168719550168 absolute error = 0.0002892 relative error = 0.02876 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08927 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 = 0.08927 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1246.2MB, alloc=40.3MB, time=15.31 x[1] = 0.1118 0.153 h = 0.001 0.003 y2[1] (numeric) = 0.102642084924 0.159849879162 y2[1] (closed_form) = 0.112875631156 0.152638701201 absolute error = 0.01252 relative error = 6.595 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.0056364003 -0.0169334155633 y1[1] (closed_form) = 1.00541102212 -0.0171364639514 absolute error = 0.0003034 relative error = 0.03017 % Correct digits = 4 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4269 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 = 0.4269 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1291.8MB, alloc=40.3MB, time=15.87 memory used=1338.0MB, alloc=40.3MB, time=16.43 x[1] = 0.1128 0.156 h = 0.0001 0.004 y2[1] (numeric) = 0.102813287836 0.163878295364 y2[1] (closed_form) = 0.113933365397 0.155638072673 absolute error = 0.01384 relative error = 7.176 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.00601926452 -0.0174034619231 y1[1] (closed_form) = 1.00576003279 -0.0176308153291 absolute error = 0.0003448 relative error = 0.03428 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2455 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 = 0.2455 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1383.8MB, alloc=40.3MB, time=17.00 memory used=1429.8MB, alloc=40.3MB, time=17.55 x[1] = 0.1129 0.16 h = 0.003 0.006 y2[1] (numeric) = 0.102986901561 0.167908963776 y2[1] (closed_form) = 0.114105438808 0.159660559171 absolute error = 0.01384 relative error = 7.055 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.00667254829 -0.0178316508402 y1[1] (closed_form) = 1.00637922732 -0.0181026571991 absolute error = 0.0003994 relative error = 0.03968 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3312 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 = 0.3312 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1475.5MB, alloc=40.3MB, time=18.12 x[1] = 0.1159 0.166 h = 0.0001 0.005 y2[1] (numeric) = 0.103162984476 0.171941938279 y2[1] (closed_form) = 0.117237656736 0.165644636231 absolute error = 0.01542 relative error = 7.598 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.00738287564 -0.018959874983 y1[1] (closed_form) = 1.0070081304 -0.0192846397327 absolute error = 0.0004959 relative error = 0.04923 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1524 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 = 0.1524 Order of pole (three term test) = 31.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1521.4MB, alloc=40.3MB, time=18.68 memory used=1567.4MB, alloc=40.3MB, time=19.24 x[1] = 0.116 0.171 h = 0.0001 0.003 y2[1] (numeric) = 0.103341739229 0.175977283111 y2[1] (closed_form) = 0.117436330118 0.170679780464 absolute error = 0.01506 relative error = 7.268 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.00824234747 -0.0194935315977 y1[1] (closed_form) = 1.00783720606 -0.0198881395948 absolute error = 0.0005656 relative error = 0.05611 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1254 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 = 0.1254 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1611.4MB, alloc=40.3MB, time=19.77 memory used=1657.8MB, alloc=40.3MB, time=20.34 x[1] = 0.1161 0.174 h = 0.001 0.001 y2[1] (numeric) = 0.103523223061 0.180015094678 y2[1] (closed_form) = 0.11759735788 0.173702039755 absolute error = 0.01543 relative error = 7.354 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.00876599219 -0.0198216279562 y1[1] (closed_form) = 1.00834202675 -0.0202579089155 absolute error = 0.0006083 relative error = 0.06032 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09967 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 = 0.09967 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1703.7MB, alloc=40.3MB, time=20.91 memory used=1749.8MB, alloc=40.3MB, time=21.48 x[1] = 0.1171 0.175 h = 0.001 0.003 y2[1] (numeric) = 0.103707440157 0.184055411627 y2[1] (closed_form) = 0.118626131847 0.174690005932 absolute error = 0.01761 relative error = 8.342 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.00884441213 -0.020107278104 y1[1] (closed_form) = 1.00839811108 -0.0205502166739 absolute error = 0.0006288 relative error = 0.06234 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4762 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 = 0.4762 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1795.6MB, alloc=40.3MB, time=22.05 x[1] = 0.1181 0.178 h = 0.0001 0.004 y2[1] (numeric) = 0.103894396811 0.188098240036 y2[1] (closed_form) = 0.119697183615 0.177694995866 absolute error = 0.01892 relative error = 8.831 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.00929884129 -0.0206047567884 y1[1] (closed_form) = 1.00880752691 -0.0210838935875 absolute error = 0.0006863 relative error = 0.06801 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2735 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 = 0.2735 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1841.5MB, alloc=40.3MB, time=22.60 memory used=1887.4MB, alloc=40.3MB, time=23.17 x[1] = 0.1182 0.182 h = 0.003 0.006 y2[1] (numeric) = 0.104084112113 0.192143602029 y2[1] (closed_form) = 0.119883429032 0.181729501103 absolute error = 0.01892 relative error = 8.692 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.01004892522 -0.0210397249553 y1[1] (closed_form) = 1.00951439597 -0.0215810253281 absolute error = 0.0007607 relative error = 0.07534 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3686 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 = 0.3686 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=1933.1MB, alloc=40.3MB, time=23.73 memory used=1979.2MB, alloc=40.3MB, time=24.30 x[1] = 0.1212 0.188 h = 0.0001 0.005 y2[1] (numeric) = 0.104276644808 0.196191551456 y2[1] (closed_form) = 0.123046398106 0.187722147852 absolute error = 0.02059 relative error = 9.174 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.01090138897 -0.0222473078433 y1[1] (closed_form) = 1.01025835835 -0.0228639871644 absolute error = 0.0008909 relative error = 0.08817 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 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 = 0.1691 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2024.9MB, alloc=40.3MB, time=24.85 memory used=2070.9MB, alloc=40.3MB, time=25.41 x[1] = 0.1213 0.193 h = 0.0001 0.003 y2[1] (numeric) = 0.104472198418 0.200242152073 y2[1] (closed_form) = 0.123263376946 0.192773458308 absolute error = 0.02022 relative error = 8.837 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.01188203468 -0.022789000333 y1[1] (closed_form) = 1.01119727997 -0.0234987849821 absolute error = 0.0009862 relative error = 0.09751 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1389 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 = 0.1389 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2116.7MB, alloc=40.3MB, time=25.98 x[1] = 0.1214 0.196 h = 0.001 0.001 y2[1] (numeric) = 0.10467083071 0.204295500413 y2[1] (closed_form) = 0.12343560549 0.195805534333 absolute error = 0.0206 relative error = 8.898 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.01247838334 -0.0231229409658 y1[1] (closed_form) = 1.01176781311 -0.0238882620851 absolute error = 0.001044 relative error = 0.1032 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1104 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 = 0.1104 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2162.7MB, alloc=40.3MB, time=26.55 memory used=2209.0MB, alloc=40.3MB, time=27.12 x[1] = 0.1224 0.197 h = 0.0001 0.004 y2[1] (numeric) = 0.104872546021 0.208351635239 y2[1] (closed_form) = 0.1244714577 0.196793290103 absolute error = 0.02275 relative error = 9.772 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.01257993525 -0.0234340357324 y1[1] (closed_form) = 1.01184015904 -0.0242085150168 absolute error = 0.001071 relative error = 0.1058 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6668 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 = 0.6668 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2254.8MB, alloc=40.3MB, time=27.68 memory used=2300.9MB, alloc=40.3MB, time=28.24 x[1] = 0.1225 0.201 h = 0.003 0.006 y2[1] (numeric) = 0.105077347298 0.212410570452 y2[1] (closed_form) = 0.124670550712 0.200839764217 absolute error = 0.02275 relative error = 9.626 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.01341096125 -0.0238749725763 y1[1] (closed_form) = 1.01262296704 -0.0247266799437 absolute error = 0.00116 relative error = 0.1146 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4014 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 = 0.4014 Order of pole (three term test) = 31.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2346.7MB, alloc=40.3MB, time=28.80 memory used=2392.8MB, alloc=40.3MB, time=29.36 x[1] = 0.1255 0.207 h = 0.0001 0.005 y2[1] (numeric) = 0.105285289505 0.216472356605 y2[1] (closed_form) = 0.127862128221 0.206841797121 absolute error = 0.02455 relative error = 10.09 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.01438206545 -0.0251493825366 y1[1] (closed_form) = 1.01346721491 -0.0260957947093 absolute error = 0.001316 relative error = 0.1298 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1838 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 = 0.1838 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2438.5MB, alloc=40.3MB, time=29.92 x[1] = 0.1256 0.212 h = 0.0001 0.003 y2[1] (numeric) = 0.105496577006 0.220537057034 y2[1] (closed_form) = 0.128095656788 0.211909065234 absolute error = 0.02419 relative error = 9.769 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.01546404868 -0.0256981862325 y1[1] (closed_form) = 1.01450129208 -0.0267566252526 absolute error = 0.001431 relative error = 0.141 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1508 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 = 0.1508 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2484.1MB, alloc=40.3MB, time=30.49 memory used=2530.4MB, alloc=40.3MB, time=31.06 x[1] = 0.1257 0.215 h = 0.001 0.001 y2[1] (numeric) = 0.105711268057 0.224604768409 y2[1] (closed_form) = 0.128278016733 0.214950812089 absolute error = 0.02454 relative error = 9.806 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.0161212003 -0.0260372542144 y1[1] (closed_form) = 1.01512876276 -0.0271625284212 absolute error = 0.0015 relative error = 0.1478 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1198 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 = 0.1198 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2576.3MB, alloc=40.3MB, time=31.64 memory used=2622.5MB, alloc=40.3MB, time=32.20 x[1] = 0.1267 0.216 h = 0.001 0.003 y2[1] (numeric) = 0.105929367134 0.228675529614 y2[1] (closed_form) = 0.129320523304 0.215938649698 absolute error = 0.02663 relative error = 10.58 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.01624202016 -0.0263697141424 y1[1] (closed_form) = 1.01521540828 -0.0275067724077 absolute error = 0.001532 relative error = 0.1508 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5716 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 = 0.5716 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2668.2MB, alloc=40.3MB, time=32.77 x[1] = 0.1277 0.219 h = 0.0001 0.004 y2[1] (numeric) = 0.106150880613 0.232749346724 y2[1] (closed_form) = 0.13041942861 0.218957267869 absolute error = 0.02791 relative error = 10.95 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.01682811687 -0.0269185458411 y1[1] (closed_form) = 1.01573788214 -0.0281138296284 absolute error = 0.001618 relative error = 0.1592 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3277 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 = 0.3277 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2714.2MB, alloc=40.3MB, time=33.33 memory used=2760.2MB, alloc=40.3MB, time=33.89 x[1] = 0.1278 0.223 h = 0.003 0.006 y2[1] (numeric) = 0.106375827869 0.236826241888 y2[1] (closed_form) = 0.130634589116 0.223019117204 absolute error = 0.02791 relative error = 10.8 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.0177566407 -0.0273670768649 y1[1] (closed_form) = 1.01660878108 -0.0286580356999 absolute error = 0.001727 relative error = 0.1699 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4407 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 = 0.4407 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2805.9MB, alloc=40.3MB, time=34.45 memory used=2852.1MB, alloc=40.3MB, time=35.01 x[1] = 0.1308 0.229 h = 0.0001 0.005 y2[1] (numeric) = 0.106604268437 0.240906268935 y2[1] (closed_form) = 0.13386219218 0.229033462834 absolute error = 0.02973 relative error = 11.21 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.01887036741 -0.0287226133327 y1[1] (closed_form) = 1.01756819591 -0.0301295987246 absolute error = 0.001917 relative error = 0.1883 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2013 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 = 0.2013 Order of pole (three term test) = 31.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2897.9MB, alloc=40.3MB, time=35.57 memory used=2944.1MB, alloc=40.3MB, time=36.14 x[1] = 0.1309 0.234 h = 0.0001 0.003 y2[1] (numeric) = 0.106836407759 0.244989490687 y2[1] (closed_form) = 0.134116386021 0.234121106838 absolute error = 0.02937 relative error = 10.88 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.02007443346 -0.0292805082203 y1[1] (closed_form) = 1.01871268108 -0.0308227013598 absolute error = 0.002057 relative error = 0.2019 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1651 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 = 0.1651 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=2989.9MB, alloc=40.3MB, time=36.70 x[1] = 0.131 0.237 h = 0.001 0.001 y2[1] (numeric) = 0.107072304708 0.249076003999 y2[1] (closed_form) = 0.13431139908 0.237175179306 absolute error = 0.02973 relative error = 10.91 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.02080483546 -0.0296260735958 y1[1] (closed_form) = 1.01940620362 -0.0312489074978 absolute error = 0.002142 relative error = 0.2101 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 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 = 0.131 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3035.9MB, alloc=40.3MB, time=37.27 memory used=3082.1MB, alloc=40.3MB, time=37.84 x[1] = 0.132 0.238 h = 0.001 0.003 y2[1] (numeric) = 0.10731196393 0.253165847901 y2[1] (closed_form) = 0.135362291695 0.238163201941 absolute error = 0.03181 relative error = 11.61 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.02094876429 -0.0299843860646 y1[1] (closed_form) = 1.01950903603 -0.0316214135167 absolute error = 0.00218 relative error = 0.2137 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6248 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 = 0.6248 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3127.9MB, alloc=40.3MB, time=38.40 memory used=3174.0MB, alloc=40.3MB, time=38.97 x[1] = 0.133 0.241 h = 0.0001 0.004 y2[1] (numeric) = 0.107555391855 0.257259028472 y2[1] (closed_form) = 0.136477925424 0.241190657123 absolute error = 0.03309 relative error = 11.94 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.02160696741 -0.0305618983134 y1[1] (closed_form) = 1.02009214664 -0.0322688500487 absolute error = 0.002282 relative error = 0.2236 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3579 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 = 0.3579 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3219.8MB, alloc=40.3MB, time=39.54 memory used=3265.8MB, alloc=40.3MB, time=40.10 x[1] = 0.1331 0.245 h = 0.003 0.006 y2[1] (numeric) = 0.107802608028 0.26135556788 y2[1] (closed_form) = 0.136710198818 0.245269683389 absolute error = 0.03308 relative error = 11.78 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.0226334276 -0.0310185437498 y1[1] (closed_form) = 1.02105140668 -0.0328395484898 absolute error = 0.002412 relative error = 0.2361 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4809 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 = 0.4809 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3311.7MB, alloc=40.3MB, time=40.66 x[1] = 0.1361 0.251 h = 0.0001 0.005 y2[1] (numeric) = 0.108053672467 0.265455519955 y2[1] (closed_form) = 0.139976701625 0.251298331088 absolute error = 0.03492 relative error = 12.14 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.02389007571 -0.0324563263878 y1[1] (closed_form) = 1.02212608268 -0.0344144544453 absolute error = 0.002636 relative error = 0.2577 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2193 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 = 0.2193 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3357.5MB, alloc=40.3MB, time=41.22 memory used=3403.5MB, alloc=40.3MB, time=41.79 x[1] = 0.1362 0.256 h = 0.0001 0.003 y2[1] (numeric) = 0.108308791796 0.269558946984 y2[1] (closed_form) = 0.140252863161 0.256408611272 absolute error = 0.03454 relative error = 11.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.02521679232 -0.03302398153 y1[1] (closed_form) = 1.023381336 -0.035140412088 absolute error = 0.002801 relative error = 0.2736 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1796 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 = 0.1796 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3449.3MB, alloc=40.3MB, time=42.35 memory used=3495.5MB, alloc=40.3MB, time=42.92 x[1] = 0.1363 0.259 h = 0.001 0.001 y2[1] (numeric) = 0.108568025555 0.273665946037 y2[1] (closed_form) = 0.140461330509 0.259476356295 absolute error = 0.03491 relative error = 11.83 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.02602078496 -0.0333764569413 y1[1] (closed_form) = 1.02414112719 -0.0355872772541 absolute error = 0.002902 relative error = 0.2832 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1425 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 = 0.1425 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3541.3MB, alloc=40.3MB, time=43.48 x[1] = 0.1373 0.26 h = 0.001 0.003 y2[1] (numeric) = 0.108831378574 0.277776556308 y2[1] (closed_form) = 0.141521318719 0.26046476933 absolute error = 0.03699 relative error = 12.48 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.02618780655 -0.0337608772499 y1[1] (closed_form) = 1.0242601065 -0.0359882391217 absolute error = 0.002946 relative error = 0.2874 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6793 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 = 0.6793 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3587.3MB, alloc=40.3MB, time=44.04 memory used=3633.4MB, alloc=40.3MB, time=44.60 x[1] = 0.1383 0.263 h = 0.0001 0.004 y2[1] (numeric) = 0.109098857337 0.281890783878 y2[1] (closed_form) = 0.14265489557 0.263502181622 absolute error = 0.03826 relative error = 12.77 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.02691834188 -0.0343676049381 y1[1] (closed_form) = 1.02490396873 -0.0366764861378 absolute error = 0.003064 relative error = 0.2988 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 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 = 0.3888 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3679.2MB, alloc=40.3MB, time=45.16 memory used=3725.3MB, alloc=40.3MB, time=45.72 x[1] = 0.1384 0.267 h = 0.003 0.006 y2[1] (numeric) = 0.109370481577 0.286008650942 y2[1] (closed_form) = 0.142905339051 0.267600190372 absolute error = 0.03826 relative error = 12.61 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.02804321609 -0.034832937173 y1[1] (closed_form) = 1.02595189411 -0.0372741608594 absolute error = 0.003215 relative error = 0.3131 % Correct digits = 3 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5221 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 = 0.5221 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3771.0MB, alloc=40.3MB, time=46.30 memory used=3817.0MB, alloc=40.3MB, time=46.86 x[1] = 0.1414 0.273 h = 0.0001 0.005 y2[1] (numeric) = 0.109646311831 0.290130211342 y2[1] (closed_form) = 0.146213636862 0.273645126931 absolute error = 0.04011 relative error = 12.93 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.02944310671 -0.0363541927622 y1[1] (closed_form) = 1.02714195396 -0.0389533784147 absolute error = 0.003471 relative error = 0.3377 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2377 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 = 0.2377 Order of pole (three term test) = 31.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3862.8MB, alloc=40.3MB, time=47.42 x[1] = 0.1415 0.278 h = 0.0001 0.003 y2[1] (numeric) = 0.109926556017 0.294255526809 y2[1] (closed_form) = 0.14651308381 0.278780308783 absolute error = 0.03972 relative error = 12.61 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.03089309086 -0.0369323423248 y1[1] (closed_form) = 1.02850837843 -0.0397128147928 absolute error = 0.003663 relative error = 0.3559 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1946 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 = 0.1946 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=3908.8MB, alloc=40.3MB, time=47.98 memory used=3955.0MB, alloc=40.3MB, time=48.55 x[1] = 0.1416 0.281 h = 0.001 0.001 y2[1] (numeric) = 0.110211274391 0.298384694658 y2[1] (closed_form) = 0.146735815944 0.281863076396 absolute error = 0.04009 relative error = 12.62 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.03177104337 -0.0372921799297 y1[1] (closed_form) = 1.02933468047 -0.0401807199198 absolute error = 0.003779 relative error = 0.3668 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1542 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 = 0.1542 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4000.9MB, alloc=40.3MB, time=49.11 memory used=4047.1MB, alloc=40.3MB, time=49.68 x[1] = 0.1426 0.282 h = 0.001 0.003 y2[1] (numeric) = 0.110500471975 0.302517754264 y2[1] (closed_form) = 0.147805613537 0.282852083264 absolute error = 0.04217 relative error = 13.21 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.03196113877 -0.0377029863293 y1[1] (closed_form) = 1.0294697674 -0.0406103481919 absolute error = 0.003829 relative error = 0.3716 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7352 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 = 0.7352 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4092.9MB, alloc=40.3MB, time=50.25 memory used=4139.1MB, alloc=40.3MB, time=50.81 x[1] = 0.1436 0.285 h = 0.0001 0.004 y2[1] (numeric) = 0.110794155317 0.306654711713 y2[1] (closed_form) = 0.148958358712 0.285900573122 absolute error = 0.04344 relative error = 13.48 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.03276424955 -0.0383395130542 y1[1] (closed_form) = 1.0301745143 -0.0413398696397 absolute error = 0.003963 relative error = 0.3844 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4206 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 = 0.4206 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4184.9MB, alloc=40.3MB, time=51.37 x[1] = 0.1437 0.289 h = 0.003 0.006 y2[1] (numeric) = 0.111092344347 0.310795589231 y2[1] (closed_form) = 0.14922804219 0.290019374322 absolute error = 0.04343 relative error = 13.31 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.03398805455 -0.0388141570314 y1[1] (closed_form) = 1.0313114434 -0.04196503753 absolute error = 0.004134 relative error = 0.4005 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5644 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 = 0.5644 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4230.6MB, alloc=40.3MB, time=51.93 memory used=4276.7MB, alloc=40.3MB, time=52.49 x[1] = 0.1467 0.295 h = 0.0001 0.005 y2[1] (numeric) = 0.111395100166 0.314940440682 y2[1] (closed_form) = 0.152581053121 0.296082584212 absolute error = 0.0453 relative error = 13.6 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.03553153064 -0.0404202200745 y1[1] (closed_form) = 1.03261703805 -0.0437496098217 absolute error = 0.004425 relative error = 0.4281 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2566 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 = 0.2566 Order of pole (three term test) = 31.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4322.5MB, alloc=40.3MB, time=53.05 memory used=4368.5MB, alloc=40.3MB, time=53.62 x[1] = 0.1468 0.3 h = 0.0001 0.003 y2[1] (numeric) = 0.111702632091 0.319089327223 y2[1] (closed_form) = 0.152905119621 0.301244939142 absolute error = 0.0449 relative error = 13.29 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.03710544852 -0.0410096638462 y1[1] (closed_form) = 1.03409507953 -0.0445431898539 absolute error = 0.004642 relative error = 0.4485 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2099 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 = 0.2099 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4414.2MB, alloc=40.3MB, time=54.18 x[1] = 0.1469 0.303 h = 0.001 0.001 y2[1] (numeric) = 0.112015001145 0.32324234644 y2[1] (closed_form) = 0.153142937046 0.304344082905 absolute error = 0.04526 relative error = 13.28 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.03805775914 -0.0413773556348 y1[1] (closed_form) = 1.03498816002 -0.0450325409788 absolute error = 0.004773 relative error = 0.4607 % Correct digits = 2 memory used=4460.4MB, alloc=40.3MB, time=54.75 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1663 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 = 0.1663 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4506.6MB, alloc=40.3MB, time=55.32 x[1] = 0.1479 0.304 h = 0.0001 0.004 y2[1] (numeric) = 0.112332212558 0.327399537911 y2[1] (closed_form) = 0.154223262421 0.305333885021 absolute error = 0.04735 relative error = 13.84 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.03827090654 -0.0418148494322 y1[1] (closed_form) = 1.03513931598 -0.0454910630373 absolute error = 0.004829 relative error = 0.4661 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.003 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 = 1.003 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4552.4MB, alloc=40.3MB, time=55.88 memory used=4598.4MB, alloc=40.3MB, time=56.44 x[1] = 0.148 0.308 h = 0.003 0.006 y2[1] (numeric) = 0.11265426963 0.331560915801 y2[1] (closed_form) = 0.154510097067 0.309472283621 absolute error = 0.04733 relative error = 13.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.03957757676 -0.042297768768 y1[1] (closed_form) = 1.03635349007 -0.04613926912 absolute error = 0.005015 relative error = 0.4834 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6016 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 = 0.6016 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4644.1MB, alloc=40.3MB, time=57.00 memory used=4690.3MB, alloc=40.3MB, time=57.56 x[1] = 0.151 0.314 h = 0.0001 0.005 y2[1] (numeric) = 0.112981229683 0.335726530728 y2[1] (closed_form) = 0.157903701276 0.315553390472 absolute error = 0.04924 relative error = 13.96 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.04124098497 -0.0439756028663 y1[1] (closed_form) = 1.03775994886 -0.0480140405886 absolute error = 0.005332 relative error = 0.5132 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2733 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 = 0.2733 Order of pole (three term test) = 31.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4736.0MB, alloc=40.3MB, time=58.12 x[1] = 0.1511 0.319 h = 0.0001 0.003 y2[1] (numeric) = 0.113313303331 0.339896443349 y2[1] (closed_form) = 0.158249680558 0.320741274242 absolute error = 0.04885 relative error = 13.66 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.04291872591 -0.0445751181572 y1[1] (closed_form) = 1.03933487464 -0.0488362369329 absolute error = 0.005568 relative error = 0.5351 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2234 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 = 0.2234 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4781.9MB, alloc=40.3MB, time=58.68 memory used=4828.2MB, alloc=40.3MB, time=59.25 x[1] = 0.1512 0.322 h = 0.001 0.001 y2[1] (numeric) = 0.113650552294 0.344070751524 y2[1] (closed_form) = 0.158500930998 0.32385579414 absolute error = 0.0492 relative error = 13.64 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.04393332744 -0.0449497609687 y1[1] (closed_form) = 1.04028593203 -0.049343592276 absolute error = 0.00571 relative error = 0.5483 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1769 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 = 0.1769 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4874.1MB, alloc=40.3MB, time=59.81 memory used=4920.4MB, alloc=40.3MB, time=60.39 x[1] = 0.1522 0.323 h = 0.001 0.003 y2[1] (numeric) = 0.113992981985 0.348249495016 y2[1] (closed_form) = 0.159590884709 0.324846577615 absolute error = 0.05125 relative error = 14.16 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.04416566586 -0.0454097420573 y1[1] (closed_form) = 1.04045123738 -0.0498269893422 absolute error = 0.005771 relative error = 0.5541 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.843 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 = 0.843 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=4966.3MB, alloc=40.3MB, time=60.96 memory used=5012.5MB, alloc=40.3MB, time=61.53 x[1] = 0.1532 0.326 h = 0.0001 0.004 y2[1] (numeric) = 0.114340599073 0.352432679919 y2[1] (closed_form) = 0.160782434477 0.327918927857 absolute error = 0.05251 relative error = 14.38 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.04510252166 -0.0461025818466 y1[1] (closed_form) = 1.04127019884 -0.0506339311263 absolute error = 0.005935 relative error = 0.5693 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4817 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 = 0.4817 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5058.3MB, alloc=40.3MB, time=62.10 x[1] = 0.1533 0.33 h = 0.003 0.006 y2[1] (numeric) = 0.114693423901 0.356620328538 y2[1] (closed_form) = 0.161090515218 0.332081513707 absolute error = 0.05249 relative error = 14.22 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.04650917452 -0.0465961007672 y1[1] (closed_form) = 1.04257410438 -0.0513106760591 absolute error = 0.006141 relative error = 0.5883 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6459 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 = 0.6459 Order of pole (three term test) = 31.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5104.0MB, alloc=40.3MB, time=62.65 memory used=5150.2MB, alloc=40.3MB, time=63.22 x[1] = 0.1563 0.336 h = 0.0001 0.005 y2[1] (numeric) = 0.115051518722 0.360812494811 y2[1] (closed_form) = 0.16453430587 0.338184616598 absolute error = 0.05441 relative error = 14.47 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.04831685465 -0.0483614810067 y1[1] (closed_form) = 1.04409646806 -0.0532929406906 absolute error = 0.006491 relative error = 0.6209 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2931 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 = 0.2931 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5196.0MB, alloc=40.3MB, time=63.77 memory used=5242.1MB, alloc=40.3MB, time=64.34 x[1] = 0.1564 0.341 h = 0.0001 0.003 y2[1] (numeric) = 0.115415095757 0.365009238788 y2[1] (closed_form) = 0.164907407587 0.343403934662 absolute error = 0.054 relative error = 14.18 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.05011988377 -0.048973936283 y1[1] (closed_form) = 1.04578396391 -0.0541506224751 absolute error = 0.006753 relative error = 0.6448 % Correct digits = 2 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) = 33.09 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 = 0.2394 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5287.9MB, alloc=40.3MB, time=64.90 x[1] = 0.1565 0.344 h = 0.001 0.001 y2[1] (numeric) = 0.115784217589 0.36921065866 y2[1] (closed_form) = 0.165175282845 0.346537370287 absolute error = 0.05435 relative error = 14.16 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.05120965252 -0.0493574448215 y1[1] (closed_form) = 1.046802371 -0.0546802431283 absolute error = 0.006911 relative error = 0.6593 % Correct digits = 2 memory used=5334.2MB, alloc=40.3MB, time=65.47 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1896 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 = 0.1896 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5380.1MB, alloc=40.3MB, time=66.04 x[1] = 0.1575 0.345 h = 0.001 0.003 y2[1] (numeric) = 0.116158889857 0.373416794419 y2[1] (closed_form) = 0.166277112327 0.347529326872 absolute error = 0.05641 relative error = 14.64 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.05146499476 -0.0498447292458 y1[1] (closed_form) = 1.04698367824 -0.0551930026442 absolute error = 0.006978 relative error = 0.6655 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9032 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 = 0.9032 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5425.9MB, alloc=44.3MB, time=66.60 memory used=5472.2MB, alloc=44.3MB, time=67.17 x[1] = 0.1585 0.348 h = 0.0001 0.004 y2[1] (numeric) = 0.116539119304 0.377627652168 y2[1] (closed_form) = 0.167491387414 0.350615979092 absolute error = 0.05767 relative error = 14.84 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.05247521171 -0.0505692966971 y1[1] (closed_form) = 1.04786401178 -0.0560427270402 absolute error = 0.007157 relative error = 0.682 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5159 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 = 0.5159 Order of pole (three term test) = 31.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5518.1MB, alloc=44.3MB, time=67.73 memory used=5564.0MB, alloc=44.3MB, time=68.29 x[1] = 0.1586 0.352 h = 0.003 0.006 y2[1] (numeric) = 0.116924926513 0.381843254258 y2[1] (closed_form) = 0.1678218255 0.35480457816 absolute error = 0.05763 relative error = 14.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.05398247877 -0.0510741964326 y1[1] (closed_form) = 1.04925808543 -0.0567486234603 absolute error = 0.007384 relative error = 0.7027 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6914 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 = 0.6914 Order of pole (three term test) = 31.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5609.8MB, alloc=44.3MB, time=68.85 x[1] = 0.1616 0.358 h = 0.0001 0.005 y2[1] (numeric) = 0.117316374414 0.38606365468 y2[1] (closed_form) = 0.171318796048 0.360931656483 absolute error = 0.05956 relative error = 14.91 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.05593483658 -0.0529287766195 y1[1] (closed_form) = 1.05089658578 -0.0588396400566 absolute error = 0.007767 relative error = 0.7379 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3135 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 = 0.3135 Order of pole (three term test) = 31.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5655.7MB, alloc=44.3MB, time=69.41 memory used=5701.9MB, alloc=44.3MB, time=69.97 x[1] = 0.1617 0.363 h = 0.0001 0.003 y2[1] (numeric) = 0.117713676948 0.390288912847 y2[1] (closed_form) = 0.171720407544 0.366184701432 absolute error = 0.05914 relative error = 14.62 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.0578639645 -0.053555166872 y1[1] (closed_form) = 1.05269722104 -0.0597335918718 absolute error = 0.008054 relative error = 0.7639 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.256 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 = 0.256 Order of pole (three term test) = 31.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5747.7MB, alloc=44.3MB, time=70.54 memory used=5794.1MB, alloc=44.3MB, time=71.12 x[1] = 0.1618 0.366 h = 0.001 0.001 y2[1] (numeric) = 0.118116897607 0.394519127313 y2[1] (closed_form) = 0.172005760523 0.369338418916 absolute error = 0.05948 relative error = 14.6 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.05902938383 -0.0539481516137 y1[1] (closed_form) = 1.05378331863 -0.0602859568118 absolute error = 0.008227 relative error = 0.7795 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2026 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 = 0.2026 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5839.9MB, alloc=44.3MB, time=71.68 memory used=5886.1MB, alloc=44.3MB, time=72.24 x[1] = 0.1628 0.367 h = 0.001 0.003 y2[1] (numeric) = 0.11852604227 0.398754338316 y2[1] (closed_form) = 0.173120199468 0.370331743901 absolute error = 0.06155 relative error = 15.06 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.05930769917 -0.054463108906 y1[1] (closed_form) = 1.05398059082 -0.0608283548403 absolute error = 0.0083 relative error = 0.7862 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.965 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 = 0.965 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5931.9MB, alloc=44.3MB, time=72.80 x[1] = 0.1638 0.37 h = 0.0001 0.004 y2[1] (numeric) = 0.118941117757 0.402994551969 y2[1] (closed_form) = 0.174358473351 0.373433822183 absolute error = 0.06281 relative error = 15.24 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.06039158817 -0.0552201821886 y1[1] (closed_form) = 1.05492249965 -0.0617214545662 absolute error = 0.008496 relative error = 0.804 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5511 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 = 0.5511 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=5977.8MB, alloc=44.3MB, time=73.36 memory used=6023.8MB, alloc=44.3MB, time=73.92 x[1] = 0.1639 0.374 h = 0.003 0.006 y2[1] (numeric) = 0.119362144908 0.407239790674 y2[1] (closed_form) = 0.174712396291 0.377650267082 absolute error = 0.06276 relative error = 15.08 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.06200014006 -0.0557372984026 y1[1] (closed_form) = 1.05640721236 -0.0624571494307 absolute error = 0.008743 relative error = 0.8262 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7383 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 = 0.7383 Order of pole (three term test) = 31.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6069.5MB, alloc=44.3MB, time=74.48 memory used=6115.7MB, alloc=44.3MB, time=75.06 x[1] = 0.1669 0.38 h = 0.0001 0.005 y2[1] (numeric) = 0.119789187372 0.411490108486 y2[1] (closed_form) = 0.178265570028 0.383803298756 absolute error = 0.0647 relative error = 15.29 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.06409760174 -0.0576828429111 y1[1] (closed_form) = 1.05816210876 -0.0646582534612 absolute error = 0.009159 relative error = 0.8639 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3345 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 = 0.3345 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6161.5MB, alloc=44.3MB, time=75.62 memory used=6207.5MB, alloc=44.3MB, time=76.18 x[1] = 0.167 0.385 h = 0.0001 0.003 y2[1] (numeric) = 0.120222460917 0.415745564157 y2[1] (closed_form) = 0.17869709951 0.389092371911 absolute error = 0.06426 relative error = 15.01 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.06615368823 -0.0583242311516 y1[1] (closed_form) = 1.0600764959 -0.0655893028202 absolute error = 0.009472 relative error = 0.8918 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.273 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 = 0.273 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6253.6MB, alloc=44.3MB, time=76.74 x[1] = 0.1671 0.388 h = 0.001 0.001 y2[1] (numeric) = 0.12066203 0.420006256633 y2[1] (closed_form) = 0.179000795811 0.392267742556 absolute error = 0.0646 relative error = 14.98 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.06739527047 -0.0587273438602 y1[1] (closed_form) = 1.06123065034 -0.0661649171799 absolute error = 0.00966 relative error = 0.9085 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.216 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 = 0.216 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6299.6MB, alloc=44.3MB, time=77.32 memory used=6345.7MB, alloc=44.3MB, time=77.88 x[1] = 0.1681 0.389 h = 0.001 0.003 y2[1] (numeric) = 0.121107900751 0.424272226418 y2[1] (closed_form) = 0.180128583978 0.393262628912 absolute error = 0.06667 relative error = 15.41 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.06769652483 -0.0592703671017 y1[1] (closed_form) = 1.06144385093 -0.06673724702 absolute error = 0.009739 relative error = 0.9157 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.029 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 = 1.029 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6391.5MB, alloc=44.3MB, time=78.44 memory used=6437.7MB, alloc=44.3MB, time=79.01 x[1] = 0.1691 0.392 h = 0.0001 0.004 y2[1] (numeric) = 0.121560080072 0.428543479634 y2[1] (closed_form) = 0.181392144673 0.396381258778 absolute error = 0.06793 relative error = 15.58 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.0688544136 -0.0600607749056 y1[1] (closed_form) = 1.06244755619 -0.0676743489303 absolute error = 0.009951 relative error = 0.9347 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5872 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 = 0.5872 Order of pole (three term test) = 31.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6483.5MB, alloc=44.3MB, time=79.56 x[1] = 0.1692 0.396 h = 0.003 0.006 y2[1] (numeric) = 0.122018589072 0.43282003874 y2[1] (closed_form) = 0.18177069718 0.400627389341 absolute error = 0.06787 relative error = 15.43 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.07056495998 -0.0605909982628 y1[1] (closed_form) = 1.0640234133 -0.0684405239204 absolute error = 0.01022 relative error = 0.9583 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7864 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 = 0.7864 Order of pole (three term test) = 31.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6529.4MB, alloc=44.3MB, time=80.12 memory used=6575.6MB, alloc=44.3MB, time=80.69 x[1] = 0.1722 0.402 h = 0.0001 0.005 y2[1] (numeric) = 0.122483492164 0.437101957863 y2[1] (closed_form) = 0.185383129074 0.40680835101 absolute error = 0.06981 relative error = 15.62 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.07280797178 -0.0626293829044 y1[1] (closed_form) = 1.06589499251 -0.0707531281916 absolute error = 0.01067 relative error = 0.9986 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.356 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 = 0.356 Order of pole (three term test) = 31.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6621.4MB, alloc=44.3MB, time=81.25 memory used=6667.4MB, alloc=44.3MB, time=81.81 x[1] = 0.1723 0.407 h = 0.0001 0.003 y2[1] (numeric) = 0.122955007054 0.441389295074 y2[1] (closed_form) = 0.185846006791 0.41213576314 absolute error = 0.06936 relative error = 15.34 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.07499192577 -0.06328690089 y1[1] (closed_form) = 1.06792378719 -0.0717221460499 absolute error = 0.01101 relative error = 1.028 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2904 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 = 0.2904 Order of pole (three term test) = 31.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6713.3MB, alloc=44.3MB, time=82.37 memory used=6759.5MB, alloc=44.3MB, time=82.94 x[1] = 0.1724 0.41 h = 0.001 0.001 y2[1] (numeric) = 0.123433199214 0.44568214974 y2[1] (closed_form) = 0.186168925429 0.415334163842 absolute error = 0.06969 relative error = 15.31 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.07631021219 -0.063700835055 y1[1] (closed_form) = 1.06914639045 -0.0723215414344 absolute error = 0.01121 relative error = 1.046 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2298 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 = 0.2298 Order of pole (three term test) = 31.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6805.4MB, alloc=44.3MB, time=83.50 x[1] = 0.1734 0.411 h = 0.0001 0.004 y2[1] (numeric) = 0.12391807504 0.449980562647 y2[1] (closed_form) = 0.187310809027 0.416330802141 absolute error = 0.07177 relative error = 15.72 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.076634368 -0.0642723410277 y1[1] (closed_form) = 1.06937548317 -0.0729241137464 absolute error = 0.01129 relative error = 1.054 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.384 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 = 1.384 Order of pole (three term test) = 31.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6851.3MB, alloc=44.3MB, time=84.07 memory used=6897.3MB, alloc=44.3MB, time=84.63 x[1] = 0.1735 0.415 h = 0.003 0.006 y2[1] (numeric) = 0.1244096383 0.454284548362 y2[1] (closed_form) = 0.187711108747 0.420604276634 absolute error = 0.0717 relative error = 15.57 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.07843048003 -0.064814207433 y1[1] (closed_form) = 1.07103060008 -0.0737160031704 absolute error = 0.01158 relative error = 1.078 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.829 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 = 0.829 Order of pole (three term test) = 31.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=6943.0MB, alloc=44.3MB, time=85.18 memory used=6989.0MB, alloc=44.3MB, time=85.75 x[1] = 0.1765 0.421 h = 0.0001 0.005 y2[1] (numeric) = 0.124907949568 0.4585941578 y2[1] (closed_form) = 0.191376655253 0.426811617548 absolute error = 0.07368 relative error = 15.75 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.08079513866 -0.0669314734155 y1[1] (closed_form) = 1.0730042189 -0.076124378964 absolute error = 0.01205 relative error = 1.12 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3751 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 = 0.3751 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7034.8MB, alloc=44.3MB, time=86.30 memory used=7080.9MB, alloc=44.3MB, time=86.87 x[1] = 0.1766 0.426 h = 0.0001 0.003 y2[1] (numeric) = 0.125413228317 0.462909448445 y2[1] (closed_form) = 0.191867185157 0.43217428577 absolute error = 0.07322 relative error = 15.48 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.08308637929 -0.0676033485648 y1[1] (closed_form) = 1.07513251711 -0.0771254355981 absolute error = 0.01241 relative error = 1.151 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3059 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 = 0.3059 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7126.9MB, alloc=44.3MB, time=87.44 x[1] = 0.1767 0.429 h = 0.001 0.001 y2[1] (numeric) = 0.125925540932 0.467230520064 y2[1] (closed_form) = 0.192207067641 0.43539386063 absolute error = 0.07353 relative error = 15.45 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.08446902091 -0.0680268619091 y1[1] (closed_form) = 1.07641466469 -0.0777449248564 absolute error = 0.01262 relative error = 1.17 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.242 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 = 0.242 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7172.8MB, alloc=44.3MB, time=88.00 memory used=7218.9MB, alloc=44.3MB, time=88.57 x[1] = 0.1777 0.43 h = 0.001 0.003 y2[1] (numeric) = 0.126444894039 0.471557413702 y2[1] (closed_form) = 0.193361662958 0.436392337778 absolute error = 0.07559 relative error = 15.84 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.08481222976 -0.0686224400211 y1[1] (closed_form) = 1.07665777353 -0.0783736022804 absolute error = 0.01271 relative error = 1.178 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.152 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 = 1.152 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7264.7MB, alloc=44.3MB, time=89.13 memory used=7311.0MB, alloc=44.3MB, time=89.71 x[1] = 0.1787 0.433 h = 0.0001 0.004 y2[1] (numeric) = 0.126971294707 0.475890135501 y2[1] (closed_form) = 0.194675529064 0.439545105871 absolute error = 0.07684 relative error = 15.98 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.08610669212 -0.0694762858283 y1[1] (closed_form) = 1.07777766086 -0.0793936255503 absolute error = 0.01295 relative error = 1.198 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6574 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 = 0.6574 Order of pole (three term test) = 31.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7356.8MB, alloc=44.3MB, time=90.28 x[1] = 0.1788 0.437 h = 0.003 0.006 y2[1] (numeric) = 0.127504764586 0.480228708049 y2[1] (closed_form) = 0.195102615291 0.44385172486 absolute error = 0.07676 relative error = 15.83 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.0880062041 -0.0700330414809 y1[1] (closed_form) = 1.07952496334 -0.0802173504665 absolute error = 0.01325 relative error = 1.224 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8799 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 = 0.8799 Order of pole (three term test) = 31.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7402.7MB, alloc=44.3MB, time=90.84 memory used=7448.7MB, alloc=44.3MB, time=91.41 x[1] = 0.1818 0.443 h = 0.0001 0.005 y2[1] (numeric) = 0.128045369614 0.48457318564 y2[1] (closed_form) = 0.19883317169 0.450090708459 absolute error = 0.07874 relative error = 16 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.09051728343 -0.0722468896194 y1[1] (closed_form) = 1.08161588983 -0.0827400595285 absolute error = 0.01376 relative error = 1.268 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3979 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 = 0.3979 Order of pole (three term test) = 31.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7494.5MB, alloc=44.3MB, time=91.98 memory used=7540.6MB, alloc=44.3MB, time=92.54 x[1] = 0.1819 0.448 h = 0.0001 0.003 y2[1] (numeric) = 0.128593331418 0.488923625037 y2[1] (closed_form) = 0.199357746123 0.455496060783 absolute error = 0.07826 relative error = 15.74 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.09293819108 -0.0729371580719 y1[1] (closed_form) = 1.08385994262 -0.0837808138071 absolute error = 0.01414 relative error = 1.301 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3244 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 = 0.3244 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7586.5MB, alloc=44.3MB, time=93.11 memory used=7632.8MB, alloc=44.3MB, time=93.70 x[1] = 0.182 0.451 h = 0.001 0.001 y2[1] (numeric) = 0.129148717498 0.493280126486 y2[1] (closed_form) = 0.199718508184 0.458741255002 absolute error = 0.07857 relative error = 15.7 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.09439860814 -0.0733728794248 y1[1] (closed_form) = 1.0852113438 -0.0844251395041 absolute error = 0.01437 relative error = 1.32 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2566 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 = 0.2566 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7678.8MB, alloc=44.3MB, time=94.28 x[1] = 0.183 0.452 h = 0.001 0.003 y2[1] (numeric) = 0.129711534769 0.497642731345 y2[1] (closed_form) = 0.200888603742 0.459741841098 absolute error = 0.08064 relative error = 16.07 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.09476463955 -0.0739977698515 y1[1] (closed_form) = 1.0854702819 -0.085084684565 absolute error = 0.01447 relative error = 1.329 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.221 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 = 1.221 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7724.5MB, alloc=44.3MB, time=94.86 memory used=7770.8MB, alloc=44.3MB, time=95.45 x[1] = 0.184 0.455 h = 0.0001 0.004 y2[1] (numeric) = 0.130281790391 0.50201144577 y2[1] (closed_form) = 0.202231515819 0.462914406448 absolute error = 0.08189 relative error = 16.21 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.09613412325 -0.0748875845561 y1[1] (closed_form) = 1.08665270596 -0.0861506915662 absolute error = 0.01472 relative error = 1.351 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6967 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 = 0.6967 Order of pole (three term test) = 31.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7816.6MB, alloc=44.3MB, time=96.03 memory used=7862.7MB, alloc=44.3MB, time=96.61 x[1] = 0.1841 0.459 h = 0.003 0.006 y2[1] (numeric) = 0.13085950633 0.50638629242 y2[1] (closed_form) = 0.202686587652 0.467256033816 absolute error = 0.08179 relative error = 16.06 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.09813785967 -0.0754602844955 y1[1] (closed_form) = 1.08849279854 -0.0870070350314 absolute error = 0.01505 relative error = 1.378 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9324 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 = 0.9324 Order of pole (three term test) = 31.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=7908.5MB, alloc=44.3MB, time=97.20 memory used=7954.6MB, alloc=44.3MB, time=97.79 x[1] = 0.1871 0.465 h = 0.0001 0.005 y2[1] (numeric) = 0.131444749406 0.510767325691 y2[1] (closed_form) = 0.206485309832 0.473528634562 absolute error = 0.08377 relative error = 16.22 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.10079586294 -0.0777729223184 y1[1] (closed_form) = 1.09070139764 -0.0896457151636 absolute error = 0.01558 relative error = 1.424 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4215 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 = 0.4215 Order of pole (three term test) = 31.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8000.4MB, alloc=44.3MB, time=98.37 x[1] = 0.1872 0.47 h = 0.0001 0.003 y2[1] (numeric) = 0.132037743511 0.515154601593 y2[1] (closed_form) = 0.20704542858 0.478979013072 absolute error = 0.08328 relative error = 15.96 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.10334749108 -0.0784829213395 y1[1] (closed_form) = 1.0930619854 -0.0907271649432 absolute error = 0.01599 relative error = 1.458 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3435 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 = 0.3435 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8046.1MB, alloc=44.3MB, time=98.95 memory used=8092.3MB, alloc=44.3MB, time=99.56 x[1] = 0.1873 0.473 h = 0.001 0.001 y2[1] (numeric) = 0.132638557314 0.519548220879 y2[1] (closed_form) = 0.207427991536 0.482251222072 absolute error = 0.08357 relative error = 15.92 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.10488630997 -0.0789316689226 y1[1] (closed_form) = 1.09448310605 -0.0913969360123 absolute error = 0.01624 relative error = 1.478 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 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 = 0.2716 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8138.2MB, alloc=44.3MB, time=100.16 memory used=8184.4MB, alloc=44.3MB, time=100.75 x[1] = 0.1883 0.474 h = 0.001 0.003 y2[1] (numeric) = 0.133247198028 0.523948225239 y2[1] (closed_form) = 0.208614354164 0.483254100418 absolute error = 0.08565 relative error = 16.27 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.10527511544 -0.0795863588385 y1[1] (closed_form) = 1.09475783765 -0.0920877098006 absolute error = 0.01634 relative error = 1.487 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.293 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 = 1.293 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8230.3MB, alloc=44.3MB, time=101.35 x[1] = 0.1893 0.477 h = 0.0001 0.004 y2[1] (numeric) = 0.133863672916 0.528354620842 y2[1] (closed_form) = 0.209987664373 0.48644759628 absolute error = 0.0869 relative error = 16.4 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.10672001332 -0.0805131740738 y1[1] (closed_form) = 1.09600308892 -0.0932004623123 absolute error = 0.01661 relative error = 1.51 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7374 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 = 0.7374 Order of pole (three term test) = 31.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8276.5MB, alloc=44.3MB, time=101.94 memory used=8322.6MB, alloc=44.3MB, time=102.53 x[1] = 0.1894 0.481 h = 0.003 0.006 y2[1] (numeric) = 0.13448800427 0.532767430427 y2[1] (closed_form) = 0.210471941833 0.490826105342 absolute error = 0.08679 relative error = 16.25 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.10882883776 -0.0811029308553 y1[1] (closed_form) = 1.09793661082 -0.0940902438952 absolute error = 0.01695 relative error = 1.538 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9866 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 = 0.9866 Order of pole (three term test) = 31.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8368.4MB, alloc=44.3MB, time=103.12 memory used=8414.6MB, alloc=44.3MB, time=103.72 x[1] = 0.1924 0.487 h = 0.0001 0.005 y2[1] (numeric) = 0.135120259837 0.537186708497 y2[1] (closed_form) = 0.2143420246 0.497134297128 absolute error = 0.08877 relative error = 16.4 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.11163428655 -0.0835166812151 y1[1] (closed_form) = 1.10026327411 -0.0968466132164 absolute error = 0.01752 relative error = 1.586 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4458 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 = 0.4458 Order of pole (three term test) = 31.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8460.5MB, alloc=44.3MB, time=104.30 memory used=8506.6MB, alloc=44.3MB, time=104.90 x[1] = 0.1925 0.492 h = 0.0001 0.003 y2[1] (numeric) = 0.135760665887 0.541612510283 y2[1] (closed_form) = 0.214939214161 0.502632056145 absolute error = 0.08825 relative error = 16.14 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.11431773788 -0.0842478200136 y1[1] (closed_form) = 1.10274122087 -0.0979698020854 absolute error = 0.01795 relative error = 1.622 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3632 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 = 0.3632 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8552.5MB, alloc=44.3MB, time=105.49 x[1] = 0.1926 0.495 h = 0.001 0.001 y2[1] (numeric) = 0.136409292315 0.546044937078 y2[1] (closed_form) = 0.215344515567 0.50593268258 absolute error = 0.08854 relative error = 16.1 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.11593561395 -0.0847104557114 y1[1] (closed_form) = 1.10423255271 -0.0986656553211 absolute error = 0.01821 relative error = 1.643 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2872 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 = 0.2872 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8598.6MB, alloc=44.3MB, time=106.08 memory used=8644.8MB, alloc=44.3MB, time=106.67 x[1] = 0.1936 0.496 h = 0.001 0.003 y2[1] (numeric) = 0.137066146646 0.550484030918 y2[1] (closed_form) = 0.216547920043 0.506938033732 absolute error = 0.09063 relative error = 16.44 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.11634714085 -0.0853954566732 y1[1] (closed_form) = 1.10452304197 -0.0993880368486 absolute error = 0.01832 relative error = 1.652 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.367 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 = 1.367 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8690.8MB, alloc=44.3MB, time=107.25 memory used=8737.1MB, alloc=44.3MB, time=107.83 x[1] = 0.1946 0.499 h = 0.0001 0.004 y2[1] (numeric) = 0.137731236246 0.554929797988 y2[1] (closed_form) = 0.217952999288 0.510153595812 absolute error = 0.09187 relative error = 16.56 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.11786786192 -0.086360357044 y1[1] (closed_form) = 1.10583142866 -0.100548332615 absolute error = 0.01861 relative error = 1.676 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7794 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 = 0.7794 Order of pole (three term test) = 31.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8782.8MB, alloc=44.3MB, time=108.40 memory used=8829.0MB, alloc=44.3MB, time=108.98 x[1] = 0.1947 0.503 h = 0.003 0.006 y2[1] (numeric) = 0.138404583754 0.559382261112 y2[1] (closed_form) = 0.218467724315 0.514570869889 absolute error = 0.09175 relative error = 16.41 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.12008267707 -0.0869683414753 y1[1] (closed_form) = 1.10785905392 -0.101472408919 absolute error = 0.01897 relative error = 1.705 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.043 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 = 1.043 Order of pole (three term test) = 31.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8874.9MB, alloc=44.3MB, time=109.55 x[1] = 0.1977 0.509 h = 0.0001 0.005 y2[1] (numeric) = 0.139086257884 0.563841474908 y2[1] (closed_form) = 0.222412403309 0.520916626191 absolute error = 0.09373 relative error = 16.55 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.12303611074 -0.089485643691 y1[1] (closed_form) = 1.11030419934 -0.10434826674 absolute error = 0.01957 relative error = 1.755 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4709 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 = 0.4709 Order of pole (three term test) = 31.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=8920.7MB, alloc=44.3MB, time=110.12 memory used=8966.9MB, alloc=44.3MB, time=110.70 x[1] = 0.1978 0.514 h = 0.0001 0.003 y2[1] (numeric) = 0.139776487402 0.568307493802 y2[1] (closed_form) = 0.22304821813 0.526464132994 absolute error = 0.09319 relative error = 16.3 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.12585253724 -0.0902394043546 y1[1] (closed_form) = 1.1129003729 -0.105514284687 absolute error = 0.02003 relative error = 1.791 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3836 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 = 0.3836 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9012.8MB, alloc=44.3MB, time=111.28 memory used=9059.2MB, alloc=44.3MB, time=111.87 x[1] = 0.1979 0.517 h = 0.001 0.001 y2[1] (numeric) = 0.140475343484 0.572780419655 y2[1] (closed_form) = 0.223477212537 0.529794587172 absolute error = 0.09347 relative error = 16.26 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.12755015486 -0.0907168342807 y1[1] (closed_form) = 1.11446243357 -0.106236885149 absolute error = 0.0203 relative error = 1.813 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3033 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 = 0.3033 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9105.2MB, alloc=44.3MB, time=112.45 x[1] = 0.1989 0.518 h = 0.0001 0.004 y2[1] (numeric) = 0.141182833979 0.577260294867 y2[1] (closed_form) = 0.224698441986 0.530802588836 absolute error = 0.09557 relative error = 16.58 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.12798434627 -0.0914326824276 y1[1] (closed_form) = 1.11476864446 -0.106991271513 absolute error = 0.02041 relative error = 1.823 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.826 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 = 1.826 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9151.3MB, alloc=44.3MB, time=113.02 memory used=9197.5MB, alloc=44.3MB, time=113.58 x[1] = 0.199 0.522 h = 0.003 0.006 y2[1] (numeric) = 0.141898963244 0.581747134546 y2[1] (closed_form) = 0.225239894755 0.535255129962 absolute error = 0.09543 relative error = 16.43 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.13028820478 -0.0920567934542 y1[1] (closed_form) = 1.11687826023 -0.107944449662 absolute error = 0.02079 relative error = 1.853 % Correct digits = 2 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) = 33.24 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 = 1.092 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9243.2MB, alloc=44.3MB, time=114.14 memory used=9289.4MB, alloc=44.3MB, time=114.71 x[1] = 0.202 0.528 h = 0.0001 0.005 y2[1] (numeric) = 0.14262379604 0.586240990122 y2[1] (closed_form) = 0.22925092786 0.541635742479 absolute error = 0.09744 relative error = 16.57 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.1333653837 -0.0946623377507 y1[1] (closed_form) = 1.11942719981 -0.110923244089 absolute error = 0.02142 relative error = 1.904 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4932 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 = 0.4932 Order of pole (three term test) = 31.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9335.1MB, alloc=44.3MB, time=115.27 memory used=9381.4MB, alloc=44.3MB, time=115.84 x[1] = 0.2021 0.533 h = 0.0001 0.003 y2[1] (numeric) = 0.143357563384 0.590741915326 y2[1] (closed_form) = 0.229920625823 0.547228462435 absolute error = 0.09688 relative error = 16.32 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.136293539 -0.0954361364859 y1[1] (closed_form) = 1.12212639623 -0.112125613455 absolute error = 0.02189 relative error = 1.941 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4018 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 = 0.4018 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9427.4MB, alloc=44.3MB, time=116.41 x[1] = 0.2022 0.536 h = 0.001 0.001 y2[1] (numeric) = 0.144100337588 0.595250012549 y2[1] (closed_form) = 0.230370413973 0.550586024862 absolute error = 0.09715 relative error = 16.28 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.13805815227 -0.0959266206205 y1[1] (closed_form) = 1.12375010223 -0.112870940099 absolute error = 0.02218 relative error = 1.964 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3176 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 = 0.3176 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9473.3MB, alloc=44.3MB, time=116.98 memory used=9519.6MB, alloc=44.3MB, time=117.56 x[1] = 0.2032 0.537 h = 0.001 0.003 y2[1] (numeric) = 0.144852126788 0.599765324524 y2[1] (closed_form) = 0.231607585939 0.551596673241 absolute error = 0.09923 relative error = 16.59 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.13851118386 -0.0966686031683 y1[1] (closed_form) = 1.12407020471 -0.113653020395 absolute error = 0.02229 relative error = 1.973 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.511 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 = 1.511 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9565.6MB, alloc=44.3MB, time=118.12 memory used=9611.8MB, alloc=44.3MB, time=118.70 x[1] = 0.2042 0.54 h = 0.0001 0.004 y2[1] (numeric) = 0.14561293856 0.60428785747 y2[1] (closed_form) = 0.233075201639 0.554856745278 absolute error = 0.1005 relative error = 16.69 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.14017203005 -0.0977063244968 y1[1] (closed_form) = 1.12549754312 -0.114903269739 absolute error = 0.02261 relative error = 1.998 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8615 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 = 0.8615 Order of pole (three term test) = 31.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9657.7MB, alloc=44.3MB, time=119.26 memory used=9703.8MB, alloc=44.3MB, time=119.83 x[1] = 0.2043 0.544 h = 0.003 0.006 y2[1] (numeric) = 0.146382796223 0.608817634383 y2[1] (closed_form) = 0.233649451978 0.55935159987 absolute error = 0.1003 relative error = 16.55 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.14258363889 -0.0983509681619 y1[1] (closed_form) = 1.1277026207 -0.115892427998 absolute error = 0.023 relative error = 2.029 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.152 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 = 1.152 Order of pole (three term test) = 31.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9749.7MB, alloc=44.3MB, time=120.40 x[1] = 0.2073 0.55 h = 0.0001 0.005 y2[1] (numeric) = 0.147161770409 0.613354710138 y2[1] (closed_form) = 0.237741193909 0.565773488247 absolute error = 0.1023 relative error = 16.67 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.14580983773 -0.101064853932 y1[1] (closed_form) = 1.1303709133 -0.118994272584 absolute error = 0.02366 relative error = 2.082 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.52 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 = 0.52 Order of pole (three term test) = 31.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9795.6MB, alloc=44.3MB, time=120.98 memory used=9841.6MB, alloc=44.3MB, time=121.54 x[1] = 0.2074 0.555 h = 0.0001 0.003 y2[1] (numeric) = 0.147950094852 0.617899137615 y2[1] (closed_form) = 0.238452459722 0.571420417242 absolute error = 0.1017 relative error = 16.43 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.14887321375 -0.101864192303 y1[1] (closed_form) = 1.13319008261 -0.120241613581 absolute error = 0.02416 relative error = 2.12 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4235 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 = 0.4235 Order of pole (three term test) = 31.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9887.5MB, alloc=44.3MB, time=122.12 memory used=9933.9MB, alloc=44.3MB, time=122.70 x[1] = 0.2075 0.558 h = 0.001 0.001 y2[1] (numeric) = 0.148747843251 0.622451019829 y2[1] (closed_form) = 0.238927747891 0.574810465358 absolute error = 0.102 relative error = 16.38 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.15071890229 -0.102371254299 y1[1] (closed_form) = 1.13488555869 -0.121014994772 absolute error = 0.02446 relative error = 2.143 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3347 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 = 0.3347 Order of pole (three term test) = 31.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=9979.8MB, alloc=44.3MB, time=123.28 x[1] = 0.2085 0.559 h = 0.001 0.003 y2[1] (numeric) = 0.149555024093 0.627010399911 y2[1] (closed_form) = 0.240184223593 0.575824096575 absolute error = 0.1041 relative error = 16.68 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.15119448173 -0.103145135031 y1[1] (closed_form) = 1.13522132013 -0.121829867983 absolute error = 0.02458 relative error = 2.153 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.593 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 = 1.593 Order of pole (three term test) = 31.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10025.7MB, alloc=44.3MB, time=123.84 memory used=10072.0MB, alloc=44.3MB, time=124.42 x[1] = 0.2095 0.562 h = 0.0001 0.004 y2[1] (numeric) = 0.15037164507 0.631577284099 y2[1] (closed_form) = 0.241687628014 0.579109516289 absolute error = 0.1053 relative error = 16.78 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.15293239883 -0.104224315888 y1[1] (closed_form) = 1.13671278427 -0.123130140954 absolute error = 0.02491 relative error = 2.179 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9078 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 = 0.9078 Order of pole (three term test) = 31.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10117.8MB, alloc=44.3MB, time=124.98 memory used=10163.9MB, alloc=44.3MB, time=125.55 x[1] = 0.2096 0.566 h = 0.003 0.006 y2[1] (numeric) = 0.151197729893 0.636151695487 y2[1] (closed_form) = 0.242295986016 0.583648599727 absolute error = 0.1051 relative error = 16.64 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.15545277588 -0.104890837866 y1[1] (closed_form) = 1.13901409833 -0.124156244567 absolute error = 0.02533 relative error = 2.21 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.214 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 = 1.214 Order of pole (three term test) = 31.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10209.7MB, alloc=44.3MB, time=126.12 memory used=10256.0MB, alloc=44.3MB, time=126.70 x[1] = 0.2126 0.572 h = 0.0001 0.005 y2[1] (numeric) = 0.152033350288 0.640733689093 y2[1] (closed_form) = 0.246471799989 0.590113737583 absolute error = 0.1071 relative error = 16.75 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.15882858403 -0.107715852456 y1[1] (closed_form) = 1.14180223707 -0.127383175806 absolute error = 0.02601 relative error = 2.264 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5477 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 = 0.5477 Order of pole (three term test) = 31.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10301.7MB, alloc=44.3MB, time=127.27 x[1] = 0.2127 0.577 h = 0.0001 0.003 y2[1] (numeric) = 0.152878742825 0.645323316908 y2[1] (closed_form) = 0.247226274899 0.595817284301 absolute error = 0.1065 relative error = 16.52 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.16202847782 -0.108542431376 y1[1] (closed_form) = 1.1447423737 -0.128676714606 absolute error = 0.02654 relative error = 2.304 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 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 = 0.446 Order of pole (three term test) = 31.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10347.6MB, alloc=44.3MB, time=127.83 memory used=10394.0MB, alloc=44.3MB, time=128.40 x[1] = 0.2128 0.58 h = 0.001 0.001 y2[1] (numeric) = 0.153733982642 0.649920682601 y2[1] (closed_form) = 0.247728070401 0.59924125286 absolute error = 0.1068 relative error = 16.47 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.16395601132 -0.109067110136 y1[1] (closed_form) = 1.14651021251 -0.129478898361 absolute error = 0.02685 relative error = 2.327 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3525 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 = 0.3525 Order of pole (three term test) = 31.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10440.1MB, alloc=44.3MB, time=128.98 memory used=10486.5MB, alloc=44.3MB, time=129.56 x[1] = 0.2138 0.581 h = 0.001 0.003 y2[1] (numeric) = 0.154599078594 0.654525829718 y2[1] (closed_form) = 0.249004659092 0.60025803602 absolute error = 0.1089 relative error = 16.76 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.16445406822 -0.109873498453 y1[1] (closed_form) = 1.14686159593 -0.130327014312 absolute error = 0.02698 relative error = 2.337 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.677 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 = 1.677 Order of pole (three term test) = 31.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10532.5MB, alloc=44.3MB, time=130.12 x[1] = 0.2148 0.584 h = 0.0001 0.004 y2[1] (numeric) = 0.155474038495 0.659138764516 y2[1] (closed_form) = 0.250545303887 0.603569950688 absolute error = 0.1101 relative error = 16.85 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.16626952743 -0.110995437307 y1[1] (closed_form) = 1.14841756257 -0.131678251571 absolute error = 0.02732 relative error = 2.364 % Correct digits = 2 memory used=10578.6MB, alloc=44.3MB, time=130.70 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9558 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 = 0.9558 Order of pole (three term test) = 31.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10624.7MB, alloc=44.3MB, time=131.26 x[1] = 0.2149 0.588 h = 0.003 0.006 y2[1] (numeric) = 0.156358886461 0.663759510195 y2[1] (closed_form) = 0.251189105511 0.608155190564 absolute error = 0.1099 relative error = 16.71 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.1688997298 -0.111685244706 y1[1] (closed_form) = 1.150815923 -0.132742305069 absolute error = 0.02776 relative error = 2.396 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.278 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 = 1.278 Order of pole (three term test) = 31.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10670.5MB, alloc=44.3MB, time=131.83 memory used=10716.7MB, alloc=44.3MB, time=132.41 x[1] = 0.2179 0.594 h = 0.0001 0.005 y2[1] (numeric) = 0.15725369536 0.668388121923 y2[1] (closed_form) = 0.25545240316 0.61466555163 absolute error = 0.1119 relative error = 16.82 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.1724257524 -0.114624296889 y1[1] (closed_form) = 1.15372442649 -0.136096444436 absolute error = 0.02847 relative error = 2.451 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5765 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 = 0.5765 Order of pole (three term test) = 31.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10762.6MB, alloc=44.3MB, time=132.98 memory used=10808.8MB, alloc=44.3MB, time=133.55 x[1] = 0.218 0.599 h = 0.0001 0.003 y2[1] (numeric) = 0.158158704716 0.673024650768 y2[1] (closed_form) = 0.256251761317 0.62042814049 absolute error = 0.1113 relative error = 16.58 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.17576351048 -0.115479894183 y1[1] (closed_form) = 1.15678656924 -0.137437456484 absolute error = 0.02902 relative error = 2.491 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4693 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 = 0.4693 Order of pole (three term test) = 31.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10854.8MB, alloc=44.3MB, time=134.13 x[1] = 0.2181 0.602 h = 0.001 0.001 y2[1] (numeric) = 0.159073991169 0.677669201086 y2[1] (closed_form) = 0.256781091462 0.623887473529 absolute error = 0.1115 relative error = 16.53 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.17777368769 -0.116023275281 y1[1] (closed_form) = 1.15862738968 -0.138269220829 absolute error = 0.02935 relative error = 2.515 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3709 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 = 0.3709 Order of pole (three term test) = 31.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10900.8MB, alloc=44.3MB, time=134.70 memory used=10947.1MB, alloc=44.3MB, time=135.28 x[1] = 0.2191 0.603 h = 0.001 0.003 y2[1] (numeric) = 0.15999956395 0.682321816855 y2[1] (closed_form) = 0.2580786123 0.624907574485 absolute error = 0.1136 relative error = 16.81 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.17829414661 -0.116862806038 y1[1] (closed_form) = 1.1589943575 -0.139151048143 absolute error = 0.02948 relative error = 2.526 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.765 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 = 1.765 Order of pole (three term test) = 31.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=10993.1MB, alloc=44.3MB, time=135.85 memory used=11039.3MB, alloc=44.3MB, time=136.43 x[1] = 0.2201 0.606 h = 0.0001 0.004 y2[1] (numeric) = 0.160935431003 0.686982504353 y2[1] (closed_form) = 0.259657972281 0.628247134777 absolute error = 0.1149 relative error = 16.9 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.18018763443 -0.118028857442 y1[1] (closed_form) = 1.16061522089 -0.140554228629 absolute error = 0.02984 relative error = 2.552 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.006 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 = 1.006 Order of pole (three term test) = 31.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11085.1MB, alloc=44.3MB, time=137.00 memory used=11131.3MB, alloc=44.3MB, time=137.57 x[1] = 0.2202 0.61 h = 0.003 0.006 y2[1] (numeric) = 0.161881616866 0.691651286888 y2[1] (closed_form) = 0.26033858041 0.632880471461 absolute error = 0.1147 relative error = 16.76 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.18292875854 -0.118743419716 y1[1] (closed_form) = 1.16311147303 -0.141657276478 absolute error = 0.03029 relative error = 2.586 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.344 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 = 1.344 Order of pole (three term test) = 31.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11177.0MB, alloc=44.3MB, time=138.14 x[1] = 0.2232 0.616 h = 0.0001 0.005 y2[1] (numeric) = 0.162838195594 0.696328219787 y2[1] (closed_form) = 0.264692823802 0.639438029682 absolute error = 0.1167 relative error = 16.86 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.18660561588 -0.121799541115 y1[1] (closed_form) = 1.16614088506 -0.145140831516 absolute error = 0.03104 relative error = 2.642 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6063 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 = 0.6063 Order of pole (three term test) = 31.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11222.8MB, alloc=44.3MB, time=138.71 memory used=11269.1MB, alloc=44.3MB, time=139.29 x[1] = 0.2233 0.621 h = 0.0001 0.003 y2[1] (numeric) = 0.163805409788 0.701013353166 y2[1] (closed_form) = 0.26553877359 0.645262101556 absolute error = 0.116 relative error = 16.63 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.19008263429 -0.122686012678 y1[1] (closed_form) = 1.16932611729 -0.146530642357 absolute error = 0.03161 relative error = 2.683 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4936 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 = 0.4936 Order of pole (three term test) = 31.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11314.9MB, alloc=44.3MB, time=139.86 memory used=11361.3MB, alloc=44.3MB, time=140.44 x[1] = 0.2234 0.624 h = 0.001 0.001 y2[1] (numeric) = 0.164783337644 0.705706792093 y2[1] (closed_form) = 0.266096686488 0.648758252816 absolute error = 0.1162 relative error = 16.57 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.19217628307 -0.123249229057 y1[1] (closed_form) = 1.17124056466 -0.147392795823 absolute error = 0.03196 relative error = 2.707 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.39 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 = 0.39 Order of pole (three term test) = 31.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11407.2MB, alloc=44.3MB, time=141.02 x[1] = 0.2244 0.625 h = 0.0001 0.004 y2[1] (numeric) = 0.16577198879 0.710408580999 y2[1] (closed_form) = 0.267415968948 0.649781834048 absolute error = 0.1184 relative error = 16.84 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.19271906329 -0.124122562817 y1[1] (closed_form) = 1.17162307852 -0.14830882213 absolute error = 0.03209 relative error = 2.718 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.348 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 = 2.348 Order of pole (three term test) = 31.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11453.6MB, alloc=44.3MB, time=141.59 memory used=11499.5MB, alloc=44.3MB, time=142.16 x[1] = 0.2245 0.629 h = 0.003 0.006 y2[1] (numeric) = 0.166771368298 0.715118735668 y2[1] (closed_form) = 0.268128766968 0.654458595881 absolute error = 0.1181 relative error = 16.7 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.19555348805 -0.124858922249 y1[1] (closed_form) = 1.17420477878 -0.149445121938 absolute error = 0.03256 relative error = 2.751 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.404 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 = 1.404 Order of pole (three term test) = 31.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11545.2MB, alloc=44.3MB, time=142.72 memory used=11591.3MB, alloc=44.3MB, time=143.30 x[1] = 0.2275 0.635 h = 0.0001 0.005 y2[1] (numeric) = 0.167781546097 0.719837308249 y2[1] (closed_form) = 0.272563511543 0.661059501194 absolute error = 0.1201 relative error = 16.8 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.19935652532 -0.128015007489 y1[1] (closed_form) = 1.17734029839 -0.153040458423 absolute error = 0.03333 relative error = 2.807 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6329 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 = 0.6329 Order of pole (three term test) = 31.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11637.2MB, alloc=44.3MB, time=143.86 memory used=11683.4MB, alloc=44.3MB, time=144.44 x[1] = 0.2276 0.64 h = 0.0001 0.003 y2[1] (numeric) = 0.168802767536 0.724564348038 y2[1] (closed_form) = 0.273450188741 0.666939046621 absolute error = 0.1195 relative error = 16.57 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.20295069679 -0.128928683655 y1[1] (closed_form) = 1.18063298733 -0.154471889345 absolute error = 0.03392 relative error = 2.849 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5151 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 = 0.5151 Order of pole (three term test) = 31.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11729.3MB, alloc=44.3MB, time=145.01 x[1] = 0.2277 0.643 h = 0.001 0.001 y2[1] (numeric) = 0.169835112198 0.729299960762 y2[1] (closed_form) = 0.274033098173 0.670468419478 absolute error = 0.1197 relative error = 16.52 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.2051145593 -0.129509330835 y1[1] (closed_form) = 1.18261172293 -0.155359983885 absolute error = 0.03427 relative error = 2.873 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.407 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 = 0.407 Order of pole (three term test) = 31.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11775.3MB, alloc=44.3MB, time=145.58 memory used=11821.6MB, alloc=44.3MB, time=146.16 x[1] = 0.2287 0.644 h = 0.001 0.003 y2[1] (numeric) = 0.170878590052 0.734044191257 y2[1] (closed_form) = 0.275371740691 0.671495396738 absolute error = 0.1218 relative error = 16.78 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.20567587474 -0.130411358116 y1[1] (closed_form) = 1.18300800258 -0.156305668146 absolute error = 0.03441 relative error = 2.884 % Correct digits = 2 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) = 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 = 1.937 Order of pole (three term test) = 31.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11867.6MB, alloc=44.3MB, time=146.73 memory used=11913.7MB, alloc=44.3MB, time=147.31 x[1] = 0.2297 0.647 h = 0.0001 0.004 y2[1] (numeric) = 0.171933209294 0.738797045846 y2[1] (closed_form) = 0.277026787269 0.674889977815 absolute error = 0.123 relative error = 16.86 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.20771372946 -0.131661992926 y1[1] (closed_form) = 1.18475138096 -0.157807456753 absolute error = 0.0348 relative error = 2.911 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.103 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 = 1.103 Order of pole (three term test) = 31.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=11959.5MB, alloc=44.3MB, time=147.88 memory used=12005.5MB, alloc=44.3MB, time=148.44 x[1] = 0.2298 0.651 h = 0.003 0.006 y2[1] (numeric) = 0.172998995289 0.743558548054 y2[1] (closed_form) = 0.277778979651 0.679618500022 absolute error = 0.1227 relative error = 16.72 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.21066119124 -0.132425971317 y1[1] (closed_form) = 1.18743265414 -0.158984791963 absolute error = 0.03528 relative error = 2.945 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.475 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 = 1.475 Order of pole (three term test) = 31.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12051.4MB, alloc=44.3MB, time=149.01 x[1] = 0.2328 0.657 h = 0.0001 0.005 y2[1] (numeric) = 0.174076024428 0.748328753544 y2[1] (closed_form) = 0.282311229771 0.686270319178 absolute error = 0.1248 relative error = 16.81 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.2146162391 -0.135705019465 y1[1] (closed_form) = 1.19069018914 -0.162713877657 absolute error = 0.03608 relative error = 3.002 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6648 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 = 0.6648 Order of pole (three term test) = 31.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12097.3MB, alloc=44.3MB, time=149.58 memory used=12143.6MB, alloc=44.3MB, time=150.15 x[1] = 0.2329 0.662 h = 0.0001 0.003 y2[1] (numeric) = 0.175164545367 0.753107710607 y2[1] (closed_form) = 0.283247743675 0.692215957118 absolute error = 0.1241 relative error = 16.59 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.21835236466 -0.136653187822 y1[1] (closed_form) = 1.19410811989 -0.164196696031 absolute error = 0.03669 relative error = 3.044 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5411 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 = 0.5411 Order of pole (three term test) = 31.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12189.4MB, alloc=44.3MB, time=150.72 memory used=12235.8MB, alloc=44.3MB, time=151.30 x[1] = 0.233 0.665 h = 0.001 0.001 y2[1] (numeric) = 0.176264639362 0.757895525736 y2[1] (closed_form) = 0.283861226714 0.695784893628 absolute error = 0.1242 relative error = 16.53 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.22060129593 -0.137255878792 y1[1] (closed_form) = 1.19616176422 -0.165116758738 absolute error = 0.03706 relative error = 3.069 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4275 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 = 0.4275 Order of pole (three term test) = 31.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12281.7MB, alloc=44.3MB, time=151.88 x[1] = 0.234 0.666 h = 0.001 0.003 y2[1] (numeric) = 0.177376316802 0.762692244256 y2[1] (closed_form) = 0.285223201365 0.696815654319 absolute error = 0.1264 relative error = 16.78 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.22118476956 -0.138192991447 y1[1] (closed_form) = 1.19657352245 -0.166097601157 absolute error = 0.03721 relative error = 3.08 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.034 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 = 2.034 Order of pole (three term test) = 31.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12327.9MB, alloc=44.3MB, time=152.45 memory used=12374.0MB, alloc=44.3MB, time=153.02 x[1] = 0.235 0.669 h = 0.0001 0.004 y2[1] (numeric) = 0.178499586027 0.767497872511 y2[1] (closed_form) = 0.286921304717 0.700241211747 absolute error = 0.1276 relative error = 16.86 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.22330211552 -0.139491896716 y1[1] (closed_form) = 1.19838303506 -0.167654344407 absolute error = 0.0376 relative error = 3.108 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.159 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 = 1.159 Order of pole (three term test) = 31.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12419.8MB, alloc=44.3MB, time=153.59 memory used=12465.9MB, alloc=44.3MB, time=154.16 x[1] = 0.2351 0.673 h = 0.003 0.006 y2[1] (numeric) = 0.179634472873 0.77231243415 y2[1] (closed_form) = 0.287714337178 0.705023474745 absolute error = 0.1273 relative error = 16.72 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.22636382654 -0.140285151398 y1[1] (closed_form) = 1.20116482903 -0.168873877114 absolute error = 0.03811 relative error = 3.142 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.549 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 = 1.549 Order of pole (three term test) = 31.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12511.6MB, alloc=44.3MB, time=154.72 memory used=12557.8MB, alloc=44.3MB, time=155.30 x[1] = 0.2381 0.679 h = 0.0001 0.005 y2[1] (numeric) = 0.180781055051 0.777135985018 y2[1] (closed_form) = 0.292347710522 0.711728183458 absolute error = 0.1293 relative error = 16.81 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.23047154696 -0.143690562449 y1[1] (closed_form) = 1.20454499492 -0.172739171907 absolute error = 0.03894 relative error = 3.2 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.698 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 = 0.698 Order of pole (three term test) = 31.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12603.7MB, alloc=44.3MB, time=155.87 x[1] = 0.2382 0.684 h = 0.0001 0.003 y2[1] (numeric) = 0.181939584649 0.781968572353 y2[1] (closed_form) = 0.293335874739 0.717742406252 absolute error = 0.1286 relative error = 16.58 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.23435116863 -0.144675314192 y1[1] (closed_form) = 1.20808937996 -0.174274850906 absolute error = 0.03957 relative error = 3.242 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5681 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 = 0.5681 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12649.6MB, alloc=44.3MB, time=156.43 memory used=12696.0MB, alloc=44.3MB, time=157.02 x[1] = 0.2383 0.687 h = 0.001 0.001 y2[1] (numeric) = 0.183110144654 0.786810303449 y2[1] (closed_form) = 0.293981043423 0.7213523905 absolute error = 0.1288 relative error = 16.53 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.23668608226 -0.145301324644 y1[1] (closed_form) = 1.21021865477 -0.175227780203 absolute error = 0.03995 relative error = 3.267 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4488 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 = 0.4488 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12742.1MB, alloc=44.3MB, time=157.58 memory used=12788.3MB, alloc=44.3MB, time=158.17 x[1] = 0.2393 0.688 h = 0.001 0.003 y2[1] (numeric) = 0.184292745892 0.791661224132 y2[1] (closed_form) = 0.295367211555 0.722387086932 absolute error = 0.1309 relative error = 16.77 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.23729161682 -0.146274260083 y1[1] (closed_form) = 1.21064585055 -0.176244323998 absolute error = 0.0401 relative error = 3.278 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.135 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 = 2.135 Order of pole (three term test) = 31.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12834.2MB, alloc=44.3MB, time=158.74 memory used=12880.6MB, alloc=44.3MB, time=159.34 x[1] = 0.2403 0.691 h = 0.0001 0.004 y2[1] (numeric) = 0.185487396852 0.796521340773 y2[1] (closed_form) = 0.297109944786 0.725844786474 absolute error = 0.1321 relative error = 16.85 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.2394889993 -0.147623017798 y1[1] (closed_form) = 1.21252195933 -0.177857153656 absolute error = 0.04051 relative error = 3.306 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.216 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 = 1.216 Order of pole (three term test) = 31.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12926.4MB, alloc=44.3MB, time=159.93 x[1] = 0.2404 0.695 h = 0.003 0.006 y2[1] (numeric) = 0.186694123857 0.801390677147 y2[1] (closed_form) = 0.297945294196 0.730682785655 absolute error = 0.1318 relative error = 16.71 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.24266621128 -0.148447272334 y1[1] (closed_form) = 1.21540525796 -0.179120088638 absolute error = 0.04104 relative error = 3.34 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.625 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 = 1.625 Order of pole (three term test) = 31.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=12972.1MB, alloc=44.3MB, time=160.48 memory used=13018.4MB, alloc=44.3MB, time=161.05 x[1] = 0.2434 0.701 h = 0.0001 0.005 y2[1] (numeric) = 0.18791300599 0.806269289288 y2[1] (closed_form) = 0.30268346688 0.73744236017 absolute error = 0.1338 relative error = 16.79 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.24692727891 -0.151982575209 y1[1] (closed_form) = 1.21890869438 -0.18312414312 absolute error = 0.04189 relative error = 3.399 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7325 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 = 0.7325 Order of pole (three term test) = 31.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13064.2MB, alloc=44.3MB, time=161.61 memory used=13110.4MB, alloc=44.3MB, time=162.18 x[1] = 0.2435 0.706 h = 0.0001 0.003 y2[1] (numeric) = 0.189144298892 0.811157223345 y2[1] (closed_form) = 0.30372513456 0.743527679381 absolute error = 0.1331 relative error = 16.57 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.25095198852 -0.153006084517 y1[1] (closed_form) = 1.22258079154 -0.184714209508 absolute error = 0.04255 relative error = 3.441 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5961 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 = 0.5961 Order of pole (three term test) = 31.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13156.4MB, alloc=44.3MB, time=162.74 x[1] = 0.2436 0.709 h = 0.001 0.001 y2[1] (numeric) = 0.190388087348 0.816054587443 y2[1] (closed_form) = 0.30440312495 0.747180206777 absolute error = 0.1332 relative error = 16.51 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.25337382736 -0.153656740482 y1[1] (closed_form) = 1.22478644535 -0.185700936442 absolute error = 0.04294 relative error = 3.467 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4709 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 = 0.4709 Order of pole (three term test) = 31.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13202.6MB, alloc=44.3MB, time=163.31 memory used=13248.9MB, alloc=44.3MB, time=163.88 x[1] = 0.2446 0.71 h = 0.001 0.003 y2[1] (numeric) = 0.191644382635 0.820961427927 y2[1] (closed_form) = 0.305814359858 0.748218987413 absolute error = 0.1354 relative error = 16.75 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.25400131938 -0.154666262893 y1[1] (closed_form) = 1.22522903638 -0.186753744708 absolute error = 0.0431 relative error = 3.477 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.24 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 = 2.24 Order of pole (three term test) = 31.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13294.9MB, alloc=44.3MB, time=164.44 memory used=13341.1MB, alloc=44.3MB, time=165.02 x[1] = 0.2456 0.713 h = 0.0001 0.004 y2[1] (numeric) = 0.192913193397 0.825877751195 y2[1] (closed_form) = 0.307603323916 0.751709999076 absolute error = 0.1366 relative error = 16.82 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.25627929803 -0.156066514924 y1[1] (closed_form) = 1.22717222056 -0.188423833642 absolute error = 0.04352 relative error = 3.505 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.276 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 = 1.276 Order of pole (three term test) = 31.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13386.8MB, alloc=44.3MB, time=165.58 memory used=13433.0MB, alloc=44.3MB, time=166.15 x[1] = 0.2457 0.717 h = 0.003 0.006 y2[1] (numeric) = 0.194194546461 0.830803581153 y2[1] (closed_form) = 0.308482499437 0.756605745377 absolute error = 0.1363 relative error = 16.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.25957330224 -0.156923560206 y1[1] (closed_form) = 1.23015804386 -0.189731419135 absolute error = 0.04406 relative error = 3.54 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.705 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 = 1.705 Order of pole (three term test) = 31.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13478.8MB, alloc=44.3MB, time=166.72 x[1] = 0.2487 0.723 h = 0.0001 0.005 y2[1] (numeric) = 0.195488522329 0.835738974033 y2[1] (closed_form) = 0.313329208155 0.763422162512 absolute error = 0.1383 relative error = 16.75 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.2639884037 -0.160592414475 y1[1] (closed_form) = 1.2337854143 -0.19387687591 absolute error = 0.04495 relative error = 3.599 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7683 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 = 0.7683 Order of pole (three term test) = 31.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13524.7MB, alloc=44.3MB, time=167.29 memory used=13570.9MB, alloc=44.3MB, time=167.86 x[1] = 0.2488 0.728 h = 0.0001 0.003 y2[1] (numeric) = 0.196795380326 0.840683974855 y2[1] (closed_form) = 0.314426273422 0.769581109641 absolute error = 0.1375 relative error = 16.53 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.26815984296 -0.1616569399 y1[1] (closed_form) = 1.23758652693 -0.195522911033 absolute error = 0.04562 relative error = 3.641 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6252 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 = 0.6252 Order of pole (three term test) = 31.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13616.9MB, alloc=44.3MB, time=168.45 memory used=13663.2MB, alloc=44.3MB, time=169.04 x[1] = 0.2489 0.731 h = 0.001 0.001 y2[1] (numeric) = 0.198115207097 0.845638692601 y2[1] (closed_form) = 0.315138246463 0.773277687335 absolute error = 0.1376 relative error = 16.48 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.2706695791 -0.162333618589 y1[1] (closed_form) = 1.23986933524 -0.196544399873 absolute error = 0.04603 relative error = 3.667 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4939 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 = 0.4939 Order of pole (three term test) = 31.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13709.1MB, alloc=44.3MB, time=169.67 memory used=13755.4MB, alloc=44.3MB, time=170.30 x[1] = 0.2499 0.732 h = 0.0001 0.004 y2[1] (numeric) = 0.199448014388 0.850603174161 y2[1] (closed_form) = 0.316575433823 0.774320696654 absolute error = 0.1398 relative error = 16.71 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.27131891869 -0.163380519237 y1[1] (closed_form) = 1.24032727777 -0.197634055829 absolute error = 0.04619 relative error = 3.678 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.973 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 = 2.973 Order of pole (three term test) = 31.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13801.3MB, alloc=44.3MB, time=171.18 x[1] = 0.25 0.736 h = 0.003 0.006 y2[1] (numeric) = 0.200793808129 0.855577436139 y2[1] (closed_form) = 0.317492846624 0.779268319478 absolute error = 0.1394 relative error = 16.57 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.27471126466 -0.1642663075 y1[1] (closed_form) = 1.24340274838 -0.198979869842 absolute error = 0.04675 relative error = 3.712 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.776 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 = 1.776 Order of pole (three term test) = 31.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13847.1MB, alloc=44.3MB, time=171.74 memory used=13893.3MB, alloc=44.3MB, time=172.32 x[1] = 0.253 0.742 h = 0.0001 0.005 y2[1] (numeric) = 0.20215266446 0.860561531584 y2[1] (closed_form) = 0.322435310466 0.786136602907 absolute error = 0.1414 relative error = 16.65 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.27925526023 -0.16804934631 y1[1] (closed_form) = 1.24713907531 -0.203247740885 absolute error = 0.04765 relative error = 3.771 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8004 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 = 0.8004 Order of pole (three term test) = 31.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=13939.1MB, alloc=44.3MB, time=172.89 memory used=13985.3MB, alloc=44.3MB, time=173.47 x[1] = 0.2531 0.747 h = 0.0001 0.003 y2[1] (numeric) = 0.203524845982 0.865555504548 y2[1] (closed_form) = 0.323580690774 0.792361660785 absolute error = 0.1406 relative error = 16.43 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.28355026492 -0.169149840272 y1[1] (closed_form) = 1.25105301216 -0.204941701948 absolute error = 0.04834 relative error = 3.813 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6513 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 = 0.6513 Order of pole (three term test) = 31.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14031.2MB, alloc=44.3MB, time=174.05 x[1] = 0.2532 0.75 h = 0.001 0.001 y2[1] (numeric) = 0.204910440986 0.8705594648 y2[1] (closed_form) = 0.324322314868 0.796097795764 absolute error = 0.1407 relative error = 16.37 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.28613401321 -0.169849295512 y1[1] (closed_form) = 1.25340330449 -0.205992978524 absolute error = 0.04876 relative error = 3.839 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5144 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 = 0.5144 Order of pole (three term test) = 31.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14077.4MB, alloc=44.3MB, time=174.63 memory used=14123.7MB, alloc=44.3MB, time=175.20 x[1] = 0.2542 0.751 h = 0.001 0.003 y2[1] (numeric) = 0.206309461625 0.875573459712 y2[1] (closed_form) = 0.325782507598 0.797144881281 absolute error = 0.1429 relative error = 16.6 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.28680147 -0.17092796997 y1[1] (closed_form) = 1.2538748736 -0.207114652195 absolute error = 0.04892 relative error = 3.85 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.447 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 = 2.447 Order of pole (three term test) = 31.47 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14169.5MB, alloc=44.3MB, time=175.77 memory used=14215.7MB, alloc=44.3MB, time=176.34 x[1] = 0.2552 0.754 h = 0.0001 0.004 y2[1] (numeric) = 0.207721916842 0.880597495732 y2[1] (closed_form) = 0.327661427051 0.800701605346 absolute error = 0.1441 relative error = 16.66 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.28922870936 -0.172427098316 y1[1] (closed_form) = 1.25594492087 -0.208893739119 absolute error = 0.04937 relative error = 3.878 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.394 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 = 1.394 Order of pole (three term test) = 31.47 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14261.7MB, alloc=44.3MB, time=176.91 memory used=14307.8MB, alloc=44.3MB, time=177.48 x[1] = 0.2553 0.758 h = 0.0001 0.004 y2[1] (numeric) = 0.209147834449 0.885631597031 y2[1] (closed_form) = 0.328625539666 0.805710779413 absolute error = 0.1437 relative error = 16.52 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.2927403208 -0.173349144698 y1[1] (closed_form) = 1.25912492715 -0.210286631604 absolute error = 0.04994 relative error = 3.912 % Correct digits = 1 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=14353.6MB, alloc=44.3MB, time=178.05 x[1] = 0.2554 0.762 h = 0.003 0.006 y2[1] (numeric) = 0.210587236713 0.890675832576 y2[1] (closed_form) = 0.329595551581 0.810732573911 absolute error = 0.1434 relative error = 16.38 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.29627194563 -0.174277425629 y1[1] (closed_form) = 1.26232489863 -0.211683893879 absolute error = 0.05051 relative error = 3.947 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.878 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 = 1.878 Order of pole (three term test) = 31.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14399.3MB, alloc=44.3MB, time=178.61 memory used=14445.6MB, alloc=44.3MB, time=179.20 x[1] = 0.2584 0.768 h = 0.0001 0.005 y2[1] (numeric) = 0.212040204328 0.895730269475 y2[1] (closed_form) = 0.334671736815 0.817676484628 absolute error = 0.1454 relative error = 16.45 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.30099722109 -0.178224907702 y1[1] (closed_form) = 1.26621372943 -0.216119287686 absolute error = 0.05144 relative error = 4.004 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8461 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 = 0.8461 Order of pole (three term test) = 31.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14491.6MB, alloc=44.3MB, time=179.77 memory used=14537.7MB, alloc=44.3MB, time=180.35 x[1] = 0.2585 0.773 h = 0.0001 0.003 y2[1] (numeric) = 0.213507004563 0.900794950535 y2[1] (closed_form) = 0.335883551278 0.823996016976 absolute error = 0.1445 relative error = 16.24 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.30546725261 -0.179378596104 y1[1] (closed_form) = 1.27028437459 -0.21787775553 absolute error = 0.05215 relative error = 4.047 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6883 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 = 0.6883 Order of pole (three term test) = 31.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14583.6MB, alloc=44.3MB, time=180.92 memory used=14630.1MB, alloc=44.3MB, time=181.51 x[1] = 0.2586 0.776 h = 0.001 0.001 y2[1] (numeric) = 0.214987728002 0.905869986676 y2[1] (closed_form) = 0.336665971527 0.827788691023 absolute error = 0.1446 relative error = 16.18 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.30815582279 -0.18011166788 y1[1] (closed_form) = 1.2727284224 -0.21896916811 absolute error = 0.05258 relative error = 4.072 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5437 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 = 0.5437 Order of pole (three term test) = 31.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14676.1MB, alloc=44.3MB, time=182.08 x[1] = 0.2596 0.777 h = 0.001 0.003 y2[1] (numeric) = 0.216482387364 0.910955425965 y2[1] (closed_form) = 0.338158497258 0.828842113114 absolute error = 0.1468 relative error = 16.4 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.30884850074 -0.181235813615 y1[1] (closed_form) = 1.27321932576 -0.220134895664 absolute error = 0.05275 relative error = 4.082 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.586 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 = 2.586 Order of pole (three term test) = 31.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14722.0MB, alloc=44.3MB, time=182.66 memory used=14768.2MB, alloc=44.3MB, time=183.23 x[1] = 0.2606 0.78 h = 0.0001 0.004 y2[1] (numeric) = 0.21799099179 0.916051274889 y2[1] (closed_form) = 0.340095966612 0.832443939954 absolute error = 0.148 relative error = 16.46 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.31137177266 -0.182801022677 y1[1] (closed_form) = 1.2753721271 -0.221982918078 absolute error = 0.05321 relative error = 4.11 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.473 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 = 1.473 Order of pole (three term test) = 31.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14814.0MB, alloc=44.3MB, time=183.79 memory used=14860.1MB, alloc=44.3MB, time=184.36 x[1] = 0.2607 0.784 h = 0.003 0.006 y2[1] (numeric) = 0.219513569742 0.921157557812 y2[1] (closed_form) = 0.34111449093 0.837529762931 absolute error = 0.1476 relative error = 16.32 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.31502431172 -0.183767887492 y1[1] (closed_form) = 1.27867800967 -0.223428835531 absolute error = 0.0538 relative error = 4.144 % Correct digits = 1 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) = 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 = 1.968 Order of pole (three term test) = 31.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14906.0MB, alloc=44.3MB, time=184.93 x[1] = 0.2637 0.79 h = 0.0001 0.005 y2[1] (numeric) = 0.221050206328 0.926274331681 y2[1] (closed_form) = 0.346310843919 0.844536711474 absolute error = 0.1496 relative error = 16.39 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.31990576002 -0.187860716932 y1[1] (closed_form) = 1.28269307582 -0.228014188885 absolute error = 0.05475 relative error = 4.202 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8865 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 = 0.8865 Order of pole (three term test) = 31.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=14952.1MB, alloc=44.3MB, time=185.51 memory used=14998.1MB, alloc=44.3MB, time=186.08 x[1] = 0.2638 0.795 h = 0.0001 0.003 y2[1] (numeric) = 0.222601172899 0.931401638049 y2[1] (closed_form) = 0.347583939952 0.850937781192 absolute error = 0.1486 relative error = 16.17 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.32452776309 -0.189062723087 y1[1] (closed_form) = 1.2868970587 -0.22983369543 absolute error = 0.05548 relative error = 4.244 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7212 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 = 0.7212 Order of pole (three term test) = 31.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15044.1MB, alloc=44.3MB, time=186.65 memory used=15090.4MB, alloc=44.3MB, time=187.23 x[1] = 0.2639 0.798 h = 0.001 0.001 y2[1] (numeric) = 0.224166562098 0.936539588784 y2[1] (closed_form) = 0.348403950026 0.85477921536 absolute error = 0.1487 relative error = 16.11 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.32730733399 -0.189826268054 y1[1] (closed_form) = 1.28942083297 -0.230962962143 absolute error = 0.05593 relative error = 4.269 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5697 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 = 0.5697 Order of pole (three term test) = 31.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15136.3MB, alloc=44.3MB, time=187.80 memory used=15182.7MB, alloc=44.3MB, time=188.37 x[1] = 0.2649 0.799 h = 0.001 0.003 y2[1] (numeric) = 0.225746387162 0.941688232554 y2[1] (closed_form) = 0.349925188953 0.85583732432 absolute error = 0.151 relative error = 16.33 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.32802149174 -0.190990336344 y1[1] (closed_form) = 1.28992697687 -0.232167434898 absolute error = 0.0561 relative error = 4.28 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.71 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 = 2.71 Order of pole (three term test) = 31.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15228.6MB, alloc=44.3MB, time=188.93 x[1] = 0.2659 0.802 h = 0.0001 0.004 y2[1] (numeric) = 0.227340657407 0.946847575874 y2[1] (closed_form) = 0.351915591737 0.859477314253 absolute error = 0.1522 relative error = 16.38 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.33062775046 -0.192614230309 y1[1] (closed_form) = 1.29214902791 -0.234077851003 absolute error = 0.05657 relative error = 4.308 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.543 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 = 1.543 Order of pole (three term test) = 31.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15274.5MB, alloc=44.3MB, time=189.50 memory used=15320.6MB, alloc=44.3MB, time=190.06 x[1] = 0.266 0.806 h = 0.003 0.006 y2[1] (numeric) = 0.228949401874 0.95201764326 y2[1] (closed_form) = 0.352984278931 0.864629246913 absolute error = 0.1517 relative error = 16.25 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.33440266293 -0.19362174877 y1[1] (closed_form) = 1.29556199159 -0.235573853852 absolute error = 0.05717 relative error = 4.342 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.062 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 = 2.062 Order of pole (three term test) = 31.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15366.5MB, alloc=44.3MB, time=190.63 memory used=15412.7MB, alloc=44.3MB, time=191.23 x[1] = 0.269 0.812 h = 0.0001 0.005 y2[1] (numeric) = 0.230572707297 0.957198491883 y2[1] (closed_form) = 0.358304802955 0.871701216028 absolute error = 0.1537 relative error = 16.31 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.33944102645 -0.197864129253 y1[1] (closed_form) = 1.29970405426 -0.240312193705 absolute error = 0.05815 relative error = 4.399 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9287 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 = 0.9287 Order of pole (three term test) = 31.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15458.5MB, alloc=44.3MB, time=191.78 memory used=15504.7MB, alloc=44.3MB, time=192.35 x[1] = 0.2691 0.817 h = 0.0001 0.003 y2[1] (numeric) = 0.232210849239 0.962390162005 y2[1] (closed_form) = 0.359641253834 0.878186444601 absolute error = 0.1527 relative error = 16.1 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.3442168545 -0.199117061271 y1[1] (closed_form) = 1.30404286723 -0.242194548948 absolute error = 0.0589 relative error = 4.441 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7555 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 = 0.7555 Order of pole (three term test) = 31.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15550.7MB, alloc=44.3MB, time=192.91 x[1] = 0.2692 0.82 h = 0.001 0.001 y2[1] (numeric) = 0.23386392247 0.967592766476 y2[1] (closed_form) = 0.360500123486 0.882078199046 absolute error = 0.1528 relative error = 16.04 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.34708852253 -0.199912668748 y1[1] (closed_form) = 1.30664725523 -0.243362773241 absolute error = 0.05936 relative error = 4.466 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5967 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 = 0.5967 Order of pole (three term test) = 31.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15596.7MB, alloc=44.3MB, time=193.48 memory used=15643.0MB, alloc=44.3MB, time=194.04 x[1] = 0.2702 0.821 h = 0.001 0.003 y2[1] (numeric) = 0.235531940762 0.972806354579 y2[1] (closed_form) = 0.362051015947 0.883141122511 absolute error = 0.1551 relative error = 16.25 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.34782402449 -0.201117564079 y1[1] (closed_form) = 1.30716858953 -0.244606658384 absolute error = 0.05953 relative error = 4.477 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.838 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 = 2.838 Order of pole (three term test) = 31.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15688.9MB, alloc=44.3MB, time=194.60 memory used=15735.3MB, alloc=44.3MB, time=195.17 x[1] = 0.2712 0.824 h = 0.0001 0.004 y2[1] (numeric) = 0.237214913614 0.97803093286 y2[1] (closed_form) = 0.364096108541 0.886820470894 absolute error = 0.1563 relative error = 16.3 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.35051390549 -0.202802098346 y1[1] (closed_form) = 1.30946045781 -0.246580857406 absolute error = 0.06002 relative error = 4.504 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.616 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 = 1.616 Order of pole (three term test) = 31.35 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15781.1MB, alloc=44.3MB, time=195.73 x[1] = 0.2713 0.828 h = 0.003 0.006 y2[1] (numeric) = 0.238912870664 0.983266525989 y2[1] (closed_form) = 0.36521664737 0.892040612884 absolute error = 0.1558 relative error = 16.16 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.35441269047 -0.203852413696 y1[1] (closed_form) = 1.31298170976 -0.248128423675 absolute error = 0.06064 relative error = 4.538 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.159 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 = 2.159 Order of pole (three term test) = 31.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15827.1MB, alloc=44.3MB, time=196.28 memory used=15873.2MB, alloc=44.3MB, time=196.84 x[1] = 0.2743 0.834 h = 0.0001 0.005 y2[1] (numeric) = 0.240625900323 0.988513191372 y2[1] (closed_form) = 0.370665417487 0.899179586003 absolute error = 0.1578 relative error = 16.22 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.35960871972 -0.208248689208 y1[1] (closed_form) = 1.31725155233 -0.253022876346 absolute error = 0.06163 relative error = 4.595 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9726 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 = 0.9726 Order of pole (three term test) = 31.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=15919.1MB, alloc=44.3MB, time=197.40 memory used=15965.2MB, alloc=44.3MB, time=197.96 x[1] = 0.2744 0.839 h = 0.0001 0.003 y2[1] (numeric) = 0.242354282502 0.993770967931 y2[1] (closed_form) = 0.372067345001 0.90575161851 absolute error = 0.1568 relative error = 16.01 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.36454027659 -0.20955524735 y1[1] (closed_form) = 1.32172673455 -0.254969950384 absolute error = 0.06241 relative error = 4.637 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7911 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 = 0.7911 Order of pole (three term test) = 31.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16011.0MB, alloc=44.3MB, time=198.53 memory used=16057.5MB, alloc=44.3MB, time=199.10 x[1] = 0.2745 0.842 h = 0.001 0.001 y2[1] (numeric) = 0.24409811417 0.999039969526 y2[1] (closed_form) = 0.372966373433 0.909695267268 absolute error = 0.1568 relative error = 15.95 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.36750516769 -0.210384562533 y1[1] (closed_form) = 1.32441265124 -0.256178272267 absolute error = 0.06288 relative error = 4.661 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6249 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 = 0.6249 Order of pole (three term test) = 31.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16103.5MB, alloc=44.3MB, time=199.66 x[1] = 0.2755 0.843 h = 0.001 0.003 y2[1] (numeric) = 0.245857409649 1.00432024608 y2[1] (closed_form) = 0.374547874408 0.910763128154 absolute error = 0.1591 relative error = 16.16 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.36826187038 -0.211631218174 y1[1] (closed_form) = 1.32494912353 -0.257462258499 absolute error = 0.06306 relative error = 4.672 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.972 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 = 2.972 Order of pole (three term test) = 31.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16149.5MB, alloc=44.3MB, time=200.22 memory used=16195.7MB, alloc=44.3MB, time=200.79 x[1] = 0.2765 0.846 h = 0.0001 0.004 y2[1] (numeric) = 0.247632178628 1.00961180416 y2[1] (closed_form) = 0.376649447306 0.914483035533 absolute error = 0.1603 relative error = 16.21 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.37103602213 -0.213378413769 y1[1] (closed_form) = 1.32731139356 -0.259501675023 absolute error = 0.06355 relative error = 4.699 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.692 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 = 1.692 Order of pole (three term test) = 31.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16241.6MB, alloc=44.3MB, time=201.34 memory used=16287.9MB, alloc=44.3MB, time=201.91 x[1] = 0.2766 0.85 h = 0.003 0.006 y2[1] (numeric) = 0.24942245136 1.01491466861 y2[1] (closed_form) = 0.37782356608 0.919773505505 absolute error = 0.1598 relative error = 16.07 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.3750602187 -0.214473744085 y1[1] (closed_form) = 1.33094217826 -0.261102331502 absolute error = 0.06419 relative error = 4.733 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.261 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 = 2.261 Order of pole (three term test) = 31.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16333.8MB, alloc=44.3MB, time=202.47 x[1] = 0.2796 0.856 h = 0.0001 0.005 y2[1] (numeric) = 0.251228317989 1.02022889706 y2[1] (closed_form) = 0.383404731443 0.9269814667 absolute error = 0.1618 relative error = 16.13 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.38041467148 -0.219028401031 y1[1] (closed_form) = 1.33534060599 -0.266156124286 absolute error = 0.06521 relative error = 4.789 % Correct digits = 1 memory used=16379.9MB, alloc=44.3MB, time=203.04 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.018 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 = 1.018 Order of pole (three term test) = 31.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16425.8MB, alloc=44.3MB, time=203.60 x[1] = 0.2797 0.861 h = 0.0001 0.003 y2[1] (numeric) = 0.253050062909 1.02555452705 y2[1] (closed_form) = 0.384874307477 0.933642972525 absolute error = 0.1607 relative error = 15.91 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.38550391149 -0.220391379408 y1[1] (closed_form) = 1.3399537437 -0.268169848527 absolute error = 0.06601 relative error = 4.831 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8283 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 = 0.8283 Order of pole (three term test) = 31.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16471.7MB, alloc=44.3MB, time=204.16 memory used=16518.0MB, alloc=44.3MB, time=204.73 x[1] = 0.2798 0.864 h = 0.001 0.001 y2[1] (numeric) = 0.254887785358 1.03089167348 y2[1] (closed_form) = 0.385814824307 0.937640103926 absolute error = 0.1607 relative error = 15.85 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.38856318114 -0.221256104397 y1[1] (closed_form) = 1.34272213184 -0.269419445304 absolute error = 0.06649 relative error = 4.855 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6542 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 = 0.6542 Order of pole (three term test) = 31.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16564.1MB, alloc=44.3MB, time=205.30 memory used=16610.4MB, alloc=44.3MB, time=205.86 x[1] = 0.2808 0.865 h = 0.0001 0.004 y2[1] (numeric) = 0.256741500229 1.03624038694 y2[1] (closed_form) = 0.387427903882 0.938713020261 absolute error = 0.1631 relative error = 16.06 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.38934093289 -0.222545482773 y1[1] (closed_form) = 1.34327368726 -0.270744243139 absolute error = 0.06667 relative error = 4.866 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.937 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 = 3.937 Order of pole (three term test) = 31.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16656.3MB, alloc=44.3MB, time=206.42 x[1] = 0.2809 0.869 h = 0.003 0.006 y2[1] (numeric) = 0.25861121473 1.04160068524 y2[1] (closed_form) = 0.388648685156 0.944066404719 absolute error = 0.1626 relative error = 15.92 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.39347084367 -0.223680074824 y1[1] (closed_form) = 1.34700043743 -0.272390532846 absolute error = 0.06732 relative error = 4.899 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.352 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 = 2.352 Order of pole (three term test) = 31.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16702.0MB, alloc=44.3MB, time=206.97 memory used=16748.2MB, alloc=44.3MB, time=207.54 x[1] = 0.2839 0.875 h = 0.0001 0.005 y2[1] (numeric) = 0.260497014252 1.04697262285 y2[1] (closed_form) = 0.394346338814 0.951336983551 absolute error = 0.1645 relative error = 15.97 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.39895789948 -0.228370248446 y1[1] (closed_form) = 1.35151216048 -0.277582597783 absolute error = 0.06836 relative error = 4.955 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.059 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 = 1.059 Order of pole (three term test) = 31.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16794.1MB, alloc=44.3MB, time=208.09 memory used=16840.3MB, alloc=44.3MB, time=208.66 x[1] = 0.284 0.88 h = 0.0001 0.003 y2[1] (numeric) = 0.262399187171 1.05235623609 y2[1] (closed_form) = 0.395874813522 0.958078503676 absolute error = 0.1634 relative error = 15.76 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.40418007206 -0.229782448438 y1[1] (closed_form) = 1.35624617846 -0.279653616731 absolute error = 0.06917 relative error = 4.995 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8616 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 = 0.8616 Order of pole (three term test) = 31.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16886.2MB, alloc=44.3MB, time=209.22 memory used=16932.6MB, alloc=44.3MB, time=209.79 x[1] = 0.2841 0.883 h = 0.001 0.001 y2[1] (numeric) = 0.264317834721 1.05775164082 y2[1] (closed_form) = 0.396851467737 0.96212347061 absolute error = 0.1634 relative error = 15.7 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.40731889521 -0.230678025144 y1[1] (closed_form) = 1.35908684304 -0.280938715146 absolute error = 0.06966 relative error = 5.019 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.6805 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 = 0.6805 Order of pole (three term test) = 31.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=16978.5MB, alloc=44.3MB, time=210.35 x[1] = 0.2851 0.884 h = 0.001 0.003 y2[1] (numeric) = 0.266252972294 1.0631588882 y2[1] (closed_form) = 0.398492455778 0.96320122134 absolute error = 0.1658 relative error = 15.9 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.40811406546 -0.232003763451 y1[1] (closed_form) = 1.35965183365 -0.28229904936 absolute error = 0.06984 relative error = 5.03 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.237 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 = 3.237 Order of pole (three term test) = 31.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17024.6MB, alloc=44.3MB, time=210.92 memory used=17070.9MB, alloc=44.3MB, time=211.48 x[1] = 0.2861 0.887 h = 0.0001 0.004 y2[1] (numeric) = 0.268204609941 1.06857798487 y2[1] (closed_form) = 0.400703495076 0.967000537974 absolute error = 0.167 relative error = 15.95 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.41104444039 -0.233871313144 y1[1] (closed_form) = 1.36214753773 -0.284462941475 absolute error = 0.07036 relative error = 5.056 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.843 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 = 1.843 Order of pole (three term test) = 31.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17116.8MB, alloc=44.3MB, time=212.04 memory used=17163.0MB, alloc=44.3MB, time=212.60 x[1] = 0.2862 0.891 h = 0.003 0.006 y2[1] (numeric) = 0.270172779115 1.07400895598 y2[1] (closed_form) = 0.401981156144 0.972428267003 absolute error = 0.1664 relative error = 15.81 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.41530269157 -0.235055191655 y1[1] (closed_form) = 1.36598625611 -0.286165279694 absolute error = 0.07102 relative error = 5.089 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.462 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 = 2.462 Order of pole (three term test) = 31.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17208.8MB, alloc=44.3MB, time=213.16 x[1] = 0.2892 0.897 h = 0.0001 0.005 y2[1] (numeric) = 0.272157573325 1.07945185963 y2[1] (closed_form) = 0.407819107306 0.979771578895 absolute error = 0.1683 relative error = 15.86 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.42094957671 -0.239912362565 y1[1] (closed_form) = 1.37062816088 -0.291522954273 absolute error = 0.07208 relative error = 5.144 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.109 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 = 1.109 Order of pole (three term test) = 31.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17255.0MB, alloc=44.3MB, time=213.72 memory used=17301.0MB, alloc=44.3MB, time=214.28 x[1] = 0.2893 0.902 h = 0.0001 0.003 y2[1] (numeric) = 0.274159285697 1.08490673073 y2[1] (closed_form) = 0.409419378271 0.986607633921 absolute error = 0.1672 relative error = 15.65 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.42633315247 -0.241386365457 y1[1] (closed_form) = 1.37550323701 -0.293664364581 absolute error = 0.07292 relative error = 5.184 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9018 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 = 0.9018 Order of pole (three term test) = 31.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17346.9MB, alloc=44.3MB, time=214.84 memory used=17393.3MB, alloc=44.3MB, time=215.41 x[1] = 0.2894 0.905 h = 0.001 0.001 y2[1] (numeric) = 0.276178019869 1.09037368621 y2[1] (closed_form) = 0.410440059948 0.990709095211 absolute error = 0.1672 relative error = 15.59 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.42956855334 -0.242320631077 y1[1] (closed_form) = 1.37842821701 -0.294993018434 absolute error = 0.07341 relative error = 5.208 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7122 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 = 0.7122 Order of pole (three term test) = 31.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17439.2MB, alloc=44.3MB, time=215.97 memory used=17485.4MB, alloc=44.3MB, time=216.54 x[1] = 0.2904 0.906 h = 0.001 0.003 y2[1] (numeric) = 0.278213791837 1.09585277792 y2[1] (closed_form) = 0.412114472254 0.991792119412 absolute error = 0.1696 relative error = 15.79 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.43038447108 -0.243690937783 y1[1] (closed_form) = 1.37900819058 -0.29639554621 absolute error = 0.0736 relative error = 5.218 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.387 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 = 3.387 Order of pole (three term test) = 31.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17531.4MB, alloc=44.3MB, time=217.10 x[1] = 0.2914 0.909 h = 0.0001 0.004 y2[1] (numeric) = 0.280266611859 1.10134401254 y2[1] (closed_form) = 0.414387297787 0.995635482114 absolute error = 0.1708 relative error = 15.84 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.43340102445 -0.245627251506 y1[1] (closed_form) = 1.38157608051 -0.298629009893 absolute error = 0.07413 relative error = 5.244 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.929 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 = 1.929 Order of pole (three term test) = 31.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17577.3MB, alloc=44.3MB, time=217.66 memory used=17623.5MB, alloc=44.3MB, time=218.22 x[1] = 0.2915 0.913 h = 0.003 0.006 y2[1] (numeric) = 0.28233651206 1.10684741538 y2[1] (closed_form) = 0.415723687005 1.00113973237 absolute error = 0.1702 relative error = 15.7 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.43778927322 -0.246862861525 y1[1] (closed_form) = 1.38552812024 -0.300389068015 absolute error = 0.07481 relative error = 5.277 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.577 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 = 2.577 Order of pole (three term test) = 31.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17669.3MB, alloc=44.3MB, time=218.78 memory used=17715.5MB, alloc=44.3MB, time=219.34 x[1] = 0.2945 0.919 h = 0.0001 0.005 y2[1] (numeric) = 0.284423587839 1.11236304482 y2[1] (closed_form) = 0.421706309917 1.00855776379 absolute error = 0.1721 relative error = 15.74 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.44359676267 -0.251891945794 y1[1] (closed_form) = 1.39030107357 -0.305915877496 absolute error = 0.07589 relative error = 5.331 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.16 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 = 1.16 Order of pole (three term test) = 31.17 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17761.4MB, alloc=44.3MB, time=219.90 memory used=17807.5MB, alloc=44.3MB, time=220.46 x[1] = 0.2946 0.924 h = 0.0001 0.003 y2[1] (numeric) = 0.286528137207 1.11789093421 y2[1] (closed_form) = 0.423380701027 1.01549109722 absolute error = 0.1709 relative error = 15.54 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.44914384504 -0.253430830386 y1[1] (closed_form) = 1.39531893111 -0.308129792437 absolute error = 0.07674 relative error = 5.37 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9436 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 = 0.9436 Order of pole (three term test) = 31.16 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17853.6MB, alloc=44.3MB, time=221.03 x[1] = 0.2947 0.927 h = 0.001 0.001 y2[1] (numeric) = 0.288650266282 1.12343120161 y2[1] (closed_form) = 0.424446832053 1.01965068477 absolute error = 0.1709 relative error = 15.47 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.45247706637 -0.254405659596 y1[1] (closed_form) = 1.39832925022 -0.309503289647 absolute error = 0.07725 relative error = 5.394 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7452 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 = 0.7452 Order of pole (three term test) = 31.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17899.5MB, alloc=44.3MB, time=221.59 memory used=17945.9MB, alloc=44.3MB, time=222.16 x[1] = 0.2957 0.928 h = 0.001 0.003 y2[1] (numeric) = 0.290789991682 1.1289838996 y2[1] (closed_form) = 0.426155684606 1.02073908572 absolute error = 0.1733 relative error = 15.67 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.45331355422 -0.255821584773 y1[1] (closed_form) = 1.39892414409 -0.310948785691 absolute error = 0.07744 relative error = 5.404 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.545 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 = 3.545 Order of pole (three term test) = 31.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=17991.8MB, alloc=44.3MB, time=222.72 memory used=18038.0MB, alloc=44.3MB, time=223.28 x[1] = 0.2967 0.931 h = 0.0001 0.004 y2[1] (numeric) = 0.292947323878 1.13454903488 y2[1] (closed_form) = 0.428492228947 1.0246277167 absolute error = 0.1745 relative error = 15.71 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.45641698332 -0.257828951772 y1[1] (closed_form) = 1.40156486972 -0.313253438106 absolute error = 0.07798 relative error = 5.43 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.018 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 = 2.018 Order of pole (three term test) = 31.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18083.8MB, alloc=44.3MB, time=223.84 x[1] = 0.2968 0.935 h = 0.003 0.006 y2[1] (numeric) = 0.295122295688 1.14012663294 y2[1] (closed_form) = 0.429889239295 1.03021068602 absolute error = 0.1739 relative error = 15.58 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.46093692716 -0.259118818805 y1[1] (closed_form) = 1.40563162216 -0.315072940267 absolute error = 0.07867 relative error = 5.462 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.696 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 = 2.696 Order of pole (three term test) = 31.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18129.7MB, alloc=44.3MB, time=224.39 memory used=18175.7MB, alloc=44.3MB, time=224.95 x[1] = 0.2998 0.941 h = 0.0001 0.005 y2[1] (numeric) = 0.297315004459 1.14571675242 y2[1] (closed_form) = 0.436020991588 1.03770542376 absolute error = 0.1758 relative error = 15.62 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.46690579957 -0.264324883708 y1[1] (closed_form) = 1.41053651121 -0.320772517585 absolute error = 0.07977 relative error = 5.515 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.214 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 = 1.214 Order of pole (three term test) = 31.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18221.6MB, alloc=44.3MB, time=225.51 memory used=18267.8MB, alloc=44.3MB, time=226.07 x[1] = 0.2999 0.946 h = 0.0001 0.003 y2[1] (numeric) = 0.299525753231 1.15131942507 y2[1] (closed_form) = 0.437771883213 1.04473880616 absolute error = 0.1746 relative error = 15.41 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.47261854287 -0.265931829752 y1[1] (closed_form) = 1.41569892158 -0.323061116788 absolute error = 0.08064 relative error = 5.554 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9873 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 = 0.9873 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18313.7MB, alloc=44.3MB, time=226.63 memory used=18360.1MB, alloc=44.3MB, time=227.20 x[1] = 0.3 0.949 h = 0.001 0.001 y2[1] (numeric) = 0.301754650675 1.15693477013 y2[1] (closed_form) = 0.438884919749 1.04895816779 absolute error = 0.1745 relative error = 15.35 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.47605085712 -0.266949158421 y1[1] (closed_form) = 1.41879563195 -0.324480785622 absolute error = 0.08117 relative error = 5.577 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.7797 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 = 0.7797 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18405.9MB, alloc=44.3MB, time=227.77 x[1] = 0.301 0.95 h = 0.001 0.003 y2[1] (numeric) = 0.304001714055 1.16256284089 y2[1] (closed_form) = 0.44062924549 1.05005204317 absolute error = 0.177 relative error = 15.54 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.4769077282 -0.268411782834 y1[1] (closed_form) = 1.41940538022 -0.325970047709 absolute error = 0.08136 relative error = 5.587 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.708 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 = 3.708 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18451.9MB, alloc=44.3MB, time=228.33 memory used=18498.1MB, alloc=44.3MB, time=228.89 x[1] = 0.302 0.953 h = 0.0001 0.004 y2[1] (numeric) = 0.306266954057 1.16820364409 y2[1] (closed_form) = 0.44303148082 1.05398717043 absolute error = 0.1782 relative error = 15.58 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.48009874192 -0.270492563469 y1[1] (closed_form) = 1.42211960806 -0.328347555463 absolute error = 0.08191 relative error = 5.612 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.111 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 = 2.111 Order of pole (three term test) = 31.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18543.9MB, alloc=44.3MB, time=229.45 memory used=18590.0MB, alloc=44.3MB, time=230.01 x[1] = 0.3021 0.957 h = 0.003 0.006 y2[1] (numeric) = 0.308550404216 1.1738572054 y2[1] (closed_form) = 0.444491051273 1.05965107841 absolute error = 0.1775 relative error = 15.45 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.48475211864 -0.271839295046 y1[1] (closed_form) = 1.42630250298 -0.330228279655 absolute error = 0.08262 relative error = 5.643 % Correct digits = 1 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) = 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 = 2.82 Order of pole (three term test) = 31.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18635.8MB, alloc=44.3MB, time=230.56 memory used=18682.1MB, alloc=44.3MB, time=231.13 x[1] = 0.3051 0.963 h = 0.0001 0.005 y2[1] (numeric) = 0.310852163884 1.17952358372 y2[1] (closed_form) = 0.450776476458 1.06722450947 absolute error = 0.1794 relative error = 15.49 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.49088315536 -0.277227561497 y1[1] (closed_form) = 1.43134023474 -0.336104367285 absolute error = 0.08374 relative error = 5.695 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.27 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 = 1.27 Order of pole (three term test) = 31.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18728.0MB, alloc=44.3MB, time=231.68 x[1] = 0.3052 0.968 h = 0.0001 0.003 y2[1] (numeric) = 0.313172541276 1.18520280917 y2[1] (closed_form) = 0.452606307179 1.07436073918 absolute error = 0.1781 relative error = 15.28 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.49676376489 -0.278905851677 y1[1] (closed_form) = 1.43664901787 -0.338469898138 absolute error = 0.08463 relative error = 5.734 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.033 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 = 1.033 Order of pole (three term test) = 31.07 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18773.8MB, alloc=44.3MB, time=232.24 memory used=18820.2MB, alloc=44.3MB, time=232.81 x[1] = 0.3053 0.971 h = 0.001 0.001 y2[1] (numeric) = 0.315511647693 1.19089500216 y2[1] (closed_form) = 0.453767740715 1.07864153901 absolute error = 0.1781 relative error = 15.22 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.5002964743 -0.279967678057 y1[1] (closed_form) = 1.43983320027 -0.339937108066 absolute error = 0.08516 relative error = 5.756 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8157 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 = 0.8157 Order of pole (three term test) = 31.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18866.3MB, alloc=44.3MB, time=233.38 memory used=18912.7MB, alloc=44.3MB, time=233.94 x[1] = 0.3063 0.972 h = 0.0001 0.004 y2[1] (numeric) = 0.317869501064 1.19660021674 y2[1] (closed_form) = 0.455548590031 1.07974098074 absolute error = 0.1806 relative error = 15.41 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.50117353181 -0.281478113593 y1[1] (closed_form) = 1.44045773362 -0.341470957387 absolute error = 0.08536 relative error = 5.766 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.908 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 = 4.908 Order of pole (three term test) = 31.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=18958.5MB, alloc=44.3MB, time=234.50 x[1] = 0.3064 0.976 h = 0.003 0.006 y2[1] (numeric) = 0.320246109823 1.2023184719 y2[1] (closed_form) = 0.457062598435 1.08547712996 absolute error = 0.1799 relative error = 15.28 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.50593945921 -0.282874284385 y1[1] (closed_form) = 1.4447425337 -0.343404437807 absolute error = 0.08608 relative error = 5.796 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.932 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 = 2.932 Order of pole (three term test) = 31.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19004.5MB, alloc=44.3MB, time=235.05 memory used=19050.7MB, alloc=44.3MB, time=235.62 x[1] = 0.3094 0.982 h = 0.0001 0.005 y2[1] (numeric) = 0.322641568185 1.20804982331 y2[1] (closed_form) = 0.463483036279 1.09312179461 absolute error = 0.1818 relative error = 15.31 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.51220623077 -0.288418487084 y1[1] (closed_form) = 1.44989751851 -0.349433944067 absolute error = 0.08721 relative error = 5.847 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.32 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 = 1.32 Order of pole (three term test) = 31.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19096.6MB, alloc=44.3MB, time=236.18 memory used=19142.7MB, alloc=44.3MB, time=236.74 x[1] = 0.3095 0.987 h = 0.0001 0.003 y2[1] (numeric) = 0.325056188949 1.21379429968 y2[1] (closed_form) = 0.46538154263 1.10034979538 absolute error = 0.1804 relative error = 15.1 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.51822845086 -0.29015881555 y1[1] (closed_form) = 1.45533474314 -0.351865773576 absolute error = 0.08811 relative error = 5.885 % Correct digits = 1 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) = 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 = 1.074 Order of pole (three term test) = 31.02 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19188.6MB, alloc=44.3MB, time=237.30 memory used=19235.0MB, alloc=44.3MB, time=237.87 x[1] = 0.3096 0.99 h = 0.001 0.001 y2[1] (numeric) = 0.327490085728 1.2195520225 y2[1] (closed_form) = 0.466585097655 1.10468542586 absolute error = 0.1804 relative error = 15.04 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.52184583987 -0.291259297345 y1[1] (closed_form) = 1.45859569527 -0.353373974005 absolute error = 0.08865 relative error = 5.907 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8479 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 = 0.8479 Order of pole (three term test) = 31.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19281.0MB, alloc=44.3MB, time=238.43 x[1] = 0.3106 0.991 h = 0.001 0.003 y2[1] (numeric) = 0.329943277032 1.22532304648 y2[1] (closed_form) = 0.468398172378 1.10579018039 absolute error = 0.1829 relative error = 15.23 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.52273956122 -0.292810448844 y1[1] (closed_form) = 1.4592334417 -0.354946703337 absolute error = 0.08885 relative error = 5.916 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.033 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 = 4.033 Order of pole (three term test) = 31.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19326.9MB, alloc=44.3MB, time=238.99 memory used=19373.1MB, alloc=44.3MB, time=239.56 x[1] = 0.3116 0.994 h = 0.0001 0.004 y2[1] (numeric) = 0.332415773969 1.23110737843 y2[1] (closed_form) = 0.470927444286 1.10981595482 absolute error = 0.1841 relative error = 15.27 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.52609302562 -0.295032196693 y1[1] (closed_form) = 1.46208718745 -0.357463491725 absolute error = 0.08941 relative error = 5.94 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.296 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 = 2.296 Order of pole (three term test) = 31.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19419.1MB, alloc=44.3MB, time=240.12 memory used=19465.2MB, alloc=44.3MB, time=240.68 x[1] = 0.3117 0.998 h = 0.003 0.006 y2[1] (numeric) = 0.334907611457 1.23690504439 y2[1] (closed_form) = 0.472507720945 1.11563725712 absolute error = 0.1834 relative error = 15.14 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.53099568 -0.296490237521 y1[1] (closed_form) = 1.46649091638 -0.35946163176 absolute error = 0.09015 relative error = 5.97 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.067 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 = 3.067 Order of pole (three term test) = 31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19511.0MB, alloc=44.3MB, time=241.24 memory used=19557.2MB, alloc=44.3MB, time=241.80 x[1] = 0.3147 1.004 h = 0.0001 0.005 y2[1] (numeric) = 0.337418892736 1.24271610375 y2[1] (closed_form) = 0.479090499715 1.12336436903 absolute error = 0.1852 relative error = 15.17 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.53742605189 -0.302226635606 y1[1] (closed_form) = 1.47178053067 -0.365674899012 absolute error = 0.0913 relative error = 6.02 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.381 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 = 1.381 Order of pole (three term test) = 30.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19603.1MB, alloc=44.3MB, time=242.36 x[1] = 0.3148 1.009 h = 0.0001 0.003 y2[1] (numeric) = 0.339949936065 1.24854058352 y2[1] (closed_form) = 0.481072609644 1.13070053128 absolute error = 0.1839 relative error = 14.96 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.54362031971 -0.304044612126 y1[1] (closed_form) = 1.47736767334 -0.368188004331 absolute error = 0.09222 relative error = 6.057 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.123 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 = 1.123 Order of pole (three term test) = 30.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19648.9MB, alloc=44.3MB, time=242.92 memory used=19695.3MB, alloc=44.3MB, time=243.49 x[1] = 0.3149 1.012 h = 0.001 0.001 y2[1] (numeric) = 0.342500857835 1.2543786064 y2[1] (closed_form) = 0.482327414374 1.13510076014 absolute error = 0.1838 relative error = 14.9 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.54734057273 -0.30519342919 y1[1] (closed_form) = 1.48071820284 -0.369746393097 absolute error = 0.09277 relative error = 6.078 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.8868 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 = 0.8868 Order of pole (three term test) = 30.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19741.2MB, alloc=44.3MB, time=244.05 memory used=19787.5MB, alloc=44.3MB, time=244.62 x[1] = 0.3159 1.013 h = 0.001 0.003 y2[1] (numeric) = 0.345071677261 1.2602302279 y2[1] (closed_form) = 0.484179014441 1.13621124901 absolute error = 0.1864 relative error = 15.09 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.5482540914 -0.306794517083 y1[1] (closed_form) = 1.4813706059 -0.371365302207 absolute error = 0.09297 relative error = 6.087 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.218 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 = 4.218 Order of pole (three term test) = 30.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19833.5MB, alloc=44.3MB, time=245.18 x[1] = 0.3169 1.016 h = 0.0001 0.004 y2[1] (numeric) = 0.347662405686 1.26609545487 y2[1] (closed_form) = 0.486779833842 1.14028709067 absolute error = 0.1876 relative error = 15.13 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.55169721114 -0.309096774933 y1[1] (closed_form) = 1.48429987333 -0.373959986455 absolute error = 0.09354 relative error = 6.111 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.401 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 = 2.401 Order of pole (three term test) = 30.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19879.6MB, alloc=44.3MB, time=245.74 memory used=19925.7MB, alloc=44.3MB, time=246.30 x[1] = 0.317 1.02 h = 0.003 0.006 y2[1] (numeric) = 0.350273078806 1.27197431354 y2[1] (closed_form) = 0.48842845687 1.14619583156 absolute error = 0.1868 relative error = 15 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.55673844952 -0.310619542622 y1[1] (closed_form) = 1.48882407287 -0.37602472413 absolute error = 0.09429 relative error = 6.14 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.208 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 = 3.208 Order of pole (three term test) = 30.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=19971.5MB, alloc=44.3MB, time=246.85 memory used=20017.7MB, alloc=44.3MB, time=247.42 x[1] = 0.32 1.026 h = 0.0001 0.005 y2[1] (numeric) = 0.352903802036 1.27786686357 y2[1] (closed_form) = 0.495178379905 1.15400737847 absolute error = 0.1886 relative error = 15.02 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.56333320593 -0.316553821502 y1[1] (closed_form) = 1.49424927924 -0.382425818777 absolute error = 0.09546 relative error = 6.189 % Correct digits = 1 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) = 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 = 1.444 Order of pole (three term test) = 30.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20063.6MB, alloc=44.3MB, time=247.98 memory used=20109.8MB, alloc=44.3MB, time=248.54 x[1] = 0.3201 1.031 h = 0.0001 0.003 y2[1] (numeric) = 0.35555489924 1.28377313016 y2[1] (closed_form) = 0.497246708025 1.16145458467 absolute error = 0.1872 relative error = 14.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.56970187741 -0.31845304161 y1[1] (closed_form) = 1.49998830116 -0.385022648709 absolute error = 0.09639 relative error = 6.224 % Correct digits = 1 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) = 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 = 1.174 Order of pole (three term test) = 30.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20155.9MB, alloc=44.3MB, time=249.10 x[1] = 0.3202 1.034 h = 0.001 0.001 y2[1] (numeric) = 0.358226489668 1.28969323727 y2[1] (closed_form) = 0.498554360765 1.16592112543 absolute error = 0.1871 relative error = 14.76 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.57352638459 -0.319652381769 y1[1] (closed_form) = 1.50342957217 -0.386632717719 absolute error = 0.09695 relative error = 6.246 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9274 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 = 0.9274 Order of pole (three term test) = 30.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20201.9MB, alloc=44.3MB, time=249.68 memory used=20248.2MB, alloc=44.3MB, time=250.25 x[1] = 0.3212 1.035 h = 0.001 0.003 y2[1] (numeric) = 0.360918593261 1.29562724124 y2[1] (closed_form) = 0.500445589348 1.1670374231 absolute error = 0.1897 relative error = 14.94 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.57445947284 -0.321304611682 y1[1] (closed_form) = 1.50409655175 -0.388298696857 absolute error = 0.09716 relative error = 6.254 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.411 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 = 4.411 Order of pole (three term test) = 30.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20294.2MB, alloc=44.3MB, time=250.81 memory used=20340.4MB, alloc=44.3MB, time=251.38 x[1] = 0.3222 1.038 h = 0.0001 0.004 y2[1] (numeric) = 0.363631221603 1.30157514894 y2[1] (closed_form) = 0.503120092573 1.1711645837 absolute error = 0.191 relative error = 14.98 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.57799299975 -0.323690031305 y1[1] (closed_form) = 1.50710207125 -0.390973143098 absolute error = 0.09774 relative error = 6.277 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.511 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 = 2.511 Order of pole (three term test) = 30.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20386.2MB, alloc=44.3MB, time=251.93 x[1] = 0.3223 1.042 h = 0.003 0.006 y2[1] (numeric) = 0.366364411192 1.30753698679 y2[1] (closed_form) = 0.504839191638 1.17716307263 absolute error = 0.1902 relative error = 14.85 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.58317471976 -0.325280471201 y1[1] (closed_form) = 1.51174832255 -0.393106474897 absolute error = 0.0985 relative error = 6.306 % Correct digits = 1 memory used=20432.3MB, alloc=44.3MB, time=252.49 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.354 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 = 3.354 Order of pole (three term test) = 30.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20478.3MB, alloc=44.3MB, time=253.05 x[1] = 0.3253 1.048 h = 0.0001 0.005 y2[1] (numeric) = 0.369118269681 1.31351281473 y2[1] (closed_form) = 0.511761158173 1.18506104181 absolute error = 0.192 relative error = 14.87 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.58993464336 -0.331418480032 y1[1] (closed_form) = 1.51731010164 -0.399699580598 absolute error = 0.09968 relative error = 6.353 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.51 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 = 1.51 Order of pole (three term test) = 30.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20524.2MB, alloc=44.3MB, time=253.61 memory used=20570.2MB, alloc=44.3MB, time=254.17 x[1] = 0.3254 1.053 h = 0.0001 0.003 y2[1] (numeric) = 0.371893126689 1.3195026561 y2[1] (closed_form) = 0.513918384301 1.19262220492 absolute error = 0.1904 relative error = 14.67 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.59648012578 -0.333402650388 y1[1] (closed_form) = 1.52320301373 -0.402382657538 absolute error = 0.1006 relative error = 6.388 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.228 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 = 1.228 Order of pole (three term test) = 30.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20616.2MB, alloc=44.3MB, time=254.73 memory used=20662.5MB, alloc=44.3MB, time=255.30 x[1] = 0.3255 1.056 h = 0.001 0.001 y2[1] (numeric) = 0.374689104412 1.32550663614 y2[1] (closed_form) = 0.515280522917 1.19715678901 absolute error = 0.1904 relative error = 14.61 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.60041030723 -0.334654768797 y1[1] (closed_form) = 1.52673621971 -0.404045943426 absolute error = 0.1012 relative error = 6.408 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.9698 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 = 0.9698 Order of pole (three term test) = 30.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20708.5MB, alloc=44.3MB, time=255.86 x[1] = 0.3265 1.057 h = 0.001 0.003 y2[1] (numeric) = 0.377506223536 1.33152481202 y2[1] (closed_form) = 0.517212502611 1.19827896336 absolute error = 0.1931 relative error = 14.79 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.60136272587 -0.33635937924 y1[1] (closed_form) = 1.52741769136 -0.405759907701 absolute error = 0.1014 relative error = 6.417 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.612 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 = 4.612 Order of pole (three term test) = 30.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20754.5MB, alloc=44.3MB, time=256.42 memory used=20800.9MB, alloc=44.3MB, time=257.00 x[1] = 0.3275 1.06 h = 0.0001 0.004 y2[1] (numeric) = 0.380344495897 1.33755719065 y2[1] (closed_form) = 0.519962871554 1.20245870083 absolute error = 0.1943 relative error = 14.83 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.60498742173 -0.338830689844 y1[1] (closed_form) = 1.53050020949 -0.408516036216 absolute error = 0.102 relative error = 6.439 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.626 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 = 2.626 Order of pole (three term test) = 30.85 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20846.8MB, alloc=44.3MB, time=257.55 memory used=20892.8MB, alloc=44.3MB, time=258.12 x[1] = 0.3276 1.064 h = 0.003 0.006 y2[1] (numeric) = 0.383203958814 1.34360379866 y2[1] (closed_form) = 0.521754629387 1.20854927172 absolute error = 0.1935 relative error = 14.7 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.61031156171 -0.340491837614 y1[1] (closed_form) = 1.53527013335 -0.410720018362 absolute error = 0.1028 relative error = 6.467 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.507 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 = 3.507 Order of pole (three term test) = 30.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=20938.6MB, alloc=44.3MB, time=258.68 memory used=20984.8MB, alloc=44.3MB, time=259.25 x[1] = 0.3306 1.07 h = 0.0001 0.005 y2[1] (numeric) = 0.386084722241 1.34966469626 y2[1] (closed_form) = 0.528853637249 1.21653564971 absolute error = 0.1952 relative error = 14.72 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.61723743239 -0.346839592094 y1[1] (closed_form) = 1.54096948326 -0.417509438169 absolute error = 0.104 relative error = 6.513 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.579 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 = 1.579 Order of pole (three term test) = 30.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21030.7MB, alloc=44.3MB, time=259.81 x[1] = 0.3307 1.075 h = 0.0001 0.003 y2[1] (numeric) = 0.388987121711 1.35573990483 y2[1] (closed_form) = 0.531102508312 1.22421371394 absolute error = 0.1936 relative error = 14.51 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.62396218449 -0.348912532757 y1[1] (closed_form) = 1.5470183465 -0.420281359725 absolute error = 0.1049 relative error = 6.547 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.284 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 = 1.284 Order of pole (three term test) = 30.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21076.7MB, alloc=44.3MB, time=260.36 memory used=21123.1MB, alloc=44.3MB, time=260.94 x[1] = 0.3308 1.078 h = 0.001 0.001 y2[1] (numeric) = 0.391911282448 1.36182955097 y2[1] (closed_form) = 0.532520811379 1.22881809111 absolute error = 0.1936 relative error = 14.45 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.62799949032 -0.350219753271 y1[1] (closed_form) = 1.55064471041 -0.421999444826 absolute error = 0.1055 relative error = 6.567 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.014 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 = 1.014 Order of pole (three term test) = 30.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21168.9MB, alloc=44.3MB, time=261.50 memory used=21215.3MB, alloc=44.3MB, time=262.07 x[1] = 0.3318 1.079 h = 0.0001 0.004 y2[1] (numeric) = 0.394857225907 1.36793369267 y2[1] (closed_form) = 0.534494684729 1.2299462032 absolute error = 0.1963 relative error = 14.64 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.62897098829 -0.351978016123 y1[1] (closed_form) = 1.5513405851 -0.423762334605 absolute error = 0.1057 relative error = 6.575 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.102 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 = 6.102 Order of pole (three term test) = 30.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21261.1MB, alloc=44.3MB, time=262.63 x[1] = 0.3319 1.083 h = 0.003 0.006 y2[1] (numeric) = 0.397824961944 1.37405235027 y2[1] (closed_form) = 0.536349639149 1.23611882512 absolute error = 0.1955 relative error = 14.51 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.6344153216 -0.353700472412 y1[1] (closed_form) = 1.55621916659 -0.426027323161 absolute error = 0.1065 relative error = 6.602 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.645 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 = 3.645 Order of pole (three term test) = 30.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21307.1MB, alloc=44.3MB, time=263.18 memory used=21353.2MB, alloc=44.3MB, time=263.75 x[1] = 0.3349 1.089 h = 0.0001 0.005 y2[1] (numeric) = 0.400814594918 1.38018558071 y2[1] (closed_form) = 0.543604032401 1.2441850843 absolute error = 0.1972 relative error = 14.52 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.64148007429 -0.360227733303 y1[1] (closed_form) = 1.5620401556 -0.432987606916 absolute error = 0.1077 relative error = 6.646 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.641 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 = 1.641 Order of pole (three term test) = 30.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21399.0MB, alloc=44.3MB, time=264.30 memory used=21445.2MB, alloc=44.3MB, time=264.87 x[1] = 0.335 1.094 h = 0.0001 0.003 y2[1] (numeric) = 0.403826465589 1.38633340372 y2[1] (closed_form) = 0.545932599855 1.2519672926 absolute error = 0.1956 relative error = 14.32 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.64835613378 -0.362377652472 y1[1] (closed_form) = 1.56822604706 -0.435836249668 absolute error = 0.1087 relative error = 6.679 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.334 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 = 1.334 Order of pole (three term test) = 30.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21491.2MB, alloc=44.3MB, time=265.43 memory used=21537.6MB, alloc=44.3MB, time=266.00 x[1] = 0.3351 1.097 h = 0.001 0.001 y2[1] (numeric) = 0.406860701842 1.39249594708 y2[1] (closed_form) = 0.547399763428 1.25663385777 absolute error = 0.1955 relative error = 14.26 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.65248383994 -0.363732618972 y1[1] (closed_form) = 1.57193427948 -0.437601676763 absolute error = 0.1093 relative error = 6.698 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.054 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 = 1.054 Order of pole (three term test) = 30.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21583.7MB, alloc=44.3MB, time=266.56 x[1] = 0.3361 1.098 h = 0.001 0.003 y2[1] (numeric) = 0.409917325803 1.39867326955 y2[1] (closed_form) = 0.549410556397 1.25776764231 absolute error = 0.1983 relative error = 14.45 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.65347103617 -0.365536589497 y1[1] (closed_form) = 1.57264307537 -0.439407282554 absolute error = 0.1095 relative error = 6.706 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.011 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 = 5.011 Order of pole (three term test) = 30.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21629.6MB, alloc=44.3MB, time=267.13 memory used=21675.8MB, alloc=44.3MB, time=267.69 x[1] = 0.3371 1.101 h = 0.0001 0.004 y2[1] (numeric) = 0.412996349793 1.40486537814 y2[1] (closed_form) = 0.552307400403 1.2620495499 absolute error = 0.1995 relative error = 14.48 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.65726488547 -0.368172722497 y1[1] (closed_form) = 1.57587194149 -0.44231976453 absolute error = 0.1101 relative error = 6.727 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.853 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 = 2.853 Order of pole (three term test) = 30.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21721.7MB, alloc=44.3MB, time=268.25 memory used=21767.9MB, alloc=44.3MB, time=268.82 x[1] = 0.3372 1.105 h = 0.003 0.006 y2[1] (numeric) = 0.416097812718 1.41107229985 y2[1] (closed_form) = 0.55423919315 1.26831869129 absolute error = 0.1986 relative error = 14.35 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.66285530136 -0.369971700096 y1[1] (closed_form) = 1.58087734412 -0.444659372678 absolute error = 0.1109 relative error = 6.753 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.811 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 = 3.811 Order of pole (three term test) = 30.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21813.7MB, alloc=44.3MB, time=269.38 memory used=21859.9MB, alloc=44.3MB, time=269.94 x[1] = 0.3402 1.111 h = 0.0001 0.005 y2[1] (numeric) = 0.419221828986 1.41729409544 y2[1] (closed_form) = 0.561680175729 1.27647711538 absolute error = 0.2003 relative error = 14.36 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.67008741933 -0.376720193533 y1[1] (closed_form) = 1.58683786057 -0.451824290492 absolute error = 0.1121 relative error = 6.796 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.715 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 = 1.715 Order of pole (three term test) = 30.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21905.8MB, alloc=44.3MB, time=270.50 x[1] = 0.3403 1.116 h = 0.0001 0.003 y2[1] (numeric) = 0.422368745578 1.42353078258 y2[1] (closed_form) = 0.564105648802 1.28438182348 absolute error = 0.1986 relative error = 14.16 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.67714739596 -0.378966201503 y1[1] (closed_form) = 1.59318370566 -0.454766791343 absolute error = 0.1131 relative error = 6.827 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.395 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 = 1.395 Order of pole (three term test) = 30.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=21951.6MB, alloc=44.3MB, time=271.06 memory used=21998.1MB, alloc=44.3MB, time=271.63 x[1] = 0.3404 1.119 h = 0.001 0.001 y2[1] (numeric) = 0.425538693567 1.42978249042 y2[1] (closed_form) = 0.565632191275 1.28912150893 absolute error = 0.1985 relative error = 14.1 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.68138496692 -0.380380722438 y1[1] (closed_form) = 1.59698747101 -0.456590071714 absolute error = 0.1137 relative error = 6.846 % Correct digits = 1 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) = 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 = 1.102 Order of pole (three term test) = 30.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22044.1MB, alloc=44.3MB, time=272.20 memory used=22090.5MB, alloc=44.3MB, time=272.76 x[1] = 0.3414 1.12 h = 0.001 0.003 y2[1] (numeric) = 0.428731695895 1.43604927864 y2[1] (closed_form) = 0.567687058319 1.29026134001 absolute error = 0.2014 relative error = 14.29 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.68239074827 -0.382240770339 y1[1] (closed_form) = 1.59771050312 -0.458446422643 absolute error = 0.1139 relative error = 6.854 % Correct digits = 1 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) = 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 = 5.239 Order of pole (three term test) = 30.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22136.3MB, alloc=44.3MB, time=273.32 x[1] = 0.3424 1.123 h = 0.0001 0.004 y2[1] (numeric) = 0.431947765152 1.44233115427 y2[1] (closed_form) = 0.570666257927 1.29459948589 absolute error = 0.2027 relative error = 14.32 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.68627797734 -0.384970972718 y1[1] (closed_form) = 1.60101861699 -0.461446379376 absolute error = 0.1145 relative error = 6.874 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.983 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 = 2.983 Order of pole (three term test) = 30.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22182.4MB, alloc=44.3MB, time=273.88 memory used=22228.3MB, alloc=44.3MB, time=274.44 x[1] = 0.3425 1.127 h = 0.003 0.006 y2[1] (numeric) = 0.435186941134 1.44862814451 y2[1] (closed_form) = 0.572677231824 1.30096755446 absolute error = 0.2018 relative error = 14.19 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.69201653435 -0.38684978226 y1[1] (closed_form) = 1.60615257722 -0.463862841145 absolute error = 0.1153 relative error = 6.899 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.984 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 = 3.984 Order of pole (three term test) = 30.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22274.2MB, alloc=44.3MB, time=275.00 memory used=22320.4MB, alloc=44.3MB, time=275.56 x[1] = 0.3455 1.133 h = 0.0001 0.005 y2[1] (numeric) = 0.438449340737 1.45494031043 y2[1] (closed_form) = 0.580310098932 1.30922012769 absolute error = 0.2034 relative error = 14.2 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.69941678355 -0.393826028296 y1[1] (closed_form) = 1.61225366766 -0.471237049766 absolute error = 0.1166 relative error = 6.94 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.793 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 = 1.793 Order of pole (three term test) = 30.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22366.3MB, alloc=44.3MB, time=276.12 memory used=22412.4MB, alloc=44.3MB, time=276.68 x[1] = 0.3456 1.138 h = 0.0001 0.003 y2[1] (numeric) = 0.441735317314 1.46126766752 y2[1] (closed_form) = 0.582835426971 1.31725037387 absolute error = 0.2016 relative error = 14 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.70666328811 -0.396172290344 y1[1] (closed_form) = 1.61876167334 -0.474276230234 absolute error = 0.1176 relative error = 6.971 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.458 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 = 1.458 Order of pole (three term test) = 30.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22458.5MB, alloc=44.3MB, time=277.24 x[1] = 0.3457 1.141 h = 0.001 0.001 y2[1] (numeric) = 0.445045005219 1.46761034638 y2[1] (closed_form) = 0.584423149707 1.3220649845 absolute error = 0.2015 relative error = 13.94 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.71101226247 -0.397648898668 y1[1] (closed_form) = 1.62266228062 -0.476159082261 absolute error = 0.1182 relative error = 6.989 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.152 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 = 1.152 Order of pole (three term test) = 30.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22504.6MB, alloc=44.3MB, time=277.80 memory used=22551.0MB, alloc=44.3MB, time=278.38 x[1] = 0.3467 1.142 h = 0.001 0.003 y2[1] (numeric) = 0.448378428231 1.47396840757 y2[1] (closed_form) = 0.586523293517 1.32321090258 absolute error = 0.2045 relative error = 14.13 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.71203634082 -0.399566396501 y1[1] (closed_form) = 1.62339944566 -0.478067193304 absolute error = 0.1184 relative error = 6.996 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.477 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 = 5.477 Order of pole (three term test) = 30.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22596.9MB, alloc=44.3MB, time=278.94 memory used=22643.2MB, alloc=44.3MB, time=279.51 x[1] = 0.3477 1.145 h = 0.0001 0.004 y2[1] (numeric) = 0.451735599218 1.48034185818 y2[1] (closed_form) = 0.589587218744 1.32760656979 absolute error = 0.2057 relative error = 14.16 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.71601774734 -0.402393715451 y1[1] (closed_form) = 1.6267876159 -0.481156764054 absolute error = 0.119 relative error = 7.016 % Correct digits = 1 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) = 34.45 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 = 3.118 Order of pole (three term test) = 30.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22689.1MB, alloc=44.3MB, time=280.07 memory used=22735.2MB, alloc=44.3MB, time=280.63 x[1] = 0.3478 1.149 h = 0.003 0.006 y2[1] (numeric) = 0.455116558891 1.48673072561 y2[1] (closed_form) = 0.591679775785 1.33407599991 absolute error = 0.2048 relative error = 14.03 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.72190654495 -0.404355765331 y1[1] (closed_form) = 1.63205191084 -0.483652378496 absolute error = 0.1198 relative error = 7.04 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.165 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 = 4.165 Order of pole (three term test) = 30.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22781.0MB, alloc=44.3MB, time=281.18 x[1] = 0.3508 1.155 h = 0.0001 0.005 y2[1] (numeric) = 0.458521426701 1.49313507121 y2[1] (closed_form) = 0.599509932068 1.3424247047 absolute error = 0.2064 relative error = 14.04 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.72947568364 -0.411566462071 y1[1] (closed_form) = 1.63829463711 -0.491240662874 absolute error = 0.1211 relative error = 7.08 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.875 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 = 1.875 Order of pole (three term test) = 30.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22826.9MB, alloc=44.3MB, time=281.74 memory used=22873.1MB, alloc=44.3MB, time=282.30 x[1] = 0.3509 1.16 h = 0.0001 0.003 y2[1] (numeric) = 0.461950562537 1.49955490827 y2[1] (closed_form) = 0.602138139222 1.35058356117 absolute error = 0.2046 relative error = 13.83 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.73691137872 -0.414017266256 y1[1] (closed_form) = 1.64496706174 -0.494379426373 absolute error = 0.1221 relative error = 7.109 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.525 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 = 1.525 Order of pole (three term test) = 30.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=22919.0MB, alloc=44.3MB, time=282.87 memory used=22965.3MB, alloc=44.3MB, time=283.44 x[1] = 0.351 1.163 h = 0.001 0.001 y2[1] (numeric) = 0.465404104125 1.5059903688 y2[1] (closed_form) = 0.603788888954 1.3554749218 absolute error = 0.2045 relative error = 13.78 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.74137332518 -0.415558569284 y1[1] (closed_form) = 1.64896585022 -0.496323618183 absolute error = 0.1227 relative error = 7.127 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.204 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 = 1.204 Order of pole (three term test) = 30.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23011.4MB, alloc=44.3MB, time=284.00 x[1] = 0.352 1.164 h = 0.001 0.003 y2[1] (numeric) = 0.468882076108 1.51244151432 y2[1] (closed_form) = 0.605935534281 1.35662695953 absolute error = 0.2075 relative error = 13.97 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.74241539876 -0.417534924972 y1[1] (closed_form) = 1.64971703927 -0.49828453121 absolute error = 0.1229 relative error = 7.134 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.725 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 = 5.725 Order of pole (three term test) = 30.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23057.5MB, alloc=44.3MB, time=284.56 memory used=23103.6MB, alloc=44.3MB, time=285.13 x[1] = 0.353 1.167 h = 0.0001 0.004 y2[1] (numeric) = 0.47238449164 1.51890835194 y2[1] (closed_form) = 0.609086607187 1.36108143761 absolute error = 0.2088 relative error = 14 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.74649178839 -0.420462492333 y1[1] (closed_form) = 1.65318609007 -0.501465914766 absolute error = 0.1236 relative error = 7.152 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.26 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 = 3.26 Order of pole (three term test) = 30.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23149.4MB, alloc=44.3MB, time=285.68 memory used=23195.4MB, alloc=44.3MB, time=286.24 x[1] = 0.3531 1.171 h = 0.003 0.006 y2[1] (numeric) = 0.475911392368 1.5253909093 y2[1] (closed_form) = 0.611263210204 1.3676546908 absolute error = 0.2078 relative error = 13.87 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.75253296707 -0.422511290764 y1[1] (closed_form) = 1.65858253782 -0.504043047413 absolute error = 0.1244 relative error = 7.176 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.354 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 = 4.354 Order of pole (three term test) = 30.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23241.3MB, alloc=44.3MB, time=286.80 memory used=23287.6MB, alloc=44.3MB, time=287.37 x[1] = 0.3561 1.177 h = 0.0001 0.005 y2[1] (numeric) = 0.47946290037 1.531889248 y2[1] (closed_form) = 0.619296172672 1.37610150738 absolute error = 0.2093 relative error = 13.87 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.76027174441 -0.42996331754 y1[1] (closed_form) = 1.6649679764 -0.511850323136 absolute error = 0.1257 relative error = 7.214 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.96 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 = 1.96 Order of pole (three term test) = 30.54 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23333.5MB, alloc=44.3MB, time=287.93 x[1] = 0.3562 1.182 h = 0.0001 0.003 y2[1] (numeric) = 0.483039382239 1.53840337906 y2[1] (closed_form) = 0.622030359993 1.38439208101 absolute error = 0.2075 relative error = 13.67 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.76789934447 -0.432523077293 y1[1] (closed_form) = 1.67180713007 -0.515091656827 absolute error = 0.1267 relative error = 7.242 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.594 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 = 1.594 Order of pole (three term test) = 30.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23379.3MB, alloc=44.3MB, time=288.48 memory used=23425.6MB, alloc=44.3MB, time=289.05 x[1] = 0.3563 1.185 h = 0.001 0.001 y2[1] (numeric) = 0.486640979165 1.54493343593 y2[1] (closed_form) = 0.623746030085 1.38936203674 absolute error = 0.2074 relative error = 13.62 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.77247586189 -0.434131758259 y1[1] (closed_form) = 1.67590546946 -0.51709900741 absolute error = 0.1273 relative error = 7.259 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.258 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 = 1.258 Order of pole (three term test) = 30.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23471.8MB, alloc=44.3MB, time=289.62 memory used=23518.2MB, alloc=44.3MB, time=290.18 x[1] = 0.3573 1.186 h = 0.0001 0.004 y2[1] (numeric) = 0.490267716679 1.55147948112 y2[1] (closed_form) = 0.62594042431 1.39052021872 absolute error = 0.2105 relative error = 13.8 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.77353561477 -0.436168415637 y1[1] (closed_form) = 1.67667056769 -0.519113791637 absolute error = 0.1275 relative error = 7.266 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.573 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 = 7.573 Order of pole (three term test) = 30.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23564.0MB, alloc=44.3MB, time=290.74 x[1] = 0.3574 1.19 h = 0.003 0.006 y2[1] (numeric) = 0.493919606278 1.55804153641 y2[1] (closed_form) = 0.628190114011 1.3971858739 absolute error = 0.2095 relative error = 13.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.7797054423 -0.438292257812 y1[1] (closed_form) = 1.68218326618 -0.521761434123 absolute error = 0.1284 relative error = 7.288 % Correct digits = 1 memory used=23610.1MB, alloc=44.3MB, time=291.30 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.523 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 = 4.523 Order of pole (three term test) = 30.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23655.9MB, alloc=44.3MB, time=291.86 x[1] = 0.3604 1.196 h = 0.0001 0.005 y2[1] (numeric) = 0.497596763902 1.56461966012 y2[1] (closed_form) = 0.636400950389 1.40572123301 absolute error = 0.211 relative error = 13.67 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.78758614966 -0.445950781975 y1[1] (closed_form) = 1.68869511025 -0.529759530445 absolute error = 0.1296 relative error = 7.324 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.036 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 = 2.036 Order of pole (three term test) = 30.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23701.8MB, alloc=44.3MB, time=292.42 memory used=23747.9MB, alloc=44.3MB, time=292.98 x[1] = 0.3605 1.201 h = 0.0001 0.003 y2[1] (numeric) = 0.501299562065 1.57121386129 y2[1] (closed_form) = 0.639227285397 1.41412901341 absolute error = 0.209 relative error = 13.47 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.79537578214 -0.4486048036 y1[1] (closed_form) = 1.69568094018 -0.53308958603 absolute error = 0.1307 relative error = 7.352 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.656 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 = 1.656 Order of pole (three term test) = 30.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23793.7MB, alloc=44.3MB, time=293.54 memory used=23840.1MB, alloc=44.3MB, time=294.11 x[1] = 0.3606 1.204 h = 0.001 0.001 y2[1] (numeric) = 0.505028145 1.5778242747 y2[1] (closed_form) = 0.64099942297 1.41916891938 absolute error = 0.2089 relative error = 13.42 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.80004901911 -0.450271740481 y1[1] (closed_form) = 1.69986687271 -0.535151589235 absolute error = 0.1313 relative error = 7.368 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.307 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 = 1.307 Order of pole (three term test) = 30.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23886.1MB, alloc=44.3MB, time=294.68 x[1] = 0.3616 1.205 h = 0.001 0.003 y2[1] (numeric) = 0.508782539012 1.5844509637 y2[1] (closed_form) = 0.643235860989 1.42033299292 absolute error = 0.2122 relative error = 13.61 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.80112325218 -0.452359779934 y1[1] (closed_form) = 1.70064450637 -0.537213457703 absolute error = 0.1315 relative error = 7.374 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.218 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 = 6.218 Order of pole (three term test) = 30.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=23932.1MB, alloc=44.3MB, time=295.24 memory used=23978.3MB, alloc=44.3MB, time=295.80 x[1] = 0.3626 1.208 h = 0.0001 0.004 y2[1] (numeric) = 0.512562757807 1.59109393547 y2[1] (closed_form) = 0.646554988799 1.42490146738 absolute error = 0.2135 relative error = 13.64 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.80537589496 -0.455479562511 y1[1] (closed_form) = 1.7042674619 -0.540570757159 absolute error = 0.1321 relative error = 7.391 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.54 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 = 3.54 Order of pole (three term test) = 30.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24024.3MB, alloc=44.3MB, time=296.36 memory used=24070.4MB, alloc=44.3MB, time=296.92 x[1] = 0.3627 1.212 h = 0.003 0.006 y2[1] (numeric) = 0.516368844846 1.59775321805 y2[1] (closed_form) = 0.648893444868 1.43167563134 absolute error = 0.2125 relative error = 13.52 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.81170213745 -0.457696859307 y1[1] (closed_form) = 1.70991583633 -0.543304478862 absolute error = 0.133 relative error = 7.413 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.728 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 = 4.728 Order of pole (three term test) = 30.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24116.2MB, alloc=44.3MB, time=297.48 memory used=24162.4MB, alloc=44.3MB, time=298.05 x[1] = 0.3657 1.218 h = 0.0001 0.005 y2[1] (numeric) = 0.520200927274 1.60442887362 y2[1] (closed_form) = 0.657317639105 1.44031284887 absolute error = 0.2139 relative error = 13.51 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.81975382743 -0.465609824578 y1[1] (closed_form) = 1.71657249485 -0.551531056354 absolute error = 0.1343 relative error = 7.447 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.128 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 = 2.128 Order of pole (three term test) = 30.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24208.2MB, alloc=44.3MB, time=298.60 x[1] = 0.3658 1.223 h = 0.0001 0.003 y2[1] (numeric) = 0.524059384639 1.61112090879 y2[1] (closed_form) = 0.660255898618 1.44885826136 absolute error = 0.2118 relative error = 13.31 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.82774048225 -0.468381241672 y1[1] (closed_form) = 1.72372952933 -0.554969440997 absolute error = 0.1353 relative error = 7.474 % Correct digits = 1 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) = 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 = 1.731 Order of pole (three term test) = 30.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24254.1MB, alloc=44.3MB, time=299.16 memory used=24300.5MB, alloc=44.3MB, time=299.73 x[1] = 0.3659 1.226 h = 0.001 0.001 y2[1] (numeric) = 0.527944364819 1.61782945986 y2[1] (closed_form) = 0.662096585669 1.45398027503 absolute error = 0.2118 relative error = 13.25 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.83253130369 -0.470120688041 y1[1] (closed_form) = 1.7280176664 -0.557098109841 absolute error = 0.136 relative error = 7.489 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.367 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 = 1.367 Order of pole (three term test) = 30.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24346.4MB, alloc=44.3MB, time=300.30 memory used=24392.7MB, alloc=44.3MB, time=300.87 x[1] = 0.3669 1.227 h = 0.001 0.003 y2[1] (numeric) = 0.531855895057 1.62455459118 y2[1] (closed_form) = 0.664383155816 1.45515053172 absolute error = 0.2151 relative error = 13.45 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.83362259642 -0.472271776601 y1[1] (closed_form) = 1.72880899229 -0.559215914983 absolute error = 0.1362 relative error = 7.495 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.499 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 = 6.499 Order of pole (three term test) = 30.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24438.7MB, alloc=44.3MB, time=301.43 x[1] = 0.3679 1.23 h = 0.0001 0.004 y2[1] (numeric) = 0.535793989366 1.63129630996 y2[1] (closed_form) = 0.667796644713 1.459781573 absolute error = 0.2164 relative error = 13.48 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.83797254589 -0.47550116885 y1[1] (closed_form) = 1.7325152998 -0.56267164658 absolute error = 0.1368 relative error = 7.511 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.7 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 = 3.7 Order of pole (three term test) = 30.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24484.9MB, alloc=44.3MB, time=302.00 memory used=24530.9MB, alloc=44.3MB, time=302.56 x[1] = 0.368 1.234 h = 0.003 0.006 y2[1] (numeric) = 0.53975869222 1.63805464449 y2[1] (closed_form) = 0.670226513161 1.46666678888 absolute error = 0.2154 relative error = 13.36 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.84445746484 -0.477815732745 y1[1] (closed_form) = 1.73830128785 -0.565494011167 absolute error = 0.1377 relative error = 7.532 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.942 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 = 4.942 Order of pole (three term test) = 30.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24576.7MB, alloc=44.3MB, time=303.11 memory used=24623.0MB, alloc=44.3MB, time=303.68 x[1] = 0.371 1.24 h = 0.0001 0.005 y2[1] (numeric) = 0.543750133592 1.6448296572 y2[1] (closed_form) = 0.67886992039 1.47540783806 absolute error = 0.2167 relative error = 13.34 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.8526808529 -0.485990568043 y1[1] (closed_form) = 1.74510387715 -0.573954372964 absolute error = 0.139 relative error = 7.564 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.224 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 = 2.224 Order of pole (three term test) = 30.35 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24668.8MB, alloc=44.3MB, time=304.24 memory used=24714.9MB, alloc=44.3MB, time=304.80 x[1] = 0.3711 1.245 h = 0.0001 0.003 y2[1] (numeric) = 0.547768700229 1.65162135219 y2[1] (closed_form) = 0.681923436971 1.48409409343 absolute error = 0.2146 relative error = 13.14 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.86086739773 -0.488884176186 y1[1] (closed_form) = 1.75243457734 -0.577504323451 absolute error = 0.14 relative error = 7.59 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.809 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 = 1.809 Order of pole (three term test) = 30.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24760.8MB, alloc=44.3MB, time=305.36 x[1] = 0.3712 1.248 h = 0.001 0.001 y2[1] (numeric) = 0.551814543751 1.65842986729 y2[1] (closed_form) = 0.683834707255 1.48930012076 absolute error = 0.2146 relative error = 13.09 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.86577749141 -0.490699046648 y1[1] (closed_form) = 1.75682637758 -0.579701628512 absolute error = 0.1407 relative error = 7.605 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.428 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 = 1.428 Order of pole (three term test) = 30.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24806.8MB, alloc=44.3MB, time=305.93 memory used=24853.1MB, alloc=44.3MB, time=306.50 x[1] = 0.3722 1.249 h = 0.001 0.003 y2[1] (numeric) = 0.555887692366 1.66525526788 y2[1] (closed_form) = 0.686172724953 1.49047656089 absolute error = 0.218 relative error = 13.29 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.86688548373 -0.49291473665 y1[1] (closed_form) = 1.75763126256 -0.581876520435 absolute error = 0.1409 relative error = 7.61 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.793 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 = 6.793 Order of pole (three term test) = 30.32 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24899.2MB, alloc=44.3MB, time=307.06 memory used=24945.4MB, alloc=44.3MB, time=307.62 x[1] = 0.3732 1.252 h = 0.0001 0.004 y2[1] (numeric) = 0.559988160404 1.67209756121 y2[1] (closed_form) = 0.689683211266 1.4951714843 absolute error = 0.2194 relative error = 13.32 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.8713335731 -0.496257218601 y1[1] (closed_form) = 1.76142180591 -0.585433124095 absolute error = 0.1415 relative error = 7.625 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.867 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 = 3.867 Order of pole (three term test) = 30.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=24991.2MB, alloc=44.3MB, time=308.18 memory used=25037.3MB, alloc=44.3MB, time=308.74 x[1] = 0.3733 1.256 h = 0.003 0.006 y2[1] (numeric) = 0.564115993377 1.67895677579 y2[1] (closed_form) = 0.69220720568 1.50217032453 absolute error = 0.2183 relative error = 13.2 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.87797947114 -0.498672970354 y1[1] (closed_form) = 1.76734738731 -0.588346767742 absolute error = 0.1424 relative error = 7.645 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.165 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 = 5.165 Order of pole (three term test) = 30.29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25083.3MB, alloc=44.3MB, time=309.30 x[1] = 0.3763 1.262 h = 0.0001 0.005 y2[1] (numeric) = 0.568271324163 1.68583297434 y2[1] (closed_form) = 0.701075805196 1.51101717482 absolute error = 0.2195 relative error = 13.18 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.88637525785 -0.507117298842 y1[1] (closed_form) = 1.77429703575 -0.597046357601 absolute error = 0.1437 relative error = 7.676 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.325 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 = 2.325 Order of pole (three term test) = 30.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25129.1MB, alloc=44.3MB, time=309.86 memory used=25175.3MB, alloc=44.3MB, time=310.42 x[1] = 0.3764 1.267 h = 0.0001 0.003 y2[1] (numeric) = 0.572454546879 1.69272615833 y2[1] (closed_form) = 0.704247996801 1.51984752119 absolute error = 0.2174 relative error = 12.98 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.89476461252 -0.510138029662 y1[1] (closed_form) = 1.78180391598 -0.600711202083 absolute error = 0.1448 relative error = 7.7 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.891 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 = 1.891 Order of pole (three term test) = 30.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25221.2MB, alloc=44.3MB, time=310.99 memory used=25267.5MB, alloc=44.3MB, time=311.57 x[1] = 0.3765 1.27 h = 0.001 0.001 y2[1] (numeric) = 0.576665816994 1.69963646718 y2[1] (closed_form) = 0.706231935846 1.52513948999 absolute error = 0.2173 relative error = 12.93 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.89979569638 -0.512031321179 y1[1] (closed_form) = 1.78630086924 -0.602979169409 absolute error = 0.1454 relative error = 7.714 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.493 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 = 1.493 Order of pole (three term test) = 30.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25313.5MB, alloc=44.3MB, time=312.15 x[1] = 0.3775 1.271 h = 0.001 0.003 y2[1] (numeric) = 0.580905163708 1.70656396729 y2[1] (closed_form) = 0.708622741419 1.52632210466 absolute error = 0.2209 relative error = 13.13 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.90092001201 -0.514313203113 y1[1] (closed_form) = 1.78711917307 -0.605212327408 absolute error = 0.1456 relative error = 7.719 % Correct digits = 1 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) = 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 = 7.1 Order of pole (three term test) = 30.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25359.7MB, alloc=44.3MB, time=312.72 memory used=25405.8MB, alloc=44.3MB, time=313.29 x[1] = 0.3785 1.274 h = 0.0001 0.004 y2[1] (numeric) = 0.585172601674 1.71350866598 y2[1] (closed_form) = 0.712232920598 1.53108223201 absolute error = 0.2223 relative error = 13.17 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.90546708012 -0.517772347616 y1[1] (closed_form) = 1.79099485099 -0.608872308692 absolute error = 0.1463 relative error = 7.734 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.042 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 = 4.042 Order of pole (three term test) = 30.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25451.6MB, alloc=44.3MB, time=313.86 memory used=25497.7MB, alloc=44.3MB, time=314.43 x[1] = 0.3786 1.278 h = 0.003 0.006 y2[1] (numeric) = 0.589468177473 1.72047059196 y2[1] (closed_form) = 0.714853823977 1.53819729889 absolute error = 0.2212 relative error = 13.04 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.91227630108 -0.520293318606 y1[1] (closed_form) = 1.79706204783 -0.611879941745 absolute error = 0.1472 relative error = 7.753 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.398 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 = 5.398 Order of pole (three term test) = 30.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25543.5MB, alloc=44.3MB, time=315.00 memory used=25589.8MB, alloc=44.3MB, time=315.57 x[1] = 0.3816 1.284 h = 0.0001 0.005 y2[1] (numeric) = 0.593792026959 1.72744980824 y2[1] (closed_form) = 0.723953722418 1.54715191543 absolute error = 0.2224 relative error = 13.02 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.92084517045 -0.529014961264 y1[1] (closed_form) = 1.80415989502 -0.620824346788 absolute error = 0.1485 relative error = 7.782 % Correct digits = 1 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) = 34.94 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 = 2.43 Order of pole (three term test) = 30.21 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25635.7MB, alloc=44.3MB, time=316.13 x[1] = 0.3817 1.289 h = 0.0001 0.003 y2[1] (numeric) = 0.598144551804 1.73444631358 y2[1] (closed_form) = 0.727248094715 1.55612963896 absolute error = 0.2201 relative error = 12.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.92944030694 -0.532167885372 y1[1] (closed_form) = 1.81184552312 -0.624607506889 absolute error = 0.1496 relative error = 7.805 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.976 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 = 1.976 Order of pole (three term test) = 30.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25681.5MB, alloc=44.3MB, time=316.70 memory used=25727.9MB, alloc=44.3MB, time=317.28 x[1] = 0.3818 1.292 h = 0.001 0.001 y2[1] (numeric) = 0.602525911424 1.74146024899 y2[1] (closed_form) = 0.729306841226 1.56150949926 absolute error = 0.2201 relative error = 12.77 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.93459412913 -0.534142679035 y1[1] (closed_form) = 1.81644915075 -0.626948219266 absolute error = 0.1502 relative error = 7.818 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.56 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 = 1.56 Order of pole (three term test) = 30.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25773.9MB, alloc=44.3MB, time=317.85 memory used=25820.4MB, alloc=44.3MB, time=318.44 x[1] = 0.3828 1.293 h = 0.0001 0.004 y2[1] (numeric) = 0.606936136044 1.74849168196 y2[1] (closed_form) = 0.731751800502 1.56269827007 absolute error = 0.2238 relative error = 12.97 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.93573437502 -0.53649238216 y1[1] (closed_form) = 1.8172807257 -0.629240852333 absolute error = 0.1504 relative error = 7.823 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.389 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 = 9.389 Order of pole (three term test) = 30.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25866.2MB, alloc=44.3MB, time=319.01 memory used=25912.3MB, alloc=44.3MB, time=319.58 x[1] = 0.3829 1.297 h = 0.003 0.006 y2[1] (numeric) = 0.61137523904 1.75554063594 y2[1] (closed_form) = 0.734456975581 1.56991668882 absolute error = 0.2227 relative error = 12.85 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.94268151847 -0.539104196748 y1[1] (closed_form) = 1.82347263713 -0.632329896104 absolute error = 0.1513 relative error = 7.841 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.608 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 = 5.608 Order of pole (three term test) = 30.16 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=25958.1MB, alloc=44.3MB, time=320.16 x[1] = 0.3859 1.303 h = 0.0001 0.005 y2[1] (numeric) = 0.615843349509 1.76260717061 y2[1] (closed_form) = 0.743759642602 1.57896849362 absolute error = 0.2238 relative error = 12.82 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.95139513253 -0.548063055227 y1[1] (closed_form) = 1.83070197896 -0.641487831439 absolute error = 0.1526 relative error = 7.868 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.524 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 = 2.524 Order of pole (three term test) = 30.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26004.0MB, alloc=44.3MB, time=320.73 memory used=26050.1MB, alloc=44.3MB, time=321.31 x[1] = 0.386 1.308 h = 0.0001 0.003 y2[1] (numeric) = 0.620340875791 1.76969128239 y2[1] (closed_form) = 0.747160250377 1.58807724939 absolute error = 0.2215 relative error = 12.62 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.96016406234 -0.551330118256 y1[1] (closed_form) = 1.83854503131 -0.645373474713 absolute error = 0.1537 relative error = 7.89 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.053 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 = 2.053 Order of pole (three term test) = 30.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26096.0MB, alloc=44.3MB, time=321.89 memory used=26142.3MB, alloc=44.3MB, time=322.48 x[1] = 0.3861 1.311 h = 0.001 0.001 y2[1] (numeric) = 0.624867980766 1.77679311371 y2[1] (closed_form) = 0.749284063937 1.59353526936 absolute error = 0.2215 relative error = 12.58 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 1.9654215243 -0.553375248212 y1[1] (closed_form) = 1.84324262448 -0.647777219775 absolute error = 0.1544 relative error = 7.903 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.621 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 = 1.621 Order of pole (three term test) = 30.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26188.3MB, alloc=44.3MB, time=323.07 x[1] = 0.3871 1.312 h = 0.001 0.003 y2[1] (numeric) = 0.629424695547 1.78391273305 y2[1] (closed_form) = 0.751776677715 1.59472998465 absolute error = 0.2253 relative error = 12.78 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 1.96657473187 -0.555782743523 y1[1] (closed_form) = 1.84408622712 -0.650121882632 absolute error = 0.1546 relative error = 7.907 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.708 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 = 7.708 Order of pole (three term test) = 30.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26234.4MB, alloc=44.3MB, time=323.64 memory used=26280.5MB, alloc=44.3MB, time=324.22 x[1] = 0.3881 1.315 h = 0.0001 0.004 y2[1] (numeric) = 0.634011035412 1.79105014777 y2[1] (closed_form) = 0.755578930836 1.59961624775 absolute error = 0.2268 relative error = 12.82 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 1.97130545635 -0.559465369665 y1[1] (closed_form) = 1.8481240679 -0.65398008457 absolute error = 0.1553 relative error = 7.92 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.388 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 = 4.388 Order of pole (three term test) = 30.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26326.3MB, alloc=44.3MB, time=324.80 memory used=26372.4MB, alloc=44.3MB, time=325.38 x[1] = 0.3882 1.319 h = 0.003 0.006 y2[1] (numeric) = 0.638627048998 1.79820538705 y2[1] (closed_form) = 0.758386352731 1.60695585189 absolute error = 0.2257 relative error = 12.7 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 1.9784203298 -0.562190098562 y1[1] (closed_form) = 1.85446150561 -0.657168339072 absolute error = 0.1562 relative error = 7.937 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.861 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 = 5.861 Order of pole (three term test) = 30.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26418.1MB, alloc=44.3MB, time=325.95 memory used=26464.4MB, alloc=44.3MB, time=326.53 x[1] = 0.3912 1.325 h = 0.0001 0.005 y2[1] (numeric) = 0.643272877904 1.80537851441 y2[1] (closed_form) = 0.767932008526 1.61611914291 absolute error = 0.2266 relative error = 12.67 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 1.98730823018 -0.571441154716 y1[1] (closed_form) = 1.86184126469 -0.666581863328 absolute error = 0.1575 relative error = 7.962 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.638 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 = 2.638 Order of pole (three term test) = 30.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26510.2MB, alloc=44.3MB, time=327.10 x[1] = 0.3913 1.33 h = 0.0001 0.003 y2[1] (numeric) = 0.647948938382 1.81256952343 y2[1] (closed_form) = 0.77146152156 1.62538153844 absolute error = 0.2243 relative error = 12.46 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 1.99628853197 -0.574850093858 y1[1] (closed_form) = 1.86986803033 -0.670592413166 absolute error = 0.1586 relative error = 7.983 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.145 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 = 2.145 Order of pole (three term test) = 30.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26556.0MB, alloc=44.3MB, time=327.68 memory used=26602.4MB, alloc=44.3MB, time=328.26 x[1] = 0.3914 1.333 h = 0.001 0.001 y2[1] (numeric) = 0.652655397456 1.81977855821 y2[1] (closed_form) = 0.773664244789 1.63093116603 absolute error = 0.2243 relative error = 12.43 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.0016720196 -0.57698261001 y1[1] (closed_form) = 1.87467523962 -0.673072915352 absolute error = 0.1593 relative error = 7.995 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.694 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 = 1.694 Order of pole (three term test) = 30.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26648.4MB, alloc=44.3MB, time=328.85 memory used=26694.7MB, alloc=44.3MB, time=329.44 x[1] = 0.3924 1.334 h = 0.001 0.003 y2[1] (numeric) = 0.65739228732 1.82700568832 y2[1] (closed_form) = 0.776213624275 1.63213199384 absolute error = 0.2282 relative error = 12.63 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.00284038891 -0.579461021931 y1[1] (closed_form) = 1.87553183267 -0.675479385724 absolute error = 0.1595 relative error = 7.999 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.056 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 = 8.056 Order of pole (three term test) = 30.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26740.6MB, alloc=44.3MB, time=330.02 memory used=26786.8MB, alloc=44.3MB, time=330.60 x[1] = 0.3934 1.337 h = 0.0001 0.004 y2[1] (numeric) = 0.662159623597 1.83425092116 y2[1] (closed_form) = 0.780123605677 1.63708731254 absolute error = 0.2298 relative error = 12.67 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.00767249588 -0.583270968976 y1[1] (closed_form) = 1.87965749225 -0.679448496513 absolute error = 0.1601 relative error = 8.011 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.586 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 = 4.586 Order of pole (three term test) = 30.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26832.6MB, alloc=44.3MB, time=331.18 x[1] = 0.3935 1.341 h = 0.003 0.006 y2[1] (numeric) = 0.666957456074 1.84151428615 y2[1] (closed_form) = 0.783036266083 1.64455079361 absolute error = 0.2286 relative error = 12.55 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.01495756464 -0.58611298107 y1[1] (closed_form) = 1.88614260204 -0.682738893345 absolute error = 0.161 relative error = 8.028 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.125 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 = 6.125 Order of pole (three term test) = 30.02 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26878.5MB, alloc=44.3MB, time=331.75 memory used=26924.7MB, alloc=44.3MB, time=332.33 x[1] = 0.3965 1.347 h = 0.0001 0.005 y2[1] (numeric) = 0.671785929551 1.84879584709 y2[1] (closed_form) = 0.792831399776 1.6538275224 absolute error = 0.2295 relative error = 12.51 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.02402037858 -0.595664656457 y1[1] (closed_form) = 1.89367394757 -0.692414019454 absolute error = 0.1623 relative error = 8.051 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.757 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 = 2.757 Order of pole (three term test) = 30.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=26970.6MB, alloc=44.3MB, time=332.91 memory used=27016.8MB, alloc=44.3MB, time=333.49 x[1] = 0.3966 1.352 h = 0.0001 0.003 y2[1] (numeric) = 0.676645468366 1.85609559455 y2[1] (closed_form) = 0.796493587409 1.66324695748 absolute error = 0.2271 relative error = 12.31 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.03321517828 -0.599220966372 y1[1] (closed_form) = 1.90188715077 -0.696553176342 absolute error = 0.1635 relative error = 8.071 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.242 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 = 2.242 Order of pole (three term test) = 29.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27062.9MB, alloc=44.3MB, time=334.07 x[1] = 0.3967 1.355 h = 0.001 0.001 y2[1] (numeric) = 0.6815362438 1.86341367432 y2[1] (closed_form) = 0.798777518849 1.66889020918 absolute error = 0.2271 relative error = 12.28 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.03872652876 -0.601444206435 y1[1] (closed_form) = 1.9068055894 -0.699112687696 absolute error = 0.1641 relative error = 8.082 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.77 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 = 1.77 Order of pole (three term test) = 29.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27109.1MB, alloc=44.3MB, time=334.65 memory used=27155.2MB, alloc=44.3MB, time=335.24 x[1] = 0.3977 1.356 h = 0.001 0.003 y2[1] (numeric) = 0.686458289152 1.87075015711 y2[1] (closed_form) = 0.801385106419 1.67009710244 absolute error = 0.2312 relative error = 12.48 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.03990961448 -0.603995281477 y1[1] (closed_form) = 1.90767500216 -0.701582262519 absolute error = 0.1643 relative error = 8.085 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.419 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 = 8.419 Order of pole (three term test) = 29.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27201.1MB, alloc=44.3MB, time=335.82 memory used=27247.5MB, alloc=44.3MB, time=336.40 x[1] = 0.3987 1.359 h = 0.0001 0.004 y2[1] (numeric) = 0.691411620406 1.87810505036 y2[1] (closed_form) = 0.805405754419 1.67512282409 absolute error = 0.2328 relative error = 12.53 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.04484396034 -0.607936504584 y1[1] (closed_form) = 1.91188943585 -0.705665053945 absolute error = 0.165 relative error = 8.097 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.793 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 = 4.793 Order of pole (three term test) = 29.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27293.3MB, alloc=44.3MB, time=336.97 memory used=27339.6MB, alloc=44.3MB, time=337.56 x[1] = 0.3988 1.363 h = 0.003 0.006 y2[1] (numeric) = 0.696396288525 1.88547838372 y2[1] (closed_form) = 0.808426721899 1.68271290559 absolute error = 0.2317 relative error = 12.41 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.05230173091 -0.610900288964 y1[1] (closed_form) = 1.91852440707 -0.709060605717 absolute error = 0.1659 relative error = 8.112 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.402 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 = 6.402 Order of pole (three term test) = 29.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27385.4MB, alloc=44.3MB, time=338.13 x[1] = 0.4018 1.369 h = 0.0001 0.005 y2[1] (numeric) = 0.701412441592 1.89287022126 y2[1] (closed_form) = 0.818477962814 1.69210501722 absolute error = 0.2324 relative error = 12.36 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.06154006231 -0.620761217591 y1[1] (closed_form) = 1.92620851635 -0.719003501232 absolute error = 0.1672 relative error = 8.134 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.881 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 = 2.881 Order of pole (three term test) = 29.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27431.2MB, alloc=44.3MB, time=338.71 memory used=27477.3MB, alloc=44.3MB, time=339.30 x[1] = 0.4019 1.374 h = 0.0001 0.003 y2[1] (numeric) = 0.70646051222 1.90028055046 y2[1] (closed_form) = 0.8222766915 1.70168493229 absolute error = 0.2299 relative error = 12.16 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.07095253813 -0.624470544004 y1[1] (closed_form) = 1.93461093635 -0.723275067769 absolute error = 0.1684 relative error = 8.152 % Correct digits = 1 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) = 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 = 2.343 Order of pole (three term test) = 29.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27523.2MB, alloc=44.3MB, time=339.87 memory used=27569.5MB, alloc=44.3MB, time=340.46 x[1] = 0.402 1.377 h = 0.001 0.001 y2[1] (numeric) = 0.711540676061 1.90770951881 y2[1] (closed_form) = 0.824644188553 1.70742384834 absolute error = 0.23 relative error = 12.13 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.07659361877 -0.626787937104 y1[1] (closed_form) = 1.93964224984 -0.725915902298 absolute error = 0.1691 relative error = 8.163 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.85 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 = 1.85 Order of pole (three term test) = 29.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27615.6MB, alloc=44.3MB, time=341.05 x[1] = 0.403 1.378 h = 0.001 0.003 y2[1] (numeric) = 0.716652967552 1.91515719818 y2[1] (closed_form) = 0.827311454534 1.70863674915 absolute error = 0.2343 relative error = 12.34 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.07779095642 -0.629413463047 y1[1] (closed_form) = 1.94052430274 -0.728449910272 absolute error = 0.1693 relative error = 8.166 % Correct digits = 1 memory used=27661.9MB, alloc=44.3MB, time=341.62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.799 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 = 8.799 Order of pole (three term test) = 29.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27707.8MB, alloc=44.3MB, time=342.20 x[1] = 0.404 1.381 h = 0.0001 0.004 y2[1] (numeric) = 0.721797403044 1.92262359606 y2[1] (closed_form) = 0.831445774326 1.71373422742 absolute error = 0.2359 relative error = 12.39 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.08282840043 -0.633490019398 y1[1] (closed_form) = 1.94482847982 -0.732649226652 absolute error = 0.1699 relative error = 8.177 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.009 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 = 5.009 Order of pole (three term test) = 29.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27753.8MB, alloc=44.3MB, time=342.77 memory used=27799.9MB, alloc=44.3MB, time=343.35 x[1] = 0.4041 1.385 h = 0.003 0.006 y2[1] (numeric) = 0.726974034709 1.93010874233 y2[1] (closed_form) = 0.834578196349 1.72145366529 absolute error = 0.2348 relative error = 12.27 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.09046142054 -0.636580187992 y1[1] (closed_form) = 1.9516155456 -0.736153028866 absolute error = 0.1709 relative error = 8.191 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.69 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 = 6.69 Order of pole (three term test) = 29.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27845.9MB, alloc=44.3MB, time=343.93 memory used=27892.1MB, alloc=44.3MB, time=344.52 x[1] = 0.4071 1.391 h = 0.0001 0.005 y2[1] (numeric) = 0.732183013991 1.93761270131 y2[1] (closed_form) = 0.844892317481 1.73096309771 absolute error = 0.2354 relative error = 12.22 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.09987584804 -0.646759220323 y1[1] (closed_form) = 1.95945360313 -0.74637001905 absolute error = 0.1722 relative error = 8.211 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.011 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 = 3.011 Order of pole (three term test) = 29.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27938.0MB, alloc=44.3MB, time=345.09 x[1] = 0.4072 1.396 h = 0.0001 0.003 y2[1] (numeric) = 0.737424781979 1.9451354573 y2[1] (closed_form) = 0.848831553353 1.74070697454 absolute error = 0.2328 relative error = 12.02 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.10950923046 -0.650627363344 y1[1] (closed_form) = 1.96804807459 -0.750777902335 absolute error = 0.1733 relative error = 8.229 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.448 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 = 2.448 Order of pole (three term test) = 29.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=27984.0MB, alloc=44.3MB, time=345.67 memory used=28030.3MB, alloc=44.3MB, time=346.27 x[1] = 0.4073 1.399 h = 0.001 0.001 y2[1] (numeric) = 0.742699518805 1.95267715951 y2[1] (closed_form) = 0.851285033834 1.7465436193 absolute error = 0.233 relative error = 11.99 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.1152819387 -0.653042432019 y1[1] (closed_form) = 1.97319394093 -0.753502437447 absolute error = 0.174 relative error = 8.239 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.934 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 = 1.934 Order of pole (three term test) = 29.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28076.2MB, alloc=44.3MB, time=346.85 memory used=28122.5MB, alloc=44.3MB, time=347.44 x[1] = 0.4083 1.4 h = 0.003 0.006 y2[1] (numeric) = 0.748007260079 1.96023788101 y2[1] (closed_form) = 0.854013477162 1.74776245861 absolute error = 0.2375 relative error = 12.21 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.116493044 -0.655744238592 y1[1] (closed_form) = 1.97408844515 -0.756102239592 absolute error = 0.1742 relative error = 8.241 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.51 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 = 19.51 Order of pole (three term test) = 29.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28168.4MB, alloc=44.3MB, time=348.02 memory used=28214.7MB, alloc=44.3MB, time=348.61 x[1] = 0.4113 1.406 h = 0.0001 0.005 y2[1] (numeric) = 0.753348116241 1.96781760698 y2[1] (closed_form) = 0.864515449485 1.75734688534 absolute error = 0.238 relative error = 12.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.12602517624 -0.66614036655 y1[1] (closed_form) = 1.98202599317 -0.766515443146 absolute error = 0.1755 relative error = 8.26 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.103 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 = 3.103 Order of pole (three term test) = 29.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28260.5MB, alloc=44.3MB, time=349.19 x[1] = 0.4114 1.411 h = 0.0001 0.003 y2[1] (numeric) = 0.758722524405 1.97541629795 y2[1] (closed_form) = 0.868557928547 1.76720192988 absolute error = 0.2354 relative error = 11.96 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.13580764983 -0.670117690649 y1[1] (closed_form) = 1.99075069374 -0.771024343915 absolute error = 0.1767 relative error = 8.277 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.523 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 = 2.523 Order of pole (three term test) = 29.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28306.4MB, alloc=44.3MB, time=349.77 memory used=28352.8MB, alloc=44.3MB, time=350.36 x[1] = 0.4115 1.414 h = 0.001 0.001 y2[1] (numeric) = 0.76413066767 1.98303410421 y2[1] (closed_form) = 0.871074515334 1.77310477112 absolute error = 0.2356 relative error = 11.93 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.14166917826 -0.672599884357 y1[1] (closed_form) = 1.9959741684 -0.773810805567 absolute error = 0.1774 relative error = 8.287 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 1.992 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 = 1.992 Order of pole (three term test) = 29.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28398.9MB, alloc=44.3MB, time=350.95 memory used=28445.3MB, alloc=44.3MB, time=351.54 x[1] = 0.4125 1.415 h = 0.001 0.003 y2[1] (numeric) = 0.769572582503 1.99067109963 y2[1] (closed_form) = 0.87384607382 1.77432606248 absolute error = 0.2402 relative error = 12.14 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.14288918045 -0.67535358417 y1[1] (closed_form) = 1.99687542396 -0.776456981128 absolute error = 0.1776 relative error = 8.289 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.475 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 = 9.475 Order of pole (three term test) = 29.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28491.3MB, alloc=44.3MB, time=352.13 x[1] = 0.4135 1.418 h = 0.0001 0.004 y2[1] (numeric) = 0.775048285894 1.99832729175 y2[1] (closed_form) = 0.878181149541 1.77954471017 absolute error = 0.2419 relative error = 12.19 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.14810036562 -0.679665004615 y1[1] (closed_form) = 2.00133021574 -0.780861952185 absolute error = 0.1783 relative error = 8.299 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.394 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 = 5.394 Order of pole (three term test) = 29.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28537.5MB, alloc=44.3MB, time=352.71 memory used=28583.4MB, alloc=44.3MB, time=353.28 x[1] = 0.4136 1.422 h = 0.003 0.006 y2[1] (numeric) = 0.78055783213 2.00600271083 y2[1] (closed_form) = 0.881512473173 1.78748584172 absolute error = 0.2407 relative error = 12.08 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.15603123918 -0.682976421899 y1[1] (closed_form) = 2.00837628302 -0.784559685562 absolute error = 0.1792 relative error = 8.312 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.205 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 = 7.205 Order of pole (three term test) = 29.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28629.2MB, alloc=44.3MB, time=353.85 memory used=28675.4MB, alloc=44.3MB, time=354.43 x[1] = 0.4166 1.428 h = 0.0001 0.005 y2[1] (numeric) = 0.786101378533 2.0136974215 y2[1] (closed_form) = 0.892289141898 1.79719066332 absolute error = 0.2411 relative error = 12.02 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.16574034968 -0.693705927801 y1[1] (closed_form) = 2.016469624 -0.795258056813 absolute error = 0.1805 relative error = 8.329 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.242 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 = 3.242 Order of pole (three term test) = 29.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28721.3MB, alloc=44.3MB, time=355.00 memory used=28767.5MB, alloc=44.3MB, time=355.77 x[1] = 0.4167 1.433 h = 0.0001 0.003 y2[1] (numeric) = 0.791679380853 2.02141140221 y2[1] (closed_form) = 0.896479145988 1.8072155364 absolute error = 0.2385 relative error = 11.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.17574922494 -0.697852120562 y1[1] (closed_form) = 2.02539118289 -0.799910187411 absolute error = 0.1817 relative error = 8.345 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.637 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 = 2.637 Order of pole (three term test) = 29.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28813.5MB, alloc=44.3MB, time=356.37 x[1] = 0.4168 1.436 h = 0.001 0.001 y2[1] (numeric) = 0.797292027098 2.02914480502 y2[1] (closed_form) = 0.89908599201 1.81321958215 absolute error = 0.2387 relative error = 11.79 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.18174560609 -0.700438096654 y1[1] (closed_form) = 2.03073205346 -0.802784554454 absolute error = 0.1824 relative error = 8.354 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.082 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 = 2.082 Order of pole (three term test) = 29.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28859.6MB, alloc=44.3MB, time=356.95 memory used=28906.0MB, alloc=44.3MB, time=357.53 x[1] = 0.4178 1.437 h = 0.001 0.003 y2[1] (numeric) = 0.802939354967 2.03689770504 y2[1] (closed_form) = 0.901921322246 1.81444662962 absolute error = 0.2435 relative error = 12.02 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.18297851292 -0.703271229084 y1[1] (closed_form) = 2.03164538336 -0.805498891064 absolute error = 0.1826 relative error = 8.356 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.902 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 = 9.902 Order of pole (three term test) = 29.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=28951.9MB, alloc=44.3MB, time=358.12 memory used=28998.1MB, alloc=44.3MB, time=358.71 x[1] = 0.4188 1.44 h = 0.0001 0.004 y2[1] (numeric) = 0.80862138184 2.04467010983 y2[1] (closed_form) = 0.906378526557 1.8197406215 absolute error = 0.2453 relative error = 12.06 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.18829508229 -0.707729343791 y1[1] (closed_form) = 2.03619251354 -0.81002842917 absolute error = 0.1833 relative error = 8.365 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.637 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 = 5.637 Order of pole (three term test) = 29.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29043.9MB, alloc=44.3MB, time=359.30 memory used=29090.1MB, alloc=44.3MB, time=359.90 x[1] = 0.4189 1.444 h = 0.003 0.006 y2[1] (numeric) = 0.814338163298 2.0524620499 y2[1] (closed_form) = 0.909830244181 1.82781859604 absolute error = 0.2441 relative error = 11.96 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.1964081924 -0.71118010773 y1[1] (closed_form) = 2.04339681219 -0.813843219109 absolute error = 0.1843 relative error = 8.377 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.529 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 = 7.529 Order of pole (three term test) = 29.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29135.9MB, alloc=44.3MB, time=360.48 x[1] = 0.4219 1.45 h = 0.0001 0.005 y2[1] (numeric) = 0.820089860256 2.06027359012 y2[1] (closed_form) = 0.920888785975 1.83764572385 absolute error = 0.2444 relative error = 11.89 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.20629475628 -0.722252472795 y1[1] (closed_form) = 2.05164714102 -0.8248335232 absolute error = 0.1856 relative error = 8.392 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.388 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 = 3.388 Order of pole (three term test) = 29.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29181.9MB, alloc=44.3MB, time=361.08 memory used=29228.0MB, alloc=44.3MB, time=361.68 x[1] = 0.422 1.455 h = 0.0001 0.003 y2[1] (numeric) = 0.825876937469 2.06810470543 y2[1] (closed_form) = 0.925230563389 1.84784401885 absolute error = 0.2416 relative error = 11.69 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.21653339579 -0.726573793737 y1[1] (closed_form) = 2.06076854081 -0.829633085305 absolute error = 0.1868 relative error = 8.407 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.755 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 = 2.755 Order of pole (three term test) = 29.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29273.9MB, alloc=44.3MB, time=362.28 memory used=29320.3MB, alloc=44.3MB, time=362.88 x[1] = 0.4221 1.458 h = 0.001 0.001 y2[1] (numeric) = 0.83169958775 2.07595554969 y2[1] (closed_form) = 0.927930257415 1.85395139853 absolute error = 0.242 relative error = 11.67 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.2226666027 -0.729267352472 y1[1] (closed_form) = 2.06622857195 -0.832597913813 absolute error = 0.1875 relative error = 8.416 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.176 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 = 2.176 Order of pole (three term test) = 29.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29366.3MB, alloc=44.3MB, time=363.47 x[1] = 0.4231 1.459 h = 0.001 0.003 y2[1] (numeric) = 0.837557850063 2.08382619926 y2[1] (closed_form) = 0.930830938263 1.85518410029 absolute error = 0.2469 relative error = 11.9 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.22391186617 -0.732181867446 y1[1] (closed_form) = 2.06715375957 -0.835381862006 absolute error = 0.1877 relative error = 8.418 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.35 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 = 10.35 Order of pole (three term test) = 29.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29412.3MB, alloc=44.3MB, time=364.06 memory used=29458.6MB, alloc=44.3MB, time=364.66 x[1] = 0.4241 1.462 h = 0.0001 0.004 y2[1] (numeric) = 0.843451742187 2.09171666174 y2[1] (closed_form) = 0.935413537957 1.86055481053 absolute error = 0.2488 relative error = 11.95 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.22933467369 -0.7367911427 y1[1] (closed_form) = 2.07179424493 -0.840039092751 absolute error = 0.1884 relative error = 8.425 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.891 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 = 5.891 Order of pole (three term test) = 29.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29504.6MB, alloc=44.3MB, time=365.24 memory used=29550.7MB, alloc=44.3MB, time=365.83 x[1] = 0.4242 1.466 h = 0.003 0.006 y2[1] (numeric) = 0.849381321029 2.09962696788 y2[1] (closed_form) = 0.938989107219 1.86877250597 absolute error = 0.2476 relative error = 11.84 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.23763271296 -0.740386363936 y1[1] (closed_form) = 2.07915916988 -0.843974358672 absolute error = 0.1893 relative error = 8.437 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.868 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 = 7.868 Order of pole (three term test) = 29.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29596.5MB, alloc=44.3MB, time=366.42 memory used=29642.8MB, alloc=44.3MB, time=367.02 x[1] = 0.4272 1.472 h = 0.0001 0.005 y2[1] (numeric) = 0.855346751185 2.10755718279 y2[1] (closed_form) = 0.950336855782 1.87872384136 absolute error = 0.2478 relative error = 11.77 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.24769717238 -0.751811301366 y1[1] (closed_form) = 2.08756768493 -0.855263530456 absolute error = 0.1906 relative error = 8.45 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.541 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 = 3.541 Order of pole (three term test) = 29.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29688.8MB, alloc=44.3MB, time=367.61 x[1] = 0.4273 1.477 h = 0.0001 0.003 y2[1] (numeric) = 0.861348506625 2.11550727778 y2[1] (closed_form) = 0.954834764458 1.88909919533 absolute error = 0.2449 relative error = 11.57 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.25816899077 -0.756314177369 y1[1] (closed_form) = 2.09689196493 -0.860214839571 absolute error = 0.1918 relative error = 8.465 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.879 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 = 2.879 Order of pole (three term test) = 29.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29734.7MB, alloc=44.3MB, time=368.19 memory used=29781.0MB, alloc=44.3MB, time=368.78 x[1] = 0.4274 1.48 h = 0.001 0.001 y2[1] (numeric) = 0.867386785087 2.12347740852 y2[1] (closed_form) = 0.957629961691 1.89531206382 absolute error = 0.2454 relative error = 11.55 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.26444102631 -0.759119220235 y1[1] (closed_form) = 2.10247295456 -0.863272754653 absolute error = 0.1926 relative error = 8.473 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.274 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 = 2.274 Order of pole (three term test) = 29.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29827.0MB, alloc=44.3MB, time=369.36 memory used=29873.4MB, alloc=44.3MB, time=369.94 x[1] = 0.4284 1.481 h = 0.0001 0.004 y2[1] (numeric) = 0.873461626835 2.13146765266 y2[1] (closed_form) = 0.960597603125 1.8965503054 absolute error = 0.2506 relative error = 11.79 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.26569807601 -0.762117112247 y1[1] (closed_form) = 2.10340977243 -0.866127799464 absolute error = 0.1928 relative error = 8.474 % Correct digits = 1 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) = 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 = 13.68 Order of pole (three term test) = 29.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=29919.2MB, alloc=44.3MB, time=370.51 memory used=29965.4MB, alloc=44.3MB, time=371.09 x[1] = 0.4285 1.485 h = 0.003 0.006 y2[1] (numeric) = 0.879573049256 2.13947803699 y2[1] (closed_form) = 0.964280904814 1.90489213211 absolute error = 0.2494 relative error = 11.68 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.27415230923 -0.765836716515 y1[1] (closed_form) = 2.11091640365 -0.870167622718 absolute error = 0.1937 relative error = 8.485 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.173 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 = 8.173 Order of pole (three term test) = 29.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30011.2MB, alloc=44.3MB, time=371.66 x[1] = 0.4315 1.491 h = 0.0001 0.005 y2[1] (numeric) = 0.885721208864 2.14750862324 y2[1] (closed_form) = 0.975882078065 1.91495546245 absolute error = 0.2494 relative error = 11.6 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.28436532698 -0.777563055749 y1[1] (closed_form) = 2.11946571737 -0.881717831422 absolute error = 0.195 relative error = 8.496 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.678 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 = 3.678 Order of pole (three term test) = 29.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30057.0MB, alloc=44.3MB, time=372.23 memory used=30103.2MB, alloc=44.3MB, time=372.80 x[1] = 0.4316 1.496 h = 0.0001 0.003 y2[1] (numeric) = 0.891906587753 2.15555937958 y2[1] (closed_form) = 0.980515785944 1.92548810173 absolute error = 0.2465 relative error = 11.41 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.29503410748 -0.7822222629 y1[1] (closed_form) = 2.12896898703 -0.886800836883 absolute error = 0.1963 relative error = 8.509 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.991 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 = 2.991 Order of pole (three term test) = 29.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30149.1MB, alloc=44.3MB, time=373.38 memory used=30195.4MB, alloc=44.3MB, time=373.95 x[1] = 0.4317 1.499 h = 0.001 0.001 y2[1] (numeric) = 0.898129387983 2.16363046334 y2[1] (closed_form) = 0.983394075357 1.93179469868 absolute error = 0.247 relative error = 11.4 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.30142338566 -0.785123266822 y1[1] (closed_form) = 2.13465671163 -0.88993956318 absolute error = 0.197 relative error = 8.517 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.362 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 = 2.362 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30241.4MB, alloc=44.3MB, time=374.53 x[1] = 0.4327 1.5 h = 0.001 0.003 y2[1] (numeric) = 0.904389650948 2.17172195331 y2[1] (closed_form) = 0.986420603841 1.93303843142 absolute error = 0.2524 relative error = 11.63 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.30268980377 -0.788192197727 y1[1] (closed_form) = 2.13560422134 -0.892856886926 absolute error = 0.1972 relative error = 8.518 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.23 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 = 11.23 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30287.6MB, alloc=44.3MB, time=375.09 memory used=30333.8MB, alloc=44.3MB, time=375.67 x[1] = 0.4337 1.503 h = 0.0001 0.004 y2[1] (numeric) = 0.910687395203 2.17983385715 y2[1] (closed_form) = 0.991244535463 1.93855716263 absolute error = 0.2544 relative error = 11.68 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.30830959698 -0.793090580123 y1[1] (closed_form) = 2.1404227814 -0.897759176755 absolute error = 0.1978 relative error = 8.524 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.394 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 = 6.394 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30379.7MB, alloc=44.3MB, time=376.24 memory used=30425.8MB, alloc=44.3MB, time=376.80 x[1] = 0.4338 1.507 h = 0.003 0.006 y2[1] (numeric) = 0.917022680203 2.18796620609 y2[1] (closed_form) = 0.995058326154 1.94704420219 absolute error = 0.2532 relative error = 11.58 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.31695380509 -0.796964377581 y1[1] (closed_form) = 2.14809465904 -0.901926056482 absolute error = 0.1988 relative error = 8.534 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.541 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 = 8.541 Order of pole (three term test) = 29.46 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30471.6MB, alloc=44.3MB, time=377.36 memory used=30517.9MB, alloc=44.3MB, time=377.94 x[1] = 0.4368 1.513 h = 0.0001 0.005 y2[1] (numeric) = 0.923395677637 2.19611906567 y2[1] (closed_form) = 1.00696276114 1.95723534058 absolute error = 0.2531 relative error = 11.5 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.32734543261 -0.809061736466 y1[1] (closed_form) = 2.15680448203 -0.913788486239 absolute error = 0.2001 relative error = 8.544 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.844 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 = 3.844 Order of pole (three term test) = 29.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30563.6MB, alloc=44.3MB, time=378.50 x[1] = 0.4369 1.518 h = 0.0001 0.003 y2[1] (numeric) = 0.929806879221 2.20429240025 y2[1] (closed_form) = 1.01176096637 1.96795198011 absolute error = 0.2501 relative error = 11.3 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.33825379291 -0.813914747276 y1[1] (closed_form) = 2.16651649436 -0.919031543195 absolute error = 0.2014 relative error = 8.556 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.126 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 = 3.126 Order of pole (three term test) = 29.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30609.5MB, alloc=44.3MB, time=379.06 memory used=30655.8MB, alloc=44.3MB, time=379.64 x[1] = 0.437 1.521 h = 0.001 0.001 y2[1] (numeric) = 0.936256492181 2.21248636903 y2[1] (closed_form) = 1.014739856 1.97436817816 absolute error = 0.2507 relative error = 11.29 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.34478565304 -0.816934671488 y1[1] (closed_form) = 2.17232864536 -0.922268407721 absolute error = 0.2021 relative error = 8.563 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.468 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 = 2.468 Order of pole (three term test) = 29.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30701.7MB, alloc=44.3MB, time=380.21 memory used=30748.0MB, alloc=44.3MB, time=380.79 x[1] = 0.438 1.522 h = 0.001 0.003 y2[1] (numeric) = 0.94274455928 2.22070105211 y2[1] (closed_form) = 1.01783642784 1.97561722263 absolute error = 0.2563 relative error = 11.53 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.34606274771 -0.820090760792 y1[1] (closed_form) = 2.17328735042 -0.925259688404 absolute error = 0.2023 relative error = 8.563 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.74 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 = 11.74 Order of pole (three term test) = 29.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30793.9MB, alloc=44.3MB, time=381.36 x[1] = 0.439 1.525 h = 0.0001 0.004 y2[1] (numeric) = 0.9492710995 2.22893645722 y2[1] (closed_form) = 1.02279550466 1.98121667646 absolute error = 0.2584 relative error = 11.59 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.35179119417 -0.825153591683 y1[1] (closed_form) = 2.17820228454 -0.930299047435 absolute error = 0.2029 relative error = 8.569 % Correct digits = 1 memory used=30840.2MB, alloc=44.3MB, time=381.92 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.682 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 = 6.682 Order of pole (three term test) = 29.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30886.0MB, alloc=44.3MB, time=382.49 x[1] = 0.4391 1.529 h = 0.003 0.006 y2[1] (numeric) = 0.95583617372 2.2371926158 y2[1] (closed_form) = 1.02674350247 1.98985190887 absolute error = 0.2573 relative error = 11.49 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.36062819034 -0.829187099654 y1[1] (closed_form) = 2.1860419346 -0.934596672629 absolute error = 0.2039 relative error = 8.578 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.925 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 = 8.925 Order of pole (three term test) = 29.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=30931.8MB, alloc=44.3MB, time=383.05 memory used=30978.1MB, alloc=44.3MB, time=383.62 x[1] = 0.4421 1.535 h = 0.0001 0.005 y2[1] (numeric) = 0.962439957573 2.24546959361 y2[1] (closed_form) = 1.03895900344 2.00017272536 absolute error = 0.257 relative error = 11.4 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.37119876211 -0.841665896687 y1[1] (closed_form) = 2.19491347133 -0.946778763074 absolute error = 0.2052 relative error = 8.586 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.017 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 = 4.017 Order of pole (three term test) = 29.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31024.0MB, alloc=44.3MB, time=384.19 memory used=31070.2MB, alloc=44.3MB, time=384.76 x[1] = 0.4422 1.54 h = 0.0001 0.003 y2[1] (numeric) = 0.969082952597 2.25376735103 y2[1] (closed_form) = 1.04392639296 2.01107713205 absolute error = 0.254 relative error = 11.21 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.38235026997 -0.846719649231 y1[1] (closed_form) = 2.20483743149 -0.952186526969 absolute error = 0.2065 relative error = 8.597 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.266 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 = 3.266 Order of pole (three term test) = 29.35 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31116.1MB, alloc=44.3MB, time=385.33 x[1] = 0.4423 1.543 h = 0.001 0.001 y2[1] (numeric) = 0.975765371315 2.26208604913 y2[1] (closed_form) = 1.04700873732 2.01760516178 absolute error = 0.2546 relative error = 11.2 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.38902680273 -0.849862704347 y1[1] (closed_form) = 2.21077590389 -0.955524360982 absolute error = 0.2072 relative error = 8.604 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.579 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 = 2.579 Order of pole (three term test) = 29.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31162.2MB, alloc=44.3MB, time=385.90 memory used=31208.5MB, alloc=44.3MB, time=386.47 x[1] = 0.4433 1.544 h = 0.001 0.003 y2[1] (numeric) = 0.982487257896 2.27042576939 y2[1] (closed_form) = 1.05017705561 2.01885936525 absolute error = 0.2605 relative error = 11.45 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.39031393387 -0.853108081529 y1[1] (closed_form) = 2.21174554377 -0.95859118598 absolute error = 0.2074 relative error = 8.604 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.27 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 = 12.27 Order of pole (three term test) = 29.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31254.4MB, alloc=44.3MB, time=387.04 memory used=31300.5MB, alloc=44.3MB, time=387.61 x[1] = 0.4443 1.547 h = 0.0001 0.004 y2[1] (numeric) = 0.989248631761 2.27878651957 y2[1] (closed_form) = 1.05527484447 2.02454093809 absolute error = 0.2627 relative error = 11.51 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.39615188239 -0.858340279877 y1[1] (closed_form) = 2.21675791752 -0.963771058023 absolute error = 0.2081 relative error = 8.608 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.983 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 = 6.983 Order of pole (three term test) = 29.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31346.4MB, alloc=44.3MB, time=388.18 memory used=31392.5MB, alloc=44.3MB, time=388.76 x[1] = 0.4444 1.551 h = 0.003 0.006 y2[1] (numeric) = 0.996049555248 2.28716833134 y2[1] (closed_form) = 1.05936086328 2.0333273796 absolute error = 0.2616 relative error = 11.41 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.40518452048 -0.862539160622 y1[1] (closed_form) = 2.224767912 -0.968203216414 absolute error = 0.2091 relative error = 8.617 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.326 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 = 9.326 Order of pole (three term test) = 29.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31438.4MB, alloc=44.3MB, time=389.32 x[1] = 0.4474 1.557 h = 0.0001 0.005 y2[1] (numeric) = 1.00289020803 2.29557127067 y2[1] (closed_form) = 1.07189540655 2.0437797308 absolute error = 0.2611 relative error = 11.31 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.41593432908 -0.875410064052 y1[1] (closed_form) = 2.23380236612 -0.98071259064 absolute error = 0.2104 relative error = 8.624 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.197 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 = 4.197 Order of pole (three term test) = 29.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31484.2MB, alloc=44.3MB, time=389.90 memory used=31530.4MB, alloc=44.3MB, time=390.46 x[1] = 0.4475 1.562 h = 0.0001 0.003 y2[1] (numeric) = 1.00977110168 2.3039952938 y2[1] (closed_form) = 1.0770367882 2.05487571776 absolute error = 0.258 relative error = 11.12 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.42733260396 -0.880671678642 y1[1] (closed_form) = 2.24394153748 -0.98628984144 absolute error = 0.2116 relative error = 8.634 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.413 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 = 3.413 Order of pole (three term test) = 29.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31576.4MB, alloc=44.3MB, time=391.05 memory used=31622.9MB, alloc=44.3MB, time=391.63 x[1] = 0.4476 1.565 h = 0.001 0.001 y2[1] (numeric) = 1.01669245416 2.31244056373 y2[1] (closed_form) = 1.08022551506 2.06151783657 absolute error = 0.2588 relative error = 11.12 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.43415592957 -0.883942185468 y1[1] (closed_form) = 2.25000826033 -0.98973155169 absolute error = 0.2124 relative error = 8.64 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.695 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 = 2.695 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31668.9MB, alloc=44.3MB, time=392.20 x[1] = 0.4486 1.566 h = 0.001 0.003 y2[1] (numeric) = 1.02365431109 2.32090716334 y2[1] (closed_form) = 1.08346731681 2.06277703198 absolute error = 0.265 relative error = 11.37 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.43545243165 -0.88727902756 y1[1] (closed_form) = 2.25098856187 -0.992875545377 absolute error = 0.2126 relative error = 8.639 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.82 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 = 12.82 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31715.2MB, alloc=44.3MB, time=392.77 memory used=31761.1MB, alloc=44.3MB, time=393.33 x[1] = 0.4496 1.569 h = 0.0001 0.004 y2[1] (numeric) = 1.03065669233 2.32939510038 y2[1] (closed_form) = 1.08870746695 2.06854212527 absolute error = 0.2672 relative error = 11.43 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.44140072759 -0.892685633281 y1[1] (closed_form) = 2.25609945247 -0.998199461027 absolute error = 0.2132 relative error = 8.643 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.297 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 = 7.297 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31807.0MB, alloc=44.3MB, time=393.89 memory used=31853.2MB, alloc=44.3MB, time=394.46 x[1] = 0.4497 1.573 h = 0.003 0.006 y2[1] (numeric) = 1.03769966171 2.3379044068 y2[1] (closed_form) = 1.09293541882 2.07748282889 absolute error = 0.2662 relative error = 11.34 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.45063190199 -0.897055697244 y1[1] (closed_form) = 2.26428240963 -1.00277004141 absolute error = 0.2142 relative error = 8.652 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.746 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 = 9.746 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31899.0MB, alloc=44.3MB, time=395.02 memory used=31945.2MB, alloc=44.3MB, time=395.58 x[1] = 0.4527 1.579 h = 0.0001 0.005 y2[1] (numeric) = 1.04478340304 2.34643514873 y2[1] (closed_form) = 1.10579715686 2.08806855701 absolute error = 0.2655 relative error = 11.24 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.46156119561 -0.910329629908 y1[1] (closed_form) = 2.27348098276 -1.01561450972 absolute error = 0.2155 relative error = 8.656 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.386 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 = 4.386 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=31991.0MB, alloc=44.3MB, time=396.14 x[1] = 0.4528 1.584 h = 0.0001 0.003 y2[1] (numeric) = 1.05190843818 2.35498727817 y2[1] (closed_form) = 1.11111746249 2.09935998408 absolute error = 0.2624 relative error = 11.05 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.47320990849 -0.915806413177 y1[1] (closed_form) = 2.2838386873 -1.02136615485 absolute error = 0.2168 relative error = 8.666 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.567 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 = 3.567 Order of pole (three term test) = 29.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32037.0MB, alloc=44.3MB, time=396.70 memory used=32083.3MB, alloc=44.3MB, time=397.28 x[1] = 0.4529 1.587 h = 0.001 0.001 y2[1] (numeric) = 1.05907499063 2.36356096004 y2[1] (closed_form) = 1.11441557471 2.1061184766 absolute error = 0.2633 relative error = 11.05 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.48018217662 -0.919208805164 y1[1] (closed_form) = 2.29003562387 -1.02491472537 absolute error = 0.2176 relative error = 8.671 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.817 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 = 2.817 Order of pole (three term test) = 29.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32129.3MB, alloc=44.3MB, time=397.84 memory used=32175.7MB, alloc=44.3MB, time=398.42 x[1] = 0.4539 1.588 h = 0.0001 0.004 y2[1] (numeric) = 1.0662831075 2.37215627863 y2[1] (closed_form) = 1.1177326316 2.10738248198 absolute error = 0.2697 relative error = 11.31 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.48148735785 -0.922639337565 y1[1] (closed_form) = 2.29102630078 -1.02813754978 absolute error = 0.2177 relative error = 8.67 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.95 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 = 16.95 Order of pole (three term test) = 29.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32221.7MB, alloc=44.3MB, time=398.98 memory used=32267.9MB, alloc=44.3MB, time=399.54 x[1] = 0.454 1.592 h = 0.003 0.006 y2[1] (numeric) = 1.0735328089 2.38077326291 y2[1] (closed_form) = 1.12208407645 2.11646019845 absolute error = 0.2687 relative error = 11.22 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.49088621925 -0.927156601823 y1[1] (closed_form) = 2.29936198451 -1.03282836853 absolute error = 0.2187 relative error = 8.678 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.12 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 = 10.12 Order of pole (three term test) = 29.17 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32313.7MB, alloc=44.3MB, time=400.10 x[1] = 0.457 1.598 h = 0.0001 0.005 y2[1] (numeric) = 1.08082426967 2.38941197558 y2[1] (closed_form) = 1.13523250029 2.12716622938 absolute error = 0.2678 relative error = 11.11 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.50196523901 -0.940774924485 y1[1] (closed_form) = 2.30870690732 -1.0459657003 absolute error = 0.22 relative error = 8.681 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.556 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 = 4.556 Order of pole (three term test) = 29.17 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32359.5MB, alloc=44.3MB, time=400.66 memory used=32405.8MB, alloc=44.3MB, time=401.22 x[1] = 0.4571 1.603 h = 0.0001 0.003 y2[1] (numeric) = 1.08815802069 2.39807236496 y2[1] (closed_form) = 1.14070847248 2.13863122546 absolute error = 0.2647 relative error = 10.92 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.51382549204 -0.946436736553 y1[1] (closed_form) = 2.31925758243 -1.05186882944 absolute error = 0.2213 relative error = 8.69 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.705 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 = 3.705 Order of pole (three term test) = 29.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32451.7MB, alloc=44.3MB, time=401.79 memory used=32498.1MB, alloc=44.3MB, time=402.36 x[1] = 0.4572 1.606 h = 0.001 0.001 y2[1] (numeric) = 1.09553429037 2.40675459774 y2[1] (closed_form) = 1.14410177957 2.14549309219 absolute error = 0.2657 relative error = 10.93 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.52092354274 -0.949952505547 y1[1] (closed_form) = 2.32556952384 -1.05551024799 absolute error = 0.222 relative error = 8.695 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 2.926 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 = 2.926 Order of pole (three term test) = 29.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32544.2MB, alloc=44.3MB, time=402.93 x[1] = 0.4582 1.607 h = 0.001 0.003 y2[1] (numeric) = 1.1029531271 2.41545875945 y2[1] (closed_form) = 1.14748500526 2.14676200624 absolute error = 0.2724 relative error = 11.19 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.52223540743 -0.953462850558 y1[1] (closed_form) = 2.32656985855 -1.05880216876 absolute error = 0.2222 relative error = 8.693 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.91 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 = 13.91 Order of pole (three term test) = 29.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32590.3MB, alloc=44.3MB, time=403.50 memory used=32636.5MB, alloc=44.3MB, time=404.06 x[1] = 0.4592 1.61 h = 0.0001 0.004 y2[1] (numeric) = 1.11041455162 2.42418485794 y2[1] (closed_form) = 1.15299902511 2.15268806063 absolute error = 0.2748 relative error = 11.25 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.52838818709 -0.959202711403 y1[1] (closed_form) = 2.3318687909 -1.06440261346 absolute error = 0.2229 relative error = 8.696 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.92 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 = 7.92 Order of pole (three term test) = 29.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32682.4MB, alloc=44.3MB, time=404.62 memory used=32728.4MB, alloc=44.3MB, time=405.18 x[1] = 0.4593 1.614 h = 0.003 0.006 y2[1] (numeric) = 1.11791863065 2.4329329256 y2[1] (closed_form) = 1.15749991496 2.16192586907 absolute error = 0.2739 relative error = 11.17 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.53799099901 -0.963902219242 y1[1] (closed_form) = 2.34038248279 -1.06923933502 absolute error = 0.2239 relative error = 8.703 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.58 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 = 10.58 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32774.3MB, alloc=44.3MB, time=405.75 memory used=32820.5MB, alloc=44.3MB, time=406.32 x[1] = 0.4623 1.62 h = 0.0001 0.005 y2[1] (numeric) = 1.12546555594 2.44170302892 y2[1] (closed_form) = 1.17099116495 2.17276876495 absolute error = 0.2728 relative error = 11.05 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.54924983037 -0.977944298679 y1[1] (closed_form) = 2.34989384914 -1.08272679133 absolute error = 0.2252 relative error = 8.705 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.761 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 = 4.761 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32866.3MB, alloc=44.3MB, time=406.88 x[1] = 0.4624 1.625 h = 0.0001 0.003 y2[1] (numeric) = 1.1330558691 2.45049511172 y2[1] (closed_form) = 1.17665553172 2.18443657237 absolute error = 0.2696 relative error = 10.87 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.56136739083 -0.983835193813 y1[1] (closed_form) = 2.36066945821 -1.08881375477 absolute error = 0.2265 relative error = 8.712 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.872 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 = 3.872 Order of pole (three term test) = 29.07 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=32912.3MB, alloc=44.3MB, time=407.44 memory used=32958.5MB, alloc=44.3MB, time=408.00 x[1] = 0.4625 1.628 h = 0.001 0.001 y2[1] (numeric) = 1.14068980438 2.45930934266 y2[1] (closed_form) = 1.18016399027 2.19141917551 absolute error = 0.2708 relative error = 10.88 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.56861840504 -0.987491291446 y1[1] (closed_form) = 2.36711539622 -1.0925677737 absolute error = 0.2273 relative error = 8.717 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.057 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 = 3.057 Order of pole (three term test) = 29.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33004.6MB, alloc=44.3MB, time=408.58 memory used=33051.0MB, alloc=44.3MB, time=409.14 x[1] = 0.4635 1.629 h = 0.001 0.003 y2[1] (numeric) = 1.14836741172 2.46814580875 y2[1] (closed_form) = 1.18362586529 2.19269254182 absolute error = 0.2777 relative error = 11.14 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.5699376058 -0.991099542136 y1[1] (closed_form) = 2.36812555771 -1.09594172432 absolute error = 0.2274 relative error = 8.715 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.54 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 = 14.54 Order of pole (three term test) = 29.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33097.0MB, alloc=44.3MB, time=409.71 memory used=33143.3MB, alloc=44.3MB, time=410.28 x[1] = 0.4645 1.632 h = 0.0001 0.004 y2[1] (numeric) = 1.15608871235 2.47700451786 y2[1] (closed_form) = 1.18929314216 2.19870619901 absolute error = 0.2803 relative error = 11.21 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.57620310131 -0.997028788701 y1[1] (closed_form) = 2.37352619559 -1.10169679566 absolute error = 0.2281 relative error = 8.717 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.277 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 = 8.277 Order of pole (three term test) = 29.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33189.2MB, alloc=44.3MB, time=410.84 x[1] = 0.4646 1.636 h = 0.003 0.006 y2[1] (numeric) = 1.16385377456 2.48588550263 y2[1] (closed_form) = 1.19394768349 2.20810726147 absolute error = 0.2794 relative error = 11.13 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.58601287714 -1.00191680339 y1[1] (closed_form) = 2.38222064922 -1.10668361076 absolute error = 0.2291 relative error = 8.724 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.05 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 = 11.05 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33235.0MB, alloc=44.3MB, time=411.40 memory used=33281.3MB, alloc=44.3MB, time=411.97 x[1] = 0.4676 1.642 h = 0.0001 0.005 y2[1] (numeric) = 1.17166279457 2.49478882968 y2[1] (closed_form) = 1.20779043935 2.21908881943 absolute error = 0.2781 relative error = 11.01 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.59745162519 -1.01639433691 y1[1] (closed_form) = 2.39189965004 -1.12052955906 absolute error = 0.2304 relative error = 8.724 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.975 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 = 4.975 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33327.1MB, alloc=44.3MB, time=412.52 memory used=33373.2MB, alloc=44.3MB, time=413.09 x[1] = 0.4677 1.647 h = 0.0001 0.003 y2[1] (numeric) = 1.1795163249 2.50371443816 y2[1] (closed_form) = 1.21364850434 2.23096343677 absolute error = 0.2749 relative error = 10.82 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.60983031547 -1.02252219106 y1[1] (closed_form) = 2.40290368634 -1.12680564505 absolute error = 0.2317 relative error = 8.731 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.046 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 = 4.046 Order of pole (three term test) = 29.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33419.2MB, alloc=44.3MB, time=413.66 x[1] = 0.4678 1.65 h = 0.001 0.001 y2[1] (numeric) = 1.18741460577 2.51266249875 y2[1] (closed_form) = 1.21727534242 2.23806914163 absolute error = 0.2762 relative error = 10.84 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.61723652907 -1.02632339492 y1[1] (closed_form) = 2.40948568428 -1.13067547922 absolute error = 0.2325 relative error = 8.735 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.195 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 = 3.195 Order of pole (three term test) = 28.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33465.3MB, alloc=44.3MB, time=414.22 memory used=33511.7MB, alloc=44.3MB, time=414.79 x[1] = 0.4688 1.651 h = 0.001 0.003 y2[1] (numeric) = 1.19535768873 2.52163309992 y2[1] (closed_form) = 1.22081774208 2.23934673338 absolute error = 0.2834 relative error = 11.11 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.61856229258 -1.03003192325 y1[1] (closed_form) = 2.41050534625 -1.13413323353 absolute error = 0.2326 relative error = 8.733 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.19 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 = 15.19 Order of pole (three term test) = 29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33557.6MB, alloc=44.3MB, time=415.35 memory used=33603.9MB, alloc=44.3MB, time=415.92 x[1] = 0.4698 1.654 h = 0.0001 0.004 y2[1] (numeric) = 1.2033455955 2.5306262496 y2[1] (closed_form) = 1.2266422623 2.24544941343 absolute error = 0.2861 relative error = 11.18 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.62494132806 -1.03615609476 y1[1] (closed_form) = 2.41600880976 -1.14004681492 absolute error = 0.2333 relative error = 8.734 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.649 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 = 8.649 Order of pole (three term test) = 28.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33649.7MB, alloc=44.3MB, time=416.49 memory used=33695.8MB, alloc=44.3MB, time=417.05 x[1] = 0.4699 1.658 h = 0.003 0.006 y2[1] (numeric) = 1.21137839602 2.53964198064 y2[1] (closed_form) = 1.23145476971 2.25501693053 absolute error = 0.2853 relative error = 11.11 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.63496112115 -1.04123904099 y1[1] (closed_form) = 2.4248868261 -1.14518802485 absolute error = 0.2344 relative error = 8.74 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.55 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 = 11.55 Order of pole (three term test) = 28.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33741.6MB, alloc=44.3MB, time=417.61 x[1] = 0.4729 1.664 h = 0.0001 0.005 y2[1] (numeric) = 1.21945629103 2.54868035982 y2[1] (closed_form) = 1.24565790377 2.26613892894 absolute error = 0.2838 relative error = 10.97 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.64657983618 -1.05616400022 y1[1] (closed_form) = 2.43473464515 -1.15940103514 absolute error = 0.2357 relative error = 8.739 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.199 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 = 5.199 Order of pole (three term test) = 28.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33787.6MB, alloc=44.3MB, time=418.17 memory used=33833.7MB, alloc=44.3MB, time=418.73 x[1] = 0.473 1.669 h = 0.0001 0.003 y2[1] (numeric) = 1.22757984421 2.55774132143 y2[1] (closed_form) = 1.25171510718 2.27822440391 absolute error = 0.2806 relative error = 10.79 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.65922352953 -1.06253689236 y1[1] (closed_form) = 2.44597066198 -1.16587167142 absolute error = 0.237 relative error = 8.746 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.228 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 = 4.228 Order of pole (three term test) = 28.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33879.6MB, alloc=44.3MB, time=419.29 memory used=33926.0MB, alloc=44.3MB, time=419.87 x[1] = 0.4731 1.672 h = 0.001 0.001 y2[1] (numeric) = 1.23574930191 2.56682503817 y2[1] (closed_form) = 1.25546363553 2.28545560429 absolute error = 0.2821 relative error = 10.82 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.66678720728 -1.06648810272 y1[1] (closed_form) = 2.45269081822 -1.16986062021 absolute error = 0.2377 relative error = 8.749 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.338 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 = 3.338 Order of pole (three term test) = 28.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=33972.0MB, alloc=44.3MB, time=420.44 x[1] = 0.4741 1.673 h = 0.001 0.003 y2[1] (numeric) = 1.24396471734 2.57593160007 y2[1] (closed_form) = 1.25908847285 2.28673717781 absolute error = 0.2896 relative error = 11.09 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.66811873052 -1.07029933231 y1[1] (closed_form) = 2.45371963914 -1.17340399249 absolute error = 0.2379 relative error = 8.747 % Correct digits = 1 memory used=34018.3MB, alloc=44.3MB, time=421.01 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.88 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 = 15.88 Order of pole (three term test) = 28.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34064.3MB, alloc=44.3MB, time=421.57 x[1] = 0.4751 1.676 h = 0.0001 0.004 y2[1] (numeric) = 1.25222611273 2.58506101504 y2[1] (closed_form) = 1.26507431519 2.29293030469 absolute error = 0.2924 relative error = 11.17 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.67461212215 -1.07662410146 y1[1] (closed_form) = 2.45932705827 -1.17948006356 absolute error = 0.2386 relative error = 8.748 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.038 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 = 9.038 Order of pole (three term test) = 28.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34110.1MB, alloc=44.3MB, time=422.13 memory used=34156.2MB, alloc=44.3MB, time=422.69 x[1] = 0.4752 1.68 h = 0.003 0.006 y2[1] (numeric) = 1.26053355967 2.59421331621 y2[1] (closed_form) = 1.27004921414 2.30266751613 absolute error = 0.2917 relative error = 11.09 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.68484502556 -1.08190856896 y1[1] (closed_form) = 2.46839148601 -1.18478008284 absolute error = 0.2397 relative error = 8.753 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.07 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 = 12.07 Order of pole (three term test) = 28.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34201.9MB, alloc=44.3MB, time=423.26 memory used=34248.2MB, alloc=44.3MB, time=423.83 x[1] = 0.4782 1.686 h = 0.0001 0.005 y2[1] (numeric) = 1.26888726356 2.60338857044 y2[1] (closed_form) = 1.28462179578 2.31393171334 absolute error = 0.2899 relative error = 10.95 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.69664370017 -1.09729320527 y1[1] (closed_form) = 2.47840929841 -1.19936893184 absolute error = 0.2409 relative error = 8.75 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.433 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 = 5.433 Order of pole (three term test) = 28.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34294.2MB, alloc=44.3MB, time=424.39 x[1] = 0.4783 1.691 h = 0.0001 0.003 y2[1] (numeric) = 1.27728779949 2.61258670704 y2[1] (closed_form) = 1.29088371777 2.32623214333 absolute error = 0.2867 relative error = 10.78 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.70955632044 -1.1039194219 y1[1] (closed_form) = 2.48988090945 -1.20603968896 absolute error = 0.2423 relative error = 8.756 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.418 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 = 4.418 Order of pole (three term test) = 28.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34340.1MB, alloc=44.3MB, time=424.95 memory used=34386.5MB, alloc=44.3MB, time=425.52 x[1] = 0.4784 1.694 h = 0.001 0.001 y2[1] (numeric) = 1.28573542007 2.62180790076 y2[1] (closed_form) = 1.29475733186 2.33359126187 absolute error = 0.2884 relative error = 10.81 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.7172797558 -1.10802566449 y1[1] (closed_form) = 2.49674135757 -1.21015113829 absolute error = 0.243 relative error = 8.759 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.489 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 = 3.489 Order of pole (three term test) = 28.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34432.6MB, alloc=44.3MB, time=426.09 memory used=34479.1MB, alloc=44.3MB, time=426.66 x[1] = 0.4794 1.695 h = 0.0001 0.004 y2[1] (numeric) = 1.29423018021 2.63105224317 y2[1] (closed_form) = 1.29846655837 2.3348765561 absolute error = 0.2962 relative error = 11.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.71861620508 -1.1119420715 y1[1] (closed_form) = 2.49777898014 -1.21378198397 absolute error = 0.2432 relative error = 8.757 % Correct digits = 1 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) = 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 = 20.99 Order of pole (three term test) = 28.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34525.0MB, alloc=44.3MB, time=427.22 memory used=34571.1MB, alloc=44.3MB, time=427.78 x[1] = 0.4795 1.699 h = 0.003 0.006 y2[1] (numeric) = 1.30277210313 2.6403197656 y2[1] (closed_form) = 1.30358279433 2.34476446742 absolute error = 0.2956 relative error = 11.02 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.72902909163 -1.11739962875 y1[1] (closed_form) = 2.50700814778 -1.21922005686 absolute error = 0.2443 relative error = 8.762 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.54 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 = 12.54 Order of pole (three term test) = 28.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34617.0MB, alloc=44.3MB, time=428.34 x[1] = 0.4825 1.705 h = 0.0001 0.005 y2[1] (numeric) = 1.31136138419 2.64961053149 y2[1] (closed_form) = 1.31847907848 2.35615700801 absolute error = 0.2935 relative error = 10.87 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.7409776826 -1.13317689503 y1[1] (closed_form) = 2.51717784127 -1.23413756062 absolute error = 0.2455 relative error = 8.758 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.643 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 = 5.643 Order of pole (three term test) = 28.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34662.8MB, alloc=44.3MB, time=428.90 memory used=34709.1MB, alloc=44.3MB, time=429.47 x[1] = 0.4826 1.71 h = 0.0001 0.003 y2[1] (numeric) = 1.31999860857 2.65892446582 y2[1] (closed_form) = 1.3249191654 2.3686483153 absolute error = 0.2903 relative error = 10.7 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.75411744282 -1.14002070152 y1[1] (closed_form) = 2.52885766091 -1.24098228127 absolute error = 0.2469 relative error = 8.763 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.589 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 = 4.589 Order of pole (three term test) = 28.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34755.1MB, alloc=44.3MB, time=430.03 memory used=34801.5MB, alloc=44.3MB, time=430.60 x[1] = 0.4827 1.713 h = 0.001 0.001 y2[1] (numeric) = 1.32868403436 2.66826174519 y2[1] (closed_form) = 1.32890167083 2.37612105044 absolute error = 0.2921 relative error = 10.73 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.76197578255 -1.14426007253 y1[1] (closed_form) = 2.5358421189 -1.24520024748 absolute error = 0.2476 relative error = 8.766 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.624 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 = 3.624 Order of pole (three term test) = 28.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34847.5MB, alloc=44.3MB, time=431.17 x[1] = 0.4837 1.714 h = 0.001 0.003 y2[1] (numeric) = 1.33741771798 2.67762246256 y2[1] (closed_form) = 1.33268508975 2.37741036215 absolute error = 0.3002 relative error = 11.02 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.76331567585 -1.14826605954 y1[1] (closed_form) = 2.53688809184 -1.24890780639 absolute error = 0.2478 relative error = 8.763 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.23 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 = 17.23 Order of pole (three term test) = 28.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34893.8MB, alloc=44.3MB, time=431.73 memory used=34939.9MB, alloc=44.3MB, time=432.30 x[1] = 0.4847 1.717 h = 0.0001 0.004 y2[1] (numeric) = 1.3461996826 2.68700662588 y2[1] (closed_form) = 1.33898117898 2.3837776324 absolute error = 0.3033 relative error = 11.09 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.77002080894 -1.15497378615 y1[1] (closed_form) = 2.54269404002 -1.25529589263 absolute error = 0.2485 relative error = 8.763 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.81 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 = 9.81 Order of pole (three term test) = 28.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=34985.7MB, alloc=44.3MB, time=432.86 memory used=35031.9MB, alloc=44.3MB, time=433.42 x[1] = 0.4848 1.721 h = 0.003 0.006 y2[1] (numeric) = 1.35503000307 2.69641426875 y2[1] (closed_form) = 1.34426830603 2.39384142778 absolute error = 0.3028 relative error = 11.03 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.78065258181 -1.16064540024 y1[1] (closed_form) = 2.55211510349 -1.26090126446 absolute error = 0.2496 relative error = 8.767 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.1 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 = 13.1 Order of pole (three term test) = 28.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35077.8MB, alloc=44.3MB, time=433.98 memory used=35123.9MB, alloc=44.3MB, time=434.55 x[1] = 0.4878 1.727 h = 0.0001 0.005 y2[1] (numeric) = 1.36390889368 2.70584545825 y2[1] (closed_form) = 1.35955143354 2.40537949502 absolute error = 0.3005 relative error = 10.88 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.79278095311 -1.17690557621 y1[1] (closed_form) = 2.56245705931 -1.27621148959 absolute error = 0.2508 relative error = 8.762 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.897 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 = 5.897 Order of pole (three term test) = 28.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35169.8MB, alloc=44.3MB, time=435.11 x[1] = 0.4879 1.732 h = 0.0001 0.003 y2[1] (numeric) = 1.37283695149 2.71530011409 y2[1] (closed_form) = 1.36620695678 2.4180935864 absolute error = 0.2973 relative error = 10.7 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.80619697036 -1.18401847734 y1[1] (closed_form) = 2.57437942985 -1.28326704353 absolute error = 0.2522 relative error = 8.767 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.795 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 = 4.795 Order of pole (three term test) = 28.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35215.7MB, alloc=44.3MB, time=435.67 memory used=35261.9MB, alloc=44.3MB, time=436.24 x[1] = 0.488 1.735 h = 0.001 0.001 y2[1] (numeric) = 1.38181444117 2.72477841495 y2[1] (closed_form) = 1.3703210693 2.42569886843 absolute error = 0.2993 relative error = 10.74 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.81421935006 -1.18842244579 y1[1] (closed_form) = 2.58150828701 -1.28761402158 absolute error = 0.253 relative error = 8.769 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.787 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 = 3.787 Order of pole (three term test) = 28.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35307.9MB, alloc=44.3MB, time=436.81 memory used=35354.3MB, alloc=44.3MB, time=437.38 x[1] = 0.489 1.736 h = 0.001 0.003 y2[1] (numeric) = 1.39084142091 2.7342804554 y2[1] (closed_form) = 1.37419261774 2.42699139108 absolute error = 0.3077 relative error = 11.03 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.81556255371 -1.19253829705 y1[1] (closed_form) = 2.58256237593 -1.29141262338 absolute error = 0.2531 relative error = 8.766 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.01 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 = 18.01 Order of pole (three term test) = 28.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35400.2MB, alloc=44.3MB, time=437.94 memory used=35446.5MB, alloc=44.3MB, time=438.51 x[1] = 0.49 1.739 h = 0.0001 0.004 y2[1] (numeric) = 1.39991791443 2.74380624342 y2[1] (closed_form) = 1.3806622108 2.43345325312 absolute error = 0.3109 relative error = 11.11 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.82238430228 -1.19946346504 y1[1] (closed_form) = 2.58847561482 -1.29797512061 absolute error = 0.2538 relative error = 8.765 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.25 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 = 10.25 Order of pole (three term test) = 28.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35492.4MB, alloc=44.3MB, time=439.07 x[1] = 0.4901 1.743 h = 0.003 0.006 y2[1] (numeric) = 1.40904399838 2.75335581284 y2[1] (closed_form) = 1.38612498653 2.44369628781 absolute error = 0.3105 relative error = 11.05 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.83323817077 -1.20535623022 y1[1] (closed_form) = 2.59809156211 -1.30375254414 absolute error = 0.2549 relative error = 8.769 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.69 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 = 13.69 Order of pole (three term test) = 28.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35538.1MB, alloc=44.3MB, time=439.62 memory used=35584.4MB, alloc=44.3MB, time=440.19 x[1] = 0.4931 1.749 h = 0.0001 0.005 y2[1] (numeric) = 1.418219892 2.76292923078 y2[1] (closed_form) = 1.40180461621 2.45538157787 absolute error = 0.308 relative error = 10.89 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.84554613069 -1.22211241846 y1[1] (closed_form) = 2.60860692478 -1.31946488285 absolute error = 0.2562 relative error = 8.763 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.162 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 = 6.162 Order of pole (three term test) = 28.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35630.2MB, alloc=44.3MB, time=440.75 memory used=35676.4MB, alloc=44.3MB, time=441.32 x[1] = 0.4932 1.754 h = 0.0001 0.003 y2[1] (numeric) = 1.42744620446 2.77252641149 y2[1] (closed_form) = 1.40868157531 2.46832269779 absolute error = 0.3048 relative error = 10.72 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.85924247699 -1.22950333519 y1[1] (closed_form) = 2.62077563643 -1.32673726738 absolute error = 0.2575 relative error = 8.767 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.011 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 = 5.011 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35722.3MB, alloc=44.3MB, time=441.88 x[1] = 0.4933 1.757 h = 0.001 0.001 y2[1] (numeric) = 1.43672320719 2.78214753576 y2[1] (closed_form) = 1.41293094433 2.47606303465 absolute error = 0.307 relative error = 10.77 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.86743127386 -1.23407731012 y1[1] (closed_form) = 2.62805112917 -1.33121690173 absolute error = 0.2583 relative error = 8.769 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 3.957 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 = 3.957 Order of pole (three term test) = 28.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35768.5MB, alloc=44.3MB, time=442.45 memory used=35814.6MB, alloc=44.3MB, time=443.02 x[1] = 0.4943 1.758 h = 0.001 0.003 y2[1] (numeric) = 1.44605096019 2.79179269978 y2[1] (closed_form) = 1.41689268886 2.47735845462 absolute error = 0.3158 relative error = 11.06 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.86877685912 -1.23830566109 y1[1] (closed_form) = 2.62911292875 -1.33510852412 absolute error = 0.2585 relative error = 8.766 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.82 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 = 18.82 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35860.5MB, alloc=44.3MB, time=443.58 memory used=35906.7MB, alloc=44.3MB, time=444.14 x[1] = 0.4953 1.761 h = 0.0001 0.004 y2[1] (numeric) = 1.45542948774 2.80146191155 y2[1] (closed_form) = 1.42354024241 2.48391634574 absolute error = 0.3191 relative error = 11.15 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.87571599903 -1.24545449436 y1[1] (closed_form) = 2.63513462384 -1.34184980341 absolute error = 0.2592 relative error = 8.764 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.71 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 = 10.71 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=35952.6MB, alloc=44.3MB, time=444.71 memory used=35998.8MB, alloc=44.3MB, time=445.28 x[1] = 0.4954 1.765 h = 0.003 0.006 y2[1] (numeric) = 1.46485886832 2.81115520514 y2[1] (closed_form) = 1.42918354627 2.49434201576 absolute error = 0.3188 relative error = 11.09 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.88679521123 -1.25157568476 y1[1] (closed_form) = 2.64494849169 -1.34780415531 absolute error = 0.2603 relative error = 8.768 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.31 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 = 14.31 Order of pole (three term test) = 28.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36044.7MB, alloc=44.3MB, time=445.84 x[1] = 0.4984 1.771 h = 0.0001 0.005 y2[1] (numeric) = 1.47433932626 2.82087264771 y2[1] (closed_form) = 1.44526955204 2.50617619947 absolute error = 0.316 relative error = 10.92 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.89928249829 -1.26884128941 y1[1] (closed_form) = 2.65563839101 -1.36392822358 absolute error = 0.2615 relative error = 8.761 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.439 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 = 6.439 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36090.5MB, alloc=44.3MB, time=446.39 memory used=36136.7MB, alloc=44.3MB, time=446.96 x[1] = 0.4985 1.776 h = 0.0001 0.003 y2[1] (numeric) = 1.4838714831 2.83061414784 y2[1] (closed_form) = 1.45237410047 2.51934864425 absolute error = 0.3129 relative error = 10.76 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.91326329512 -1.27651936895 y1[1] (closed_form) = 2.6680572957 -1.37142359231 absolute error = 0.2629 relative error = 8.765 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.236 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 = 5.236 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36182.5MB, alloc=44.3MB, time=447.52 memory used=36228.8MB, alloc=44.3MB, time=448.09 x[1] = 0.4986 1.779 h = 0.001 0.001 y2[1] (numeric) = 1.49345561717 2.84037988845 y2[1] (closed_form) = 1.45676246856 2.5272265739 absolute error = 0.3153 relative error = 10.81 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.92162091418 -1.28126889609 y1[1] (closed_form) = 2.67548169637 -1.3760396221 absolute error = 0.2638 relative error = 8.767 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.135 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 = 4.135 Order of pole (three term test) = 28.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36274.8MB, alloc=44.3MB, time=448.66 x[1] = 0.4996 1.78 h = 0.001 0.003 y2[1] (numeric) = 1.50309179034 2.85016996738 y2[1] (closed_form) = 1.46081651754 2.52852455786 absolute error = 0.3244 relative error = 11.11 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 2.92296791771 -1.28561243835 y1[1] (closed_form) = 2.67655078311 -1.38002628698 absolute error = 0.2639 relative error = 8.763 % Correct digits = 1 memory used=36321.3MB, alloc=44.3MB, time=449.24 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.66 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 = 19.66 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36367.2MB, alloc=44.3MB, time=449.80 x[1] = 0.5006 1.783 h = 0.0001 0.004 y2[1] (numeric) = 1.51278002748 2.85998439268 y2[1] (closed_form) = 1.46764659177 2.53517991762 absolute error = 0.3279 relative error = 11.19 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.93002521159 -1.29299130821 y1[1] (closed_form) = 2.68268210764 -1.3869508262 absolute error = 0.2646 relative error = 8.761 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.19 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 = 11.19 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36413.2MB, alloc=44.3MB, time=450.36 memory used=36459.4MB, alloc=44.3MB, time=450.92 x[1] = 0.5007 1.787 h = 0.003 0.006 y2[1] (numeric) = 1.52252040893 2.86982319862 y2[1] (closed_form) = 1.47347542812 2.54579166015 absolute error = 0.3277 relative error = 11.14 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.94133305404 -1.29934838186 y1[1] (closed_form) = 2.69269698176 -1.39308710997 absolute error = 0.2657 relative error = 8.765 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.95 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 = 14.95 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36505.3MB, alloc=44.3MB, time=451.49 memory used=36551.6MB, alloc=44.3MB, time=452.06 x[1] = 0.5037 1.793 h = 0.0001 0.005 y2[1] (numeric) = 1.53231316423 2.87968645239 y2[1] (closed_form) = 1.48997790389 2.55777638144 absolute error = 0.3247 relative error = 10.97 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 2.95399933361 -1.31713711462 y1[1] (closed_form) = 2.70356253107 -1.40963275221 absolute error = 0.267 relative error = 8.756 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.728 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 = 6.728 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36597.4MB, alloc=44.3MB, time=452.62 x[1] = 0.5038 1.798 h = 0.0001 0.003 y2[1] (numeric) = 1.54215892754 2.88957405671 y2[1] (closed_form) = 1.49731635283 2.5711844998 absolute error = 0.3215 relative error = 10.81 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 2.96826875155 -1.32511173549 y1[1] (closed_form) = 2.71623554282 -1.41735741875 absolute error = 0.2684 relative error = 8.76 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.472 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 = 5.472 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36643.5MB, alloc=44.3MB, time=453.18 memory used=36689.7MB, alloc=44.3MB, time=453.76 x[1] = 0.5039 1.801 h = 0.001 0.001 y2[1] (numeric) = 1.55205798427 2.89948619665 y2[1] (closed_form) = 1.50184755801 2.57920259052 absolute error = 0.3242 relative error = 10.86 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 2.97679762538 -1.33004250033 y1[1] (closed_form) = 2.72381115982 -1.42211368003 absolute error = 0.2692 relative error = 8.762 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.321 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 = 4.321 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36735.8MB, alloc=44.3MB, time=454.33 memory used=36782.1MB, alloc=44.3MB, time=454.90 x[1] = 0.5049 1.802 h = 0.0001 0.004 y2[1] (numeric) = 1.56201039822 2.90942297176 y2[1] (closed_form) = 1.50599606249 2.58050278477 absolute error = 0.3337 relative error = 11.17 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 2.97814504817 -1.33450398261 y1[1] (closed_form) = 2.72488709138 -1.42619745435 absolute error = 0.2693 relative error = 8.758 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26 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 = 26 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36828.0MB, alloc=44.3MB, time=455.46 memory used=36874.1MB, alloc=44.3MB, time=456.02 x[1] = 0.505 1.806 h = 0.003 0.006 y2[1] (numeric) = 1.57201619613 2.91938441596 y2[1] (closed_form) = 1.51198643104 2.59127977001 absolute error = 0.3336 relative error = 11.12 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 2.98964595382 -1.34106345815 y1[1] (closed_form) = 2.7350797442 -1.4324919994 absolute error = 0.2705 relative error = 8.761 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.53 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 = 15.53 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36920.1MB, alloc=44.3MB, time=456.58 x[1] = 0.508 1.812 h = 0.0001 0.005 y2[1] (numeric) = 1.58207559638 2.92937059302 y2[1] (closed_form) = 1.52885382557 2.60340049252 absolute error = 0.3303 relative error = 10.94 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.0024610823 -1.35929883292 y1[1] (closed_form) = 2.74610255054 -1.44940646943 absolute error = 0.2717 relative error = 8.751 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.989 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 = 6.989 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=36965.9MB, alloc=44.3MB, time=457.14 memory used=37012.1MB, alloc=44.3MB, time=457.70 x[1] = 0.5081 1.817 h = 0.0001 0.003 y2[1] (numeric) = 1.5921892443 2.93938140058 y2[1] (closed_form) = 1.53639590654 2.61701788508 absolute error = 0.3272 relative error = 10.78 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.0169742392 -1.36752790972 y1[1] (closed_form) = 2.7590003078 -1.45733059711 absolute error = 0.2732 relative error = 8.754 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.683 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 = 5.683 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37058.1MB, alloc=44.3MB, time=458.27 memory used=37104.6MB, alloc=44.3MB, time=458.85 x[1] = 0.5082 1.82 h = 0.001 0.001 y2[1] (numeric) = 1.60235743148 2.94941702565 y2[1] (closed_form) = 1.54105149735 2.62516046725 absolute error = 0.33 relative error = 10.84 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.02564770374 -1.3726141558 y1[1] (closed_form) = 2.76670969743 -1.46220887309 absolute error = 0.274 relative error = 8.756 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.488 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 = 4.488 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37150.6MB, alloc=44.3MB, time=459.41 x[1] = 0.5092 1.821 h = 0.001 0.003 y2[1] (numeric) = 1.61258022342 2.9594775693 y2[1] (closed_form) = 1.54528304152 2.62646342561 absolute error = 0.3397 relative error = 11.15 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.02699468469 -1.3771760653 y1[1] (closed_form) = 2.7677923428 -1.46637785212 absolute error = 0.2741 relative error = 8.752 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.34 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 = 21.34 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37196.9MB, alloc=44.3MB, time=459.98 memory used=37242.9MB, alloc=44.3MB, time=460.54 x[1] = 0.5102 1.824 h = 0.0001 0.004 y2[1] (numeric) = 1.62285764607 2.96956303958 y2[1] (closed_form) = 1.55246404434 2.63330629674 absolute error = 0.3435 relative error = 11.24 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.03427052499 -1.38499372666 y1[1] (closed_form) = 2.77413312325 -1.47365434959 absolute error = 0.2748 relative error = 8.749 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.15 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 = 12.15 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37288.9MB, alloc=44.3MB, time=461.10 memory used=37335.1MB, alloc=44.3MB, time=461.67 x[1] = 0.5103 1.828 h = 0.003 0.006 y2[1] (numeric) = 1.63318978338 2.97967347122 y2[1] (closed_form) = 1.55864955826 2.64427592448 absolute error = 0.3436 relative error = 11.19 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.04600618775 -1.39180326488 y1[1] (closed_form) = 2.78453271859 -1.48014044657 absolute error = 0.276 relative error = 8.752 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.23 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 = 16.23 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37380.8MB, alloc=44.3MB, time=462.22 memory used=37427.1MB, alloc=44.3MB, time=462.79 x[1] = 0.5133 1.834 h = 0.0001 0.005 y2[1] (numeric) = 1.64357687488 2.98980893144 y2[1] (closed_form) = 1.57595278916 2.65655029309 absolute error = 0.3401 relative error = 11.01 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.05899948631 -1.41058775459 y1[1] (closed_form) = 2.79573332059 -1.49749542029 absolute error = 0.2772 relative error = 8.742 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.303 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 = 7.303 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37473.0MB, alloc=44.3MB, time=463.36 x[1] = 0.5134 1.839 h = 0.0001 0.003 y2[1] (numeric) = 1.65401957905 2.99996931171 y2[1] (closed_form) = 1.5837408941 2.67041167214 absolute error = 0.337 relative error = 10.85 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.07380904215 -1.41913121116 y1[1] (closed_form) = 2.80889271409 -1.5056609845 absolute error = 0.2787 relative error = 8.745 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.939 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 = 5.939 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37519.0MB, alloc=44.3MB, time=463.92 memory used=37565.2MB, alloc=44.3MB, time=464.49 x[1] = 0.5135 1.842 h = 0.001 0.001 y2[1] (numeric) = 1.66451819487 3.01015480125 y2[1] (closed_form) = 1.58854669439 2.67869932449 absolute error = 0.3401 relative error = 10.92 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.0826582956 -1.42440950983 y1[1] (closed_form) = 2.81675776056 -1.51068686727 absolute error = 0.2795 relative error = 8.746 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.69 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 = 4.69 Order of pole (three term test) = 28.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37611.2MB, alloc=44.3MB, time=465.10 memory used=37657.4MB, alloc=44.3MB, time=465.67 x[1] = 0.5145 1.843 h = 0.001 0.003 y2[1] (numeric) = 1.67507278988 3.02036550284 y2[1] (closed_form) = 1.59287681815 2.68000380539 absolute error = 0.3501 relative error = 11.23 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.08400376283 -1.4290945587 y1[1] (closed_form) = 2.81784640109 -1.51495693041 absolute error = 0.2797 relative error = 8.741 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.3 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 = 22.3 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37703.3MB, alloc=44.3MB, time=466.24 memory used=37749.6MB, alloc=44.3MB, time=466.80 x[1] = 0.5155 1.846 h = 0.0001 0.004 y2[1] (numeric) = 1.68568339062 3.03060142457 y2[1] (closed_form) = 1.60025396363 2.68694833093 absolute error = 0.3541 relative error = 11.32 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.09139983349 -1.43716116033 y1[1] (closed_form) = 2.82430026333 -1.52243009444 absolute error = 0.2804 relative error = 8.739 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.7 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 = 12.7 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37795.4MB, alloc=44.3MB, time=467.36 x[1] = 0.5156 1.85 h = 0.003 0.006 y2[1] (numeric) = 1.69635008308 3.04086260137 y2[1] (closed_form) = 1.60664000133 2.69811415991 absolute error = 0.3543 relative error = 11.28 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.1033736519 -1.44422878155 y1[1] (closed_form) = 2.83491002992 -1.52911312588 absolute error = 0.2816 relative error = 8.741 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.96 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 = 16.96 Order of pole (three term test) = 28.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37841.1MB, alloc=44.3MB, time=467.92 memory used=37887.3MB, alloc=44.3MB, time=468.48 x[1] = 0.5186 1.856 h = 0.0001 0.005 y2[1] (numeric) = 1.70707311231 3.05114910043 y2[1] (closed_form) = 1.62438982014 2.71054373536 absolute error = 0.3505 relative error = 11.09 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.11654455375 -1.46357703404 y1[1] (closed_form) = 2.84628948669 -1.54691912799 absolute error = 0.2828 relative error = 8.73 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.632 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 = 7.632 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=37933.3MB, alloc=44.3MB, time=469.05 memory used=37979.5MB, alloc=44.3MB, time=469.61 x[1] = 0.5187 1.861 h = 0.0001 0.003 y2[1] (numeric) = 1.7178531502 3.06146080681 y2[1] (closed_form) = 1.63243073254 2.72465360429 absolute error = 0.3475 relative error = 10.94 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.13165482215 -1.47244495614 y1[1] (closed_form) = 2.85971461176 -1.5553329206 absolute error = 0.2843 relative error = 8.733 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.206 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 = 6.206 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38025.5MB, alloc=44.3MB, time=470.18 x[1] = 0.5188 1.864 h = 0.001 0.001 y2[1] (numeric) = 1.72869050333 3.07179791189 y2[1] (closed_form) = 1.63739086621 2.73308898455 absolute error = 0.3508 relative error = 11.01 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.14068237716 -1.47792142 y1[1] (closed_form) = 2.86773772881 -1.56051053584 absolute error = 0.2852 relative error = 8.734 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 4.901 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 = 4.901 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38071.8MB, alloc=44.3MB, time=470.75 memory used=38117.9MB, alloc=44.3MB, time=471.32 x[1] = 0.5198 1.865 h = 0.001 0.003 y2[1] (numeric) = 1.73958524131 3.08216052027 y2[1] (closed_form) = 1.641821848 2.73439457288 absolute error = 0.3612 relative error = 11.33 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.14202522116 -1.48273253018 y1[1] (closed_form) = 2.86883186496 -1.5648838838 absolute error = 0.2853 relative error = 8.73 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.31 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 = 23.31 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38163.9MB, alloc=44.3MB, time=471.88 memory used=38210.2MB, alloc=44.3MB, time=472.44 x[1] = 0.5208 1.868 h = 0.0001 0.004 y2[1] (numeric) = 1.7505373913 3.09254864003 y2[1] (closed_form) = 1.64940011912 2.74144219853 absolute error = 0.3654 relative error = 11.42 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.14954222199 -1.49105505222 y1[1] (closed_form) = 2.87540000859 -1.57255862673 absolute error = 0.286 relative error = 8.727 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.27 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 = 13.27 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38256.0MB, alloc=44.3MB, time=473.00 memory used=38302.1MB, alloc=44.3MB, time=473.57 x[1] = 0.5209 1.872 h = 0.003 0.006 y2[1] (numeric) = 1.76154704135 3.10296230634 y2[1] (closed_form) = 1.65599219623 2.75280783015 absolute error = 0.3657 relative error = 11.38 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.16175763161 -1.49838897723 y1[1] (closed_form) = 2.88622322507 -1.57944411397 absolute error = 0.2872 relative error = 8.729 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.72 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 = 17.72 Order of pole (three term test) = 28.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38348.1MB, alloc=44.3MB, time=474.13 x[1] = 0.5239 1.878 h = 0.0001 0.005 y2[1] (numeric) = 1.77261444218 3.11340158628 y2[1] (closed_form) = 1.67419959429 2.7653941398 absolute error = 0.3617 relative error = 11.19 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.17510548281 -1.5183159721 y1[1] (closed_form) = 2.89778257209 -1.59771191652 absolute error = 0.2885 relative error = 8.717 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.975 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 = 7.975 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38394.0MB, alloc=44.3MB, time=474.69 memory used=38440.3MB, alloc=44.3MB, time=475.25 x[1] = 0.524 1.883 h = 0.0001 0.003 y2[1] (numeric) = 1.78374027938 3.1238663583 y2[1] (closed_form) = 1.68250027086 2.77975705634 absolute error = 0.3587 relative error = 11.04 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.19052082478 -1.52751869764 y1[1] (closed_form) = 2.91147758729 -1.60638090454 absolute error = 0.29 relative error = 8.72 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.485 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 = 6.485 Order of pole (three term test) = 28.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38486.3MB, alloc=44.3MB, time=475.82 memory used=38532.6MB, alloc=44.3MB, time=476.39 x[1] = 0.5241 1.886 h = 0.001 0.001 y2[1] (numeric) = 1.79492486728 3.134356816 y2[1] (closed_form) = 1.68761896662 2.78834285361 absolute error = 0.3623 relative error = 11.12 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.19972922033 -1.5331995916 y1[1] (closed_form) = 2.91966122533 -1.61171448399 absolute error = 0.2909 relative error = 8.722 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.121 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 = 5.121 Order of pole (three term test) = 28.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38578.6MB, alloc=44.3MB, time=476.95 x[1] = 0.5251 1.887 h = 0.001 0.003 y2[1] (numeric) = 1.80616827764 3.1448730658 y2[1] (closed_form) = 1.69215313111 2.78964911122 absolute error = 0.3731 relative error = 11.43 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.20106829145 -1.53813974606 y1[1] (closed_form) = 2.92076033601 -1.61619336584 absolute error = 0.291 relative error = 8.717 % Correct digits = 1 memory used=38625.0MB, alloc=44.3MB, time=477.52 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.35 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 = 24.35 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38670.9MB, alloc=44.3MB, time=478.08 x[1] = 0.5261 1.89 h = 0.0001 0.004 y2[1] (numeric) = 1.81747053825 3.15541511577 y2[1] (closed_form) = 1.69993762662 2.79680128276 absolute error = 0.3774 relative error = 11.53 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.20870690277 -1.54672533151 y1[1] (closed_form) = 2.9274439657 -1.62407471858 absolute error = 0.2917 relative error = 8.713 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.86 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 = 13.86 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38716.9MB, alloc=44.3MB, time=478.64 memory used=38763.0MB, alloc=44.3MB, time=479.21 x[1] = 0.5262 1.894 h = 0.003 0.006 y2[1] (numeric) = 1.82883173927 3.16598300129 y2[1] (closed_form) = 1.70674139927 2.8083703615 absolute error = 0.3779 relative error = 11.5 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.22116737575 -1.55433398608 y1[1] (closed_form) = 2.9384839608 -1.63116832502 absolute error = 0.2929 relative error = 8.716 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.52 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 = 18.52 Order of pole (three term test) = 28.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38808.9MB, alloc=44.3MB, time=479.76 memory used=38855.2MB, alloc=44.3MB, time=480.34 x[1] = 0.5292 1.9 h = 0.0001 0.005 y2[1] (numeric) = 1.8402521372 3.17657678935 y2[1] (closed_form) = 1.7254176131 2.82111489744 absolute error = 0.3736 relative error = 11.3 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.23469143128 -1.57485504118 y1[1] (closed_form) = 2.95022420787 -1.64990895256 absolute error = 0.2942 relative error = 8.704 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.333 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 = 8.333 Order of pole (three term test) = 28.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38901.2MB, alloc=44.3MB, time=480.90 x[1] = 0.5293 1.905 h = 0.0001 0.003 y2[1] (numeric) = 1.85173243164 3.18719635156 y2[1] (closed_form) = 1.733985188 2.8357354741 absolute error = 0.3707 relative error = 11.15 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.25041625464 -1.58440316598 y1[1] (closed_form) = 2.96419333531 -1.65884028232 absolute error = 0.2957 relative error = 8.707 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.777 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 = 6.777 Order of pole (three term test) = 28.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=38947.2MB, alloc=44.3MB, time=481.46 memory used=38993.4MB, alloc=44.3MB, time=482.04 x[1] = 0.5294 1.908 h = 0.001 0.001 y2[1] (numeric) = 1.86327294487 3.19784188374 y2[1] (closed_form) = 1.73926678195 2.84447440907 absolute error = 0.3745 relative error = 11.23 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.25980805571 -1.59029491067 y1[1] (closed_form) = 2.97253998156 -1.66433416623 absolute error = 0.2967 relative error = 8.708 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.351 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 = 5.351 Order of pole (three term test) = 28.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39039.5MB, alloc=44.3MB, time=482.60 memory used=39085.8MB, alloc=44.3MB, time=483.17 x[1] = 0.5304 1.909 h = 0.0001 0.004 y2[1] (numeric) = 1.87487375081 3.20851349416 y2[1] (closed_form) = 1.74390650101 2.84578087407 absolute error = 0.3857 relative error = 11.55 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.2611421629 -1.59536715451 y1[1] (closed_form) = 2.97364352332 -1.66892088033 absolute error = 0.2968 relative error = 8.703 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.2 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 = 32.2 Order of pole (three term test) = 28.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39131.6MB, alloc=44.3MB, time=483.73 memory used=39177.8MB, alloc=44.3MB, time=484.30 x[1] = 0.5305 1.913 h = 0.003 0.006 y2[1] (numeric) = 1.8865348802 3.21921121954 y2[1] (closed_form) = 1.75089464989 2.85753064089 absolute error = 0.3863 relative error = 11.53 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.27380953368 -1.60321133767 y1[1] (closed_form) = 2.98487539181 -1.67619563777 absolute error = 0.298 relative error = 8.705 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.23 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 = 19.23 Order of pole (three term test) = 28.7 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39223.8MB, alloc=44.3MB, time=484.86 x[1] = 0.5335 1.919 h = 0.0001 0.005 y2[1] (numeric) = 1.89825657714 3.22993512347 y2[1] (closed_form) = 1.76998168555 2.87041831057 absolute error = 0.3817 relative error = 11.32 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.2874797877 -1.62423939458 y1[1] (closed_form) = 2.99677795485 -1.6953501114 absolute error = 0.2993 relative error = 8.692 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.656 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 = 8.656 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39269.6MB, alloc=44.3MB, time=485.42 memory used=39315.8MB, alloc=44.3MB, time=485.99 x[1] = 0.5336 1.924 h = 0.0001 0.003 y2[1] (numeric) = 1.91003955355 3.24068507163 y2[1] (closed_form) = 1.77878170411 2.88526770653 absolute error = 0.3789 relative error = 11.18 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.30346591302 -1.63408364006 y1[1] (closed_form) = 3.01098970289 -1.70450978391 absolute error = 0.3008 relative error = 8.695 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.039 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 = 7.039 Order of pole (three term test) = 28.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39361.8MB, alloc=44.3MB, time=486.56 memory used=39408.1MB, alloc=44.3MB, time=487.13 x[1] = 0.5337 1.927 h = 0.001 0.001 y2[1] (numeric) = 1.92188413865 3.25146126186 y2[1] (closed_form) = 1.78420520264 2.89414267305 absolute error = 0.3829 relative error = 11.26 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.31301253026 -1.64015611728 y1[1] (closed_form) = 3.01948066303 -1.71014323015 absolute error = 0.3018 relative error = 8.696 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.559 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 = 5.559 Order of pole (three term test) = 28.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39454.1MB, alloc=44.3MB, time=487.69 x[1] = 0.5347 1.928 h = 0.001 0.003 y2[1] (numeric) = 1.93379040832 3.26226380408 y2[1] (closed_form) = 1.78893772112 2.8954502247 absolute error = 0.3944 relative error = 11.59 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.31434155847 -1.64534080975 y1[1] (closed_form) = 3.0205888888 -1.71482459787 absolute error = 0.3019 relative error = 8.691 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.43 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 = 26.43 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39500.5MB, alloc=44.3MB, time=488.26 memory used=39546.5MB, alloc=44.3MB, time=488.83 x[1] = 0.5357 1.931 h = 0.0001 0.004 y2[1] (numeric) = 1.94575839158 3.27309270637 y2[1] (closed_form) = 1.79711864415 2.90280338338 absolute error = 0.399 relative error = 11.69 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.32220481739 -1.65442779357 y1[1] (closed_form) = 3.02749324057 -1.72310280025 absolute error = 0.3026 relative error = 8.687 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.05 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 = 15.05 Order of pole (three term test) = 28.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39592.5MB, alloc=44.3MB, time=489.39 memory used=39638.7MB, alloc=44.3MB, time=489.95 x[1] = 0.5358 1.935 h = 0.003 0.006 y2[1] (numeric) = 1.95778818263 3.28394800452 y2[1] (closed_form) = 1.80432935455 2.91476356601 absolute error = 0.3998 relative error = 11.66 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.33512371318 -1.66256271791 y1[1] (closed_form) = 3.0389482873 -1.73059656385 absolute error = 0.3039 relative error = 8.69 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.1 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 = 20.1 Order of pole (three term test) = 28.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39684.5MB, alloc=44.3MB, time=490.51 memory used=39730.8MB, alloc=44.3MB, time=491.09 x[1] = 0.5388 1.941 h = 0.0001 0.005 y2[1] (numeric) = 1.96988004913 3.29482976531 y2[1] (closed_form) = 1.82390676918 2.9278122789 absolute error = 0.395 relative error = 11.45 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.34896854656 -1.68421385145 y1[1] (closed_form) = 3.0510336924 -1.75024505552 absolute error = 0.3052 relative error = 8.676 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.045 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 = 9.045 Order of pole (three term test) = 28.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39776.7MB, alloc=44.3MB, time=491.65 x[1] = 0.5389 1.946 h = 0.0001 0.003 y2[1] (numeric) = 1.98203471755 3.30573784721 y2[1] (closed_form) = 1.83298739173 2.94292815528 absolute error = 0.3922 relative error = 11.31 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.36527235938 -1.69442364026 y1[1] (closed_form) = 3.06552766938 -1.75968080709 absolute error = 0.3068 relative error = 8.679 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.356 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 = 7.356 Order of pole (three term test) = 28.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39822.7MB, alloc=44.3MB, time=492.21 memory used=39869.1MB, alloc=44.3MB, time=492.78 x[1] = 0.539 1.949 h = 0.001 0.001 y2[1] (numeric) = 1.99425252543 3.31667245033 y2[1] (closed_form) = 1.83858211836 2.95196146174 absolute error = 0.3965 relative error = 11.4 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.37500715434 -1.70071917562 y1[1] (closed_form) = 3.07418641914 -1.76548290105 absolute error = 0.3077 relative error = 8.68 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 5.809 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 = 5.809 Order of pole (three term test) = 28.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=39915.1MB, alloc=44.3MB, time=493.35 memory used=39961.5MB, alloc=44.3MB, time=493.92 x[1] = 0.54 1.95 h = 0.001 0.003 y2[1] (numeric) = 2.00653355094 3.32763368647 y2[1] (closed_form) = 1.84342474007 2.95326832507 absolute error = 0.4084 relative error = 11.73 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.37632891742 -1.70604171423 y1[1] (closed_form) = 3.0752980314 -1.77027651919 absolute error = 0.3078 relative error = 8.674 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.62 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 = 27.62 Order of pole (three term test) = 28.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40007.4MB, alloc=44.3MB, time=494.48 memory used=40053.7MB, alloc=44.3MB, time=495.05 x[1] = 0.541 1.953 h = 0.0001 0.004 y2[1] (numeric) = 2.01887782379 3.33862156373 y2[1] (closed_form) = 1.85182711982 2.96073022699 absolute error = 0.4132 relative error = 11.83 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.38431559322 -1.71541294088 y1[1] (closed_form) = 3.08232140286 -1.77877638708 absolute error = 0.3086 relative error = 8.671 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.72 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 = 15.72 Order of pole (three term test) = 28.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40099.4MB, alloc=44.3MB, time=495.60 x[1] = 0.5411 1.957 h = 0.003 0.006 y2[1] (numeric) = 2.03128544043 3.34963611809 y2[1] (closed_form) = 1.85926646858 2.97290459669 absolute error = 0.4141 relative error = 11.81 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.39748959204 -1.72384765893 y1[1] (closed_form) = 3.09400310278 -1.78649524493 absolute error = 0.3099 relative error = 8.674 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21 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 = 21 Order of pole (three term test) = 28.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40145.3MB, alloc=44.3MB, time=496.16 memory used=40191.4MB, alloc=44.3MB, time=496.73 x[1] = 0.5441 1.963 h = 0.0001 0.005 y2[1] (numeric) = 2.0437566747 3.36067741614 y2[1] (closed_form) = 1.87934623117 2.98611573619 absolute error = 0.4091 relative error = 11.59 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.41150797213 -1.74613821693 y1[1] (closed_form) = 3.10627227759 -1.80664953138 absolute error = 0.3112 relative error = 8.66 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.452 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 = 9.452 Order of pole (three term test) = 28.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40237.3MB, alloc=44.3MB, time=497.29 memory used=40283.4MB, alloc=44.3MB, time=497.85 x[1] = 0.5442 1.968 h = 0.0001 0.003 y2[1] (numeric) = 2.0562922679 3.37174530887 y2[1] (closed_form) = 1.88871512307 3.00150286692 absolute error = 0.4064 relative error = 11.46 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.42813401593 -1.75672493328 y1[1] (closed_form) = 3.12105289106 -1.81636904422 absolute error = 0.3128 relative error = 8.663 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.686 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 = 7.686 Order of pole (three term test) = 28.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40329.4MB, alloc=44.3MB, time=498.42 x[1] = 0.5443 1.971 h = 0.001 0.001 y2[1] (numeric) = 2.06889256608 3.38283999864 y2[1] (closed_form) = 1.89448573528 3.01069732701 absolute error = 0.411 relative error = 11.55 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.43805962847 -1.76325042338 y1[1] (closed_form) = 3.12988202499 -1.8223444506 absolute error = 0.3138 relative error = 8.664 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.07 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 = 6.07 Order of pole (three term test) = 28.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40375.5MB, alloc=44.3MB, time=498.99 memory used=40421.7MB, alloc=44.3MB, time=499.56 x[1] = 0.5453 1.972 h = 0.001 0.003 y2[1] (numeric) = 2.08155764979 3.39396159922 y2[1] (closed_form) = 1.89944097289 3.01200296845 absolute error = 0.4232 relative error = 11.88 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.43937280731 -1.76871404164 y1[1] (closed_form) = 3.1309964126 -1.82725276392 absolute error = 0.3139 relative error = 8.658 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.87 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 = 28.87 Order of pole (three term test) = 28.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40467.6MB, alloc=44.3MB, time=500.12 memory used=40514.0MB, alloc=44.3MB, time=500.69 x[1] = 0.5463 1.975 h = 0.0001 0.004 y2[1] (numeric) = 2.09428754941 3.40511011868 y2[1] (closed_form) = 1.90807038043 3.01957505609 absolute error = 0.4282 relative error = 11.99 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.44748349097 -1.77837732684 y1[1] (closed_form) = 3.13814002356 -1.83597981057 absolute error = 0.3147 relative error = 8.655 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.43 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 = 16.43 Order of pole (three term test) = 28.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40559.8MB, alloc=44.3MB, time=501.25 memory used=40605.9MB, alloc=44.3MB, time=501.81 x[1] = 0.5464 1.979 h = 0.003 0.006 y2[1] (numeric) = 2.10708236371 3.41628559319 y2[1] (closed_form) = 1.91574459861 3.03196742845 absolute error = 0.4293 relative error = 11.97 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.46091620543 -1.78712111457 y1[1] (closed_form) = 3.15005190244 -1.84393000626 absolute error = 0.316 relative error = 8.658 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.95 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 = 21.95 Order of pole (three term test) = 28.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40651.7MB, alloc=44.3MB, time=502.37 x[1] = 0.5494 1.985 h = 0.0001 0.005 y2[1] (numeric) = 2.11994237285 3.42748808913 y2[1] (closed_form) = 1.93633894504 3.04534233485 absolute error = 0.424 relative error = 11.75 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.4751069923 -1.81006780979 y1[1] (closed_form) = 3.16250574041 -1.86460213767 absolute error = 0.3173 relative error = 8.643 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.877 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 = 9.877 Order of pole (three term test) = 28.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40697.6MB, alloc=44.3MB, time=502.94 memory used=40743.9MB, alloc=44.3MB, time=503.50 x[1] = 0.5495 1.99 h = 0.0001 0.003 y2[1] (numeric) = 2.13286833325 3.43871744975 y2[1] (closed_form) = 1.94600396634 3.06100555027 absolute error = 0.4214 relative error = 11.62 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.49205985494 -1.82104311902 y1[1] (closed_form) = 3.17757746242 -1.87461329023 absolute error = 0.319 relative error = 8.647 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.032 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 = 8.032 Order of pole (three term test) = 28.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40789.7MB, alloc=44.3MB, time=504.06 memory used=40836.1MB, alloc=44.3MB, time=504.63 x[1] = 0.5496 1.993 h = 0.001 0.001 y2[1] (numeric) = 2.14586059969 3.44997387971 y2[1] (closed_form) = 1.95195523939 3.07036401017 absolute error = 0.4263 relative error = 11.72 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.50217894925 -1.82780563017 y1[1] (closed_form) = 3.18657961237 -1.88076679246 absolute error = 0.32 relative error = 8.648 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.343 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 = 6.343 Order of pole (three term test) = 28.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40882.1MB, alloc=44.3MB, time=505.20 memory used=40928.5MB, alloc=44.3MB, time=505.79 x[1] = 0.5506 1.994 h = 0.001 0.003 y2[1] (numeric) = 2.15891925514 3.46125749473 y2[1] (closed_form) = 1.95702565659 3.07166786934 absolute error = 0.4388 relative error = 12.05 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.50348217828 -1.83341362798 y1[1] (closed_form) = 3.1876961387 -1.88579229866 absolute error = 0.3201 relative error = 8.643 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.16 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 = 30.16 Order of pole (three term test) = 29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=40974.4MB, alloc=44.3MB, time=506.34 x[1] = 0.5516 1.997 h = 0.0001 0.004 y2[1] (numeric) = 2.1720443307 3.47256830288 y2[1] (closed_form) = 1.96588779222 3.07935158244 absolute error = 0.444 relative error = 12.15 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.51171743392 -1.84337696738 y1[1] (closed_form) = 3.19496121079 -1.89475216896 absolute error = 0.3209 relative error = 8.639 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.17 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 = 17.17 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41020.3MB, alloc=44.3MB, time=506.90 memory used=41066.5MB, alloc=44.3MB, time=507.47 x[1] = 0.5517 2.001 h = 0.003 0.006 y2[1] (numeric) = 2.18523592748 3.48390634052 y2[1] (closed_form) = 1.97380326878 3.09196581766 absolute error = 0.4453 relative error = 12.14 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.52541251065 -1.8524393292 y1[1] (closed_form) = 3.2071068454 -1.90294010523 absolute error = 0.3223 relative error = 8.642 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.93 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 = 22.93 Order of pole (three term test) = 29.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41112.3MB, alloc=44.3MB, time=508.02 memory used=41158.5MB, alloc=44.3MB, time=508.59 x[1] = 0.5547 2.007 h = 0.0001 0.005 y2[1] (numeric) = 2.19849433213 3.49527167376 y2[1] (closed_form) = 1.99492470776 3.10550578593 absolute error = 0.4397 relative error = 11.91 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.5397744525 -1.87605924661 y1[1] (closed_form) = 3.21974620341 -1.92414241094 absolute error = 0.3236 relative error = 8.628 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.32 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 = 10.32 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41204.4MB, alloc=44.3MB, time=509.15 x[1] = 0.5548 2.012 h = 0.0001 0.003 y2[1] (numeric) = 2.2118203165 3.50666413789 y2[1] (closed_form) = 2.00489391789 3.12144997321 absolute error = 0.4373 relative error = 11.79 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.55705876553 -1.88743510153 y1[1] (closed_form) = 3.23511357073 -1.93445328254 absolute error = 0.3254 relative error = 8.632 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.393 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 = 8.393 Order of pole (three term test) = 29.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41250.5MB, alloc=44.3MB, time=509.72 memory used=41296.7MB, alloc=44.3MB, time=510.29 x[1] = 0.5549 2.015 h = 0.001 0.001 y2[1] (numeric) = 2.22521424429 3.51808393985 y2[1] (closed_form) = 2.01103074767 3.13097531169 absolute error = 0.4424 relative error = 11.89 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.56737402963 -1.89444187355 y1[1] (closed_form) = 3.24429140587 -1.94078978559 absolute error = 0.3264 relative error = 8.634 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.628 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 = 6.628 Order of pole (three term test) = 29.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41342.8MB, alloc=44.3MB, time=510.86 memory used=41389.1MB, alloc=44.3MB, time=511.43 x[1] = 0.5559 2.016 h = 0.0001 0.004 y2[1] (numeric) = 2.23867620096 3.52953119736 y2[1] (closed_form) = 2.01621896027 3.13227680055 absolute error = 0.4553 relative error = 12.22 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.56866589536 -1.90019761838 y1[1] (closed_form) = 3.24540940793 -1.94593503632 absolute error = 0.3265 relative error = 8.628 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.88 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 = 39.88 Order of pole (three term test) = 29.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41435.1MB, alloc=44.3MB, time=512.00 memory used=41481.3MB, alloc=44.3MB, time=512.56 x[1] = 0.556 2.02 h = 0.003 0.006 y2[1] (numeric) = 2.25220622177 3.5410059502 y2[1] (closed_form) = 2.02434463728 3.14508811377 absolute error = 0.4568 relative error = 12.21 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.58258241691 -1.90953288715 y1[1] (closed_form) = 3.25776209368 -1.95433001975 absolute error = 0.3279 relative error = 8.631 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.82 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 = 23.82 Order of pole (three term test) = 29.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41527.0MB, alloc=44.3MB, time=513.12 x[1] = 0.559 2.026 h = 0.0001 0.005 y2[1] (numeric) = 2.26580457953 3.55250826112 y2[1] (closed_form) = 2.04592802297 3.1587776491 absolute error = 0.451 relative error = 11.98 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.5970859468 -1.93372714965 y1[1] (closed_form) = 3.27056831816 -1.97599654921 absolute error = 0.3292 relative error = 8.616 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.72 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 = 10.72 Order of pole (three term test) = 29.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41572.8MB, alloc=44.3MB, time=513.68 memory used=41619.1MB, alloc=44.3MB, time=514.25 x[1] = 0.5591 2.031 h = 0.0001 0.003 y2[1] (numeric) = 2.2794720597 3.5640379585 y2[1] (closed_form) = 2.05616225107 3.17497140266 absolute error = 0.4486 relative error = 11.86 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.61465003766 -1.94544613941 y1[1] (closed_form) = 3.28619755461 -1.98656843903 absolute error = 0.331 relative error = 8.62 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.718 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 = 8.718 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41664.9MB, alloc=44.3MB, time=514.82 memory used=41711.3MB, alloc=44.3MB, time=515.39 x[1] = 0.5592 2.034 h = 0.001 0.001 y2[1] (numeric) = 2.29320903379 3.57559525136 y2[1] (closed_form) = 2.06246078148 3.18464500699 absolute error = 0.454 relative error = 11.96 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.62513084707 -1.95266212509 y1[1] (closed_form) = 3.2955310414 -1.99306434906 absolute error = 0.3321 relative error = 8.622 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 6.885 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 = 6.885 Order of pole (three term test) = 29.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41757.4MB, alloc=44.3MB, time=515.95 x[1] = 0.5602 2.035 h = 0.001 0.003 y2[1] (numeric) = 2.30701558946 3.58718025922 y2[1] (closed_form) = 2.06775256195 3.18594540945 absolute error = 0.4672 relative error = 12.3 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.62641212601 -1.95854361705 y1[1] (closed_form) = 3.29665123082 -1.99831475075 absolute error = 0.3322 relative error = 8.616 % Correct digits = 1 memory used=41803.8MB, alloc=44.3MB, time=516.52 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.74 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 = 32.74 Order of pole (three term test) = 29.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41849.8MB, alloc=44.3MB, time=517.09 x[1] = 0.5612 2.038 h = 0.0001 0.004 y2[1] (numeric) = 2.32089175916 3.59879299014 y2[1] (closed_form) = 2.07706200658 3.19384359015 absolute error = 0.4727 relative error = 12.41 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.63487713108 -1.96907844497 y1[1] (closed_form) = 3.30414850674 -2.00772185709 absolute error = 0.333 relative error = 8.612 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.64 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 = 18.64 Order of pole (three term test) = 29.29 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41895.7MB, alloc=44.3MB, time=517.64 memory used=41941.9MB, alloc=44.3MB, time=518.21 x[1] = 0.5613 2.042 h = 0.003 0.006 y2[1] (numeric) = 2.33483764854 3.61043348082 y2[1] (closed_form) = 2.08544121655 3.20688414955 absolute error = 0.4744 relative error = 12.4 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.64906278886 -1.97875034162 y1[1] (closed_form) = 3.31674182085 -2.01636688756 absolute error = 0.3344 relative error = 8.616 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.89 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 = 24.89 Order of pole (three term test) = 29.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=41987.7MB, alloc=44.3MB, time=518.76 memory used=42033.9MB, alloc=44.3MB, time=519.34 x[1] = 0.5643 2.048 h = 0.0001 0.005 y2[1] (numeric) = 2.34885355667 3.62210179687 y2[1] (closed_form) = 2.10757570324 3.2207411846 absolute error = 0.4683 relative error = 12.17 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.66373486162 -2.00365017602 y1[1] (closed_form) = 3.3297352089 -2.03858728735 absolute error = 0.3358 relative error = 8.601 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.2 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 = 11.2 Order of pole (three term test) = 29.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42079.7MB, alloc=44.3MB, time=519.89 x[1] = 0.5644 2.053 h = 0.0001 0.003 y2[1] (numeric) = 2.36294028508 3.63379775825 y2[1] (closed_form) = 2.11812960437 3.2372252581 absolute error = 0.466 relative error = 12.05 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.68163900987 -2.01579242574 y1[1] (closed_form) = 3.34566880747 -2.04947442494 absolute error = 0.3377 relative error = 8.606 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.11 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 = 9.11 Order of pole (three term test) = 29.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42125.8MB, alloc=44.3MB, time=520.46 memory used=42172.0MB, alloc=44.3MB, time=521.03 x[1] = 0.5645 2.056 h = 0.001 0.001 y2[1] (numeric) = 2.37709821462 3.6455215763 y2[1] (closed_form) = 2.12462309739 3.24707124707 absolute error = 0.4717 relative error = 12.16 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.69232098055 -2.02326643141 y1[1] (closed_form) = 3.3551831078 -2.05616276333 absolute error = 0.3387 relative error = 8.608 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.194 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 = 7.194 Order of pole (three term test) = 29.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42217.9MB, alloc=44.3MB, time=521.59 memory used=42264.2MB, alloc=44.3MB, time=522.16 x[1] = 0.5655 2.057 h = 0.001 0.003 y2[1] (numeric) = 2.39132743555 3.65727337261 y2[1] (closed_form) = 2.13003769077 3.24836814098 absolute error = 0.4853 relative error = 12.49 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.69358816881 -2.02930203343 y1[1] (closed_form) = 3.35630349799 -2.06153781323 absolute error = 0.3388 relative error = 8.602 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.21 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 = 34.21 Order of pole (three term test) = 29.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42310.1MB, alloc=44.3MB, time=522.72 memory used=42356.4MB, alloc=44.3MB, time=523.29 x[1] = 0.5665 2.06 h = 0.0001 0.004 y2[1] (numeric) = 2.40562798109 3.66905315521 y2[1] (closed_form) = 2.13959689371 3.25638211815 absolute error = 0.491 relative error = 12.6 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.70217917984 -2.04016060965 y1[1] (closed_form) = 3.36392580584 -2.07119462999 absolute error = 0.3397 relative error = 8.598 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.48 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 = 19.48 Order of pole (three term test) = 29.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42402.2MB, alloc=44.3MB, time=523.85 x[1] = 0.5666 2.064 h = 0.003 0.006 y2[1] (numeric) = 2.41999995939 3.68086096098 y2[1] (closed_form) = 2.1482364982 3.26965591504 absolute error = 0.4929 relative error = 12.6 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.71663771791 -2.05017933717 y1[1] (closed_form) = 3.37676347372 -2.08009658595 absolute error = 0.3412 relative error = 8.603 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.01 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 = 26.01 Order of pole (three term test) = 29.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42448.0MB, alloc=44.3MB, time=524.41 memory used=42494.2MB, alloc=44.3MB, time=524.98 x[1] = 0.5696 2.07 h = 0.0001 0.005 y2[1] (numeric) = 2.43444367644 3.69269685515 y2[1] (closed_form) = 2.17093540923 3.2836816054 absolute error = 0.4865 relative error = 12.36 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.73147672995 -2.07580296174 y1[1] (closed_form) = 3.38994476712 -2.10288401714 absolute error = 0.3426 relative error = 8.588 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.71 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 = 11.71 Order of pole (three term test) = 29.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42540.1MB, alloc=44.3MB, time=525.54 memory used=42586.3MB, alloc=44.3MB, time=526.10 x[1] = 0.5697 2.075 h = 0.0001 0.003 y2[1] (numeric) = 2.4489599501 3.70456064897 y2[1] (closed_form) = 2.18181763952 3.30046105296 absolute error = 0.4844 relative error = 12.24 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.74972569248 -2.0883813031 y1[1] (closed_form) = 3.40618745323 -2.1140950822 absolute error = 0.3445 relative error = 8.593 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.52 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 = 9.52 Order of pole (three term test) = 29.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42632.3MB, alloc=44.3MB, time=526.66 x[1] = 0.5698 2.078 h = 0.001 0.001 y2[1] (numeric) = 2.46354917077 3.7164525561 y2[1] (closed_form) = 2.18851135195 3.31048240117 absolute error = 0.4904 relative error = 12.36 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.76061158039 -2.09612109895 y1[1] (closed_form) = 3.41588534504 -2.12098111721 absolute error = 0.3456 relative error = 8.596 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.518 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 = 7.518 Order of pole (three term test) = 29.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42678.5MB, alloc=44.3MB, time=527.23 memory used=42724.7MB, alloc=44.3MB, time=527.80 x[1] = 0.5708 2.079 h = 0.001 0.003 y2[1] (numeric) = 2.47821143141 3.72837270022 y2[1] (closed_form) = 2.19405152932 3.31177511504 absolute error = 0.5043 relative error = 12.69 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.76186311645 -2.10231438344 y1[1] (closed_form) = 3.41700519327 -2.12648352722 absolute error = 0.3457 relative error = 8.59 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.75 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 = 35.75 Order of pole (three term test) = 29.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42770.7MB, alloc=44.3MB, time=528.36 memory used=42816.9MB, alloc=44.3MB, time=528.92 x[1] = 0.5718 2.082 h = 0.0001 0.004 y2[1] (numeric) = 2.49294676601 3.74032108934 y2[1] (closed_form) = 2.20386671783 3.31990631307 absolute error = 0.5102 relative error = 12.8 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.77058057707 -2.11350544699 y1[1] (closed_form) = 3.42475375608 -2.13639623483 absolute error = 0.3466 relative error = 8.586 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.35 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 = 20.35 Order of pole (three term test) = 29.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42862.8MB, alloc=44.3MB, time=529.49 memory used=42909.0MB, alloc=44.3MB, time=530.05 x[1] = 0.5719 2.086 h = 0.003 0.006 y2[1] (numeric) = 2.50775528529 3.7522977605 y2[1] (closed_form) = 2.21277375154 3.33341738436 absolute error = 0.5123 relative error = 12.8 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.78531577083 -2.12388145738 y1[1] (closed_form) = 3.43783955463 -2.14556216886 absolute error = 0.3482 relative error = 8.591 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.18 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 = 27.18 Order of pole (three term test) = 29.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=42954.8MB, alloc=44.3MB, time=530.61 x[1] = 0.5749 2.092 h = 0.0001 0.005 y2[1] (numeric) = 2.5226373023 3.76430277853 y2[1] (closed_form) = 2.23605070687 3.34761283087 absolute error = 0.5057 relative error = 12.56 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.80031998792 -2.15024749195 y1[1] (closed_form) = 3.45120944861 -2.16893009487 absolute error = 0.3496 relative error = 8.577 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.23 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 = 12.23 Order of pole (three term test) = 29.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43000.8MB, alloc=44.3MB, time=531.17 memory used=43046.8MB, alloc=44.3MB, time=531.74 x[1] = 0.575 2.097 h = 0.0001 0.003 y2[1] (numeric) = 2.53759365157 3.77633594566 y2[1] (closed_form) = 2.24727014106 3.36469276468 absolute error = 0.5037 relative error = 12.45 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.81891856205 -2.16327506994 y1[1] (closed_form) = 3.46776601303 -2.18047398685 absolute error = 0.3516 relative error = 8.583 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.948 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 = 9.948 Order of pole (three term test) = 29.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43092.6MB, alloc=44.3MB, time=532.30 memory used=43138.9MB, alloc=44.3MB, time=532.88 x[1] = 0.5751 2.1 h = 0.001 0.001 y2[1] (numeric) = 2.55262473327 3.78839747789 y2[1] (closed_form) = 2.25416946186 3.37489248002 absolute error = 0.51 relative error = 12.57 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.83001114478 -2.17128861525 y1[1] (closed_form) = 3.47765031187 -2.18756311972 absolute error = 0.3527 relative error = 8.586 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 7.856 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 = 7.856 Order of pole (three term test) = 29.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43184.9MB, alloc=44.3MB, time=533.44 memory used=43231.2MB, alloc=44.3MB, time=534.01 x[1] = 0.5761 2.101 h = 0.001 0.003 y2[1] (numeric) = 2.56773064314 3.80048750104 y2[1] (closed_form) = 2.25983805061 3.37618031115 absolute error = 0.5242 relative error = 12.9 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.83124541344 -2.17764322681 y1[1] (closed_form) = 3.47876884545 -2.19319565968 absolute error = 0.3528 relative error = 8.579 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.36 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 = 37.36 Order of pole (three term test) = 29.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43277.1MB, alloc=44.3MB, time=534.57 x[1] = 0.5771 2.104 h = 0.0001 0.004 y2[1] (numeric) = 2.58291141595 3.8126060231 y2[1] (closed_form) = 2.269915596 3.38443014816 absolute error = 0.5304 relative error = 13.01 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.84008973181 -2.18917571556 y1[1] (closed_form) = 3.48664488415 -2.20337058466 absolute error = 0.3537 relative error = 8.576 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.27 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 = 21.27 Order of pole (three term test) = 29.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43323.0MB, alloc=44.3MB, time=535.14 memory used=43369.2MB, alloc=44.3MB, time=535.71 x[1] = 0.5772 2.108 h = 0.003 0.006 y2[1] (numeric) = 2.59816716507 3.82475308123 y2[1] (closed_form) = 2.27909727085 3.39818257659 absolute error = 0.5327 relative error = 13.02 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.85510538718 -2.19991971543 y1[1] (closed_form) = 3.49998264181 -2.21280772757 absolute error = 0.3554 relative error = 8.582 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.41 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 = 28.41 Order of pole (three term test) = 29.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43415.1MB, alloc=44.3MB, time=536.26 memory used=43461.3MB, alloc=44.3MB, time=536.83 x[1] = 0.5802 2.114 h = 0.0001 0.005 y2[1] (numeric) = 2.61349821072 3.83692873983 y2[1] (closed_form) = 2.30296619363 3.41254882267 absolute error = 0.5259 relative error = 12.77 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.87027293927 -2.22704718931 y1[1] (closed_form) = 3.51354178219 -2.23676992047 absolute error = 0.3569 relative error = 8.568 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.78 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 = 12.78 Order of pole (three term test) = 30.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43507.0MB, alloc=44.3MB, time=537.40 x[1] = 0.5803 2.119 h = 0.0001 0.003 y2[1] (numeric) = 2.62890540447 3.84913279185 y2[1] (closed_form) = 2.31453193025 3.4299344133 absolute error = 0.524 relative error = 12.66 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.8892259617 -2.24053746934 y1[1] (closed_form) = 3.53041708123 -2.24865576378 absolute error = 0.3589 relative error = 8.574 % Correct digits = 1 memory used=43553.1MB, alloc=44.3MB, time=537.96 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) = 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 = 10.4 Order of pole (three term test) = 30.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43599.3MB, alloc=44.3MB, time=538.53 x[1] = 0.5804 2.122 h = 0.001 0.001 y2[1] (numeric) = 2.64438915651 3.8613654556 y2[1] (closed_form) = 2.32164238373 3.440315537 absolute error = 0.5305 relative error = 12.78 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.9005280378 -2.24883291669 y1[1] (closed_form) = 3.54049064025 -2.25595353178 absolute error = 0.3601 relative error = 8.578 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.209 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 = 8.209 Order of pole (three term test) = 30.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43645.3MB, alloc=44.3MB, time=539.10 memory used=43691.7MB, alloc=44.3MB, time=539.66 x[1] = 0.5814 2.123 h = 0.0001 0.004 y2[1] (numeric) = 2.6599495654 3.87362685908 y2[1] (closed_form) = 2.32744226864 3.44159775053 absolute error = 0.5452 relative error = 13.12 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.90174336859 -2.25535257343 y1[1] (closed_form) = 3.54160705553 -2.26171903056 absolute error = 0.3602 relative error = 8.572 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.4 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 = 49.4 Order of pole (three term test) = 30.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43737.6MB, alloc=44.3MB, time=540.22 memory used=43783.8MB, alloc=44.3MB, time=540.79 x[1] = 0.5815 2.127 h = 0.003 0.006 y2[1] (numeric) = 2.67558667151 3.88591704533 y2[1] (closed_form) = 2.33686331695 3.45556462738 absolute error = 0.5477 relative error = 13.13 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.91699567061 -2.26641159727 y1[1] (closed_form) = 3.55516814758 -2.27139248606 absolute error = 0.3619 relative error = 8.577 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.51 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 = 29.51 Order of pole (three term test) = 30.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43829.6MB, alloc=44.3MB, time=541.35 x[1] = 0.5845 2.133 h = 0.0001 0.005 y2[1] (numeric) = 2.69130077965 3.8982360755 y2[1] (closed_form) = 2.36125112078 3.47008596468 absolute error = 0.5406 relative error = 12.88 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 3.93229780379 -2.29418844341 y1[1] (closed_form) = 3.56889797026 -2.29587520898 absolute error = 0.3634 relative error = 8.564 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.28 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 = 13.28 Order of pole (three term test) = 30.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43875.4MB, alloc=44.3MB, time=541.91 memory used=43921.6MB, alloc=44.3MB, time=542.48 x[1] = 0.5846 2.138 h = 0.0001 0.003 y2[1] (numeric) = 2.70709275636 3.91058373446 y2[1] (closed_form) = 2.3731186778 3.48774311659 absolute error = 0.5388 relative error = 12.77 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 3.95154992234 -2.30807483543 y1[1] (closed_form) = 3.58605578976 -2.30805899813 absolute error = 0.3655 relative error = 8.57 % Correct digits = 1 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) = 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 = 10.8 Order of pole (three term test) = 30.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=43967.6MB, alloc=44.3MB, time=543.04 memory used=44014.0MB, alloc=44.3MB, time=543.62 x[1] = 0.5847 2.141 h = 0.001 0.001 y2[1] (numeric) = 2.72296302062 3.92296024267 y2[1] (closed_form) = 2.38041318584 3.49828545858 absolute error = 0.5456 relative error = 12.89 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 3.96302872893 -2.31661157647 y1[1] (closed_form) = 3.59629714873 -2.31553859124 absolute error = 0.3667 relative error = 8.574 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.527 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 = 8.527 Order of pole (three term test) = 30.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44060.2MB, alloc=44.3MB, time=544.18 x[1] = 0.5857 2.142 h = 0.001 0.003 y2[1] (numeric) = 2.73891167346 3.93536573006 y2[1] (closed_form) = 2.38632852029 3.49956383476 absolute error = 0.5606 relative error = 13.23 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 3.96422695869 -2.32327166785 y1[1] (closed_form) = 3.5974127035 -2.32142088655 absolute error = 0.3668 relative error = 8.568 % Correct digits = 1 memory used=44106.6MB, alloc=44.3MB, time=544.75 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.55 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 = 40.55 Order of pole (three term test) = 30.44 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44152.6MB, alloc=44.3MB, time=545.32 x[1] = 0.5867 2.145 h = 0.0001 0.004 y2[1] (numeric) = 2.75493875116 3.94780020457 y2[1] (closed_form) = 2.39691026223 3.50804149198 absolute error = 0.5671 relative error = 13.35 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 3.97330478167 -2.33545400442 y1[1] (closed_form) = 3.60553249203 -2.33209953621 absolute error = 0.3678 relative error = 8.565 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.08 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 = 23.08 Order of pole (three term test) = 30.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44198.5MB, alloc=44.3MB, time=545.88 memory used=44244.6MB, alloc=44.3MB, time=546.44 x[1] = 0.5868 2.149 h = 0.003 0.006 y2[1] (numeric) = 2.77104437216 3.96026370364 y2[1] (closed_form) = 2.40661980788 3.52225753658 absolute error = 0.5698 relative error = 13.36 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 3.98884460128 -2.34690134741 y1[1] (closed_form) = 3.61935289583 -2.34205809711 absolute error = 0.3695 relative error = 8.572 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.83 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 = 30.83 Order of pole (three term test) = 30.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44290.4MB, alloc=44.3MB, time=547.00 memory used=44336.6MB, alloc=44.3MB, time=547.57 x[1] = 0.5898 2.155 h = 0.0001 0.005 y2[1] (numeric) = 2.78722887055 3.97275629079 y2[1] (closed_form) = 2.43162630562 3.53695162734 absolute error = 0.5625 relative error = 13.1 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.00430625675 -2.37547565024 y1[1] (closed_form) = 3.63327319814 -2.36716155095 absolute error = 0.3711 relative error = 8.558 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.88 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 = 13.88 Order of pole (three term test) = 30.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44382.5MB, alloc=44.3MB, time=548.13 x[1] = 0.5899 2.16 h = 0.0001 0.003 y2[1] (numeric) = 2.80349313056 3.98527774112 y2[1] (closed_form) = 2.44385764621 3.55492432831 absolute error = 0.5608 relative error = 13 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.02392179435 -2.38985032334 y1[1] (closed_form) = 3.65075907846 -2.37970482705 absolute error = 0.3733 relative error = 8.566 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.28 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 = 11.28 Order of pole (three term test) = 30.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44428.5MB, alloc=44.3MB, time=548.69 memory used=44474.7MB, alloc=44.3MB, time=549.26 x[1] = 0.59 2.163 h = 0.001 0.001 y2[1] (numeric) = 2.81983758161 3.99782827743 y2[1] (closed_form) = 2.45137390054 3.5656538966 absolute error = 0.5679 relative error = 13.13 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.03561528021 -2.3986844544 y1[1] (closed_form) = 3.66119517679 -2.38740369699 absolute error = 0.3746 relative error = 8.57 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 8.911 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 = 8.911 Order of pole (three term test) = 30.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44520.8MB, alloc=44.3MB, time=549.82 memory used=44567.2MB, alloc=44.3MB, time=550.39 x[1] = 0.591 2.164 h = 0.001 0.003 y2[1] (numeric) = 2.83626232774 4.01040803189 y2[1] (closed_form) = 2.45742606549 3.56692523469 absolute error = 0.5833 relative error = 13.47 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.03679135267 -2.40551661338 y1[1] (closed_form) = 3.66230706737 -2.39342438636 absolute error = 0.3747 relative error = 8.564 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.37 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 = 42.37 Order of pole (three term test) = 30.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44613.0MB, alloc=44.3MB, time=550.96 memory used=44659.3MB, alloc=44.3MB, time=551.53 x[1] = 0.592 2.167 h = 0.0001 0.004 y2[1] (numeric) = 2.85276740606 4.02301701239 y2[1] (closed_form) = 2.46828919926 3.57552562754 absolute error = 0.59 relative error = 13.58 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.04599697476 -2.41806684797 y1[1] (closed_form) = 3.67055788601 -2.40438417325 absolute error = 0.3757 relative error = 8.562 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.12 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 = 24.12 Order of pole (three term test) = 30.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44705.3MB, alloc=44.3MB, time=552.09 x[1] = 0.5921 2.171 h = 0.003 0.006 y2[1] (numeric) = 2.8693529378 4.0356552565 y2[1] (closed_form) = 2.47829498449 3.58999505687 absolute error = 0.5929 relative error = 13.59 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.06182820417 -2.42991399519 y1[1] (closed_form) = 3.68464158009 -2.41463560306 absolute error = 0.3775 relative error = 8.569 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.22 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 = 32.22 Order of pole (three term test) = 30.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44751.1MB, alloc=44.3MB, time=552.64 memory used=44797.4MB, alloc=44.3MB, time=553.22 x[1] = 0.5951 2.177 h = 0.0001 0.005 y2[1] (numeric) = 2.88601926474 4.04832282715 y2[1] (closed_form) = 2.5039350041 3.60486276852 absolute error = 0.5854 relative error = 13.34 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.07744708583 -2.45930603101 y1[1] (closed_form) = 3.69875285405 -2.44037447951 absolute error = 0.3792 relative error = 8.557 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.5 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 = 14.5 Order of pole (three term test) = 31.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44843.2MB, alloc=44.3MB, time=553.78 memory used=44889.6MB, alloc=44.3MB, time=554.35 x[1] = 0.5952 2.182 h = 0.0001 0.003 y2[1] (numeric) = 2.90276728911 4.06101948931 y2[1] (closed_form) = 2.51653989636 3.62315636013 absolute error = 0.5839 relative error = 13.24 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.09743099083 -2.47418343009 y1[1] (closed_form) = 3.7165718421 -2.45328703935 absolute error = 0.3814 relative error = 8.565 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.79 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 = 11.79 Order of pole (three term test) = 31.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=44935.6MB, alloc=44.3MB, time=554.92 x[1] = 0.5953 2.185 h = 0.001 0.001 y2[1] (numeric) = 2.91959745106 4.0737454681 y2[1] (closed_form) = 2.52428382614 3.63407629366 absolute error = 0.5913 relative error = 13.36 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.10934201336 -2.48332369465 y1[1] (closed_form) = 3.72720564232 -2.46121113009 absolute error = 0.3828 relative error = 8.57 % Correct digits = 1 memory used=44981.9MB, alloc=44.3MB, time=555.49 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.311 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 = 9.311 Order of pole (three term test) = 31.14 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45028.1MB, alloc=44.3MB, time=556.06 x[1] = 0.5963 2.186 h = 0.001 0.003 y2[1] (numeric) = 2.93650985765 4.08650089798 y2[1] (closed_form) = 2.53047587741 3.63533976182 absolute error = 0.607 relative error = 13.7 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.11049408729 -2.49033186218 y1[1] (closed_form) = 3.72831297152 -2.46737321779 absolute error = 0.3829 relative error = 8.564 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.28 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 = 44.28 Order of pole (three term test) = 31.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45074.0MB, alloc=44.3MB, time=556.62 memory used=45120.2MB, alloc=44.3MB, time=557.19 x[1] = 0.5973 2.189 h = 0.0001 0.004 y2[1] (numeric) = 2.95350454686 4.09928578679 y2[1] (closed_form) = 2.54162736153 3.64406427794 absolute error = 0.6139 relative error = 13.82 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.11982775961 -2.50325975409 y1[1] (closed_form) = 3.736696026 -2.47862106298 absolute error = 0.3839 relative error = 8.562 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.21 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 = 25.21 Order of pole (three term test) = 31.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45166.1MB, alloc=44.3MB, time=557.75 memory used=45212.2MB, alloc=44.3MB, time=558.32 x[1] = 0.5974 2.193 h = 0.003 0.006 y2[1] (numeric) = 2.97058164281 4.11210017222 y2[1] (closed_form) = 2.55193732273 3.65879135542 absolute error = 0.6171 relative error = 13.83 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.13595431805 -2.51551846802 y1[1] (closed_form) = 3.75104704061 -2.48917332011 absolute error = 0.3858 relative error = 8.57 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.67 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 = 33.67 Order of pole (three term test) = 31.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45258.0MB, alloc=44.3MB, time=558.88 x[1] = 0.6004 2.199 h = 0.0001 0.005 y2[1] (numeric) = 2.98774149511 4.12494411654 y2[1] (closed_form) = 2.57822602149 3.67383348676 absolute error = 0.6093 relative error = 13.57 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.1517279723 -2.54574895491 y1[1] (closed_form) = 3.76534971711 -2.51556264512 absolute error = 0.3876 relative error = 8.558 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.15 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 = 15.15 Order of pole (three term test) = 31.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45304.0MB, alloc=44.3MB, time=559.44 memory used=45350.3MB, alloc=44.3MB, time=560.01 x[1] = 0.6005 2.204 h = 0.0001 0.003 y2[1] (numeric) = 3.00498502437 4.13781737429 y2[1] (closed_form) = 2.59121447866 3.69245336982 absolute error = 0.6079 relative error = 13.48 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.17208522816 -2.56114387404 y1[1] (closed_form) = 3.78350692552 -2.52885453152 absolute error = 0.3899 relative error = 8.568 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.32 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 = 12.32 Order of pole (three term test) = 31.55 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45396.1MB, alloc=44.3MB, time=560.58 memory used=45442.4MB, alloc=44.3MB, time=561.15 x[1] = 0.6006 2.207 h = 0.001 0.001 y2[1] (numeric) = 3.02231268167 4.15072017292 y2[1] (closed_form) = 2.59919216125 3.7035668412 absolute error = 0.6156 relative error = 13.61 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.18421666288 -2.57059922618 y1[1] (closed_form) = 3.7943414278 -2.53700993584 absolute error = 0.3913 relative error = 8.573 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 9.73 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 = 9.73 Order of pole (three term test) = 31.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45488.4MB, alloc=44.3MB, time=561.72 memory used=45534.7MB, alloc=44.3MB, time=562.29 x[1] = 0.6016 2.208 h = 0.001 0.003 y2[1] (numeric) = 3.03972457723 4.1636526492 y2[1] (closed_form) = 2.6055272166 3.70482157139 absolute error = 0.6317 relative error = 13.95 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.18534283521 -2.57778742172 y1[1] (closed_form) = 3.79544326336 -2.54331648955 absolute error = 0.3914 relative error = 8.567 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.27 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 = 46.27 Order of pole (three term test) = 31.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45580.7MB, alloc=44.3MB, time=562.85 x[1] = 0.6026 2.211 h = 0.0001 0.004 y2[1] (numeric) = 3.0572207499 4.17661481092 y2[1] (closed_form) = 2.61697417 3.71367158775 absolute error = 0.6389 relative error = 14.06 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.19480476335 -2.59110294989 y1[1] (closed_form) = 3.8039597525 -2.55485947626 absolute error = 0.3925 relative error = 8.566 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.34 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 = 26.34 Order of pole (three term test) = 31.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45626.6MB, alloc=44.3MB, time=563.42 memory used=45672.7MB, alloc=44.3MB, time=563.98 x[1] = 0.6027 2.215 h = 0.003 0.006 y2[1] (numeric) = 3.07480132673 4.18960669587 y2[1] (closed_form) = 2.62759644233 3.72866062332 absolute error = 0.6422 relative error = 14.08 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.21123059603 -2.60378527671 y1[1] (closed_form) = 3.81858216963 -2.56572071865 absolute error = 0.3945 relative error = 8.575 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.18 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 = 35.18 Order of pole (three term test) = 31.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45718.5MB, alloc=44.3MB, time=564.54 memory used=45764.8MB, alloc=44.3MB, time=565.11 x[1] = 0.6057 2.221 h = 0.0001 0.005 y2[1] (numeric) = 3.09246666537 4.20262836562 y2[1] (closed_form) = 2.65454931394 3.74387790143 absolute error = 0.6342 relative error = 13.82 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.22715640571 -2.63487538326 y1[1] (closed_form) = 3.83307661513 -2.59277585934 absolute error = 0.3963 relative error = 8.564 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.83 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 = 15.83 Order of pole (three term test) = 31.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45810.7MB, alloc=44.3MB, time=565.67 x[1] = 0.6058 2.226 h = 0.0001 0.003 y2[1] (numeric) = 3.11021770514 4.21567956394 y2[1] (closed_form) = 2.66793160025 3.76282953601 absolute error = 0.633 relative error = 13.72 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.2478920297 -2.65080297349 y1[1] (closed_form) = 3.85157722229 -2.60645736697 absolute error = 0.3988 relative error = 8.575 % Correct digits = 1 memory used=45856.8MB, alloc=44.3MB, time=566.23 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) = 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 = 12.88 Order of pole (three term test) = 32.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45902.9MB, alloc=44.3MB, time=566.80 x[1] = 0.6059 2.229 h = 0.001 0.001 y2[1] (numeric) = 3.12805490835 4.2287605206 y2[1] (closed_form) = 2.67614926471 3.77413975159 absolute error = 0.641 relative error = 13.85 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.26024676945 -2.6605825826 y1[1] (closed_form) = 3.86261546433 -2.61485032989 absolute error = 0.4003 relative error = 8.581 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.17 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 = 10.17 Order of pole (three term test) = 32.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=45949.0MB, alloc=44.3MB, time=567.37 memory used=45995.4MB, alloc=44.3MB, time=567.94 x[1] = 0.6069 2.23 h = 0.0001 0.004 y2[1] (numeric) = 3.14597838842 4.24187137475 y2[1] (closed_form) = 2.68263050506 3.77538483842 absolute error = 0.6575 relative error = 14.2 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.26134507345 -2.66795490551 y1[1] (closed_form) = 3.86371083781 -2.62130448189 absolute error = 0.4004 relative error = 8.575 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.18 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 = 61.18 Order of pole (three term test) = 32.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46041.3MB, alloc=44.3MB, time=568.50 memory used=46087.5MB, alloc=44.3MB, time=569.07 x[1] = 0.607 2.234 h = 0.003 0.006 y2[1] (numeric) = 3.16398819151 4.25501217291 y2[1] (closed_form) = 2.69352508289 3.79060670154 absolute error = 0.6611 relative error = 14.22 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.27802333293 -2.68099965381 y1[1] (closed_form) = 3.87857399405 -2.63243507682 absolute error = 0.4024 relative error = 8.584 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.54 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 = 36.54 Order of pole (three term test) = 32.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46133.4MB, alloc=44.3MB, time=569.63 x[1] = 0.61 2.24 h = 0.0001 0.005 y2[1] (numeric) = 3.18208465806 4.2681829736 y2[1] (closed_form) = 2.72106022476 3.80598343431 absolute error = 0.6528 relative error = 13.95 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.29407381595 -2.71282261405 y1[1] (closed_form) = 3.89324193641 -2.66007361175 absolute error = 0.4043 relative error = 8.574 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.45 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 = 16.45 Order of pole (three term test) = 32.4 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46179.4MB, alloc=44.3MB, time=570.19 memory used=46225.7MB, alloc=44.3MB, time=570.76 x[1] = 0.6101 2.245 h = 0.0001 0.003 y2[1] (numeric) = 3.20026874389 4.28138351119 y2[1] (closed_form) = 2.73478587995 3.82522990964 absolute error = 0.6517 relative error = 13.86 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.31512860281 -2.72920593898 y1[1] (closed_form) = 3.91204713947 -2.67409475692 absolute error = 0.4068 relative error = 8.585 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.37 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 = 13.37 Order of pole (three term test) = 32.48 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46271.6MB, alloc=44.3MB, time=571.32 memory used=46318.0MB, alloc=44.3MB, time=571.90 x[1] = 0.6102 2.248 h = 0.001 0.001 y2[1] (numeric) = 3.21854092115 4.29461401761 y2[1] (closed_form) = 2.74321282313 3.83671503191 absolute error = 0.66 relative error = 13.99 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.32767165183 -2.73926293106 y1[1] (closed_form) = 3.92326614897 -2.68269484522 absolute error = 0.4083 relative error = 8.592 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 10.56 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 = 10.56 Order of pole (three term test) = 32.53 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46364.0MB, alloc=44.3MB, time=572.46 memory used=46410.3MB, alloc=44.3MB, time=573.04 x[1] = 0.6112 2.249 h = 0.001 0.003 y2[1] (numeric) = 3.23690130607 4.30787463408 y2[1] (closed_form) = 2.74982262126 3.8379528578 absolute error = 0.6768 relative error = 14.34 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.32874517989 -2.74679188664 y1[1] (closed_form) = 3.92435696629 -2.6892786967 absolute error = 0.4085 relative error = 8.586 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.23 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 = 50.23 Order of pole (three term test) = 32.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46456.2MB, alloc=44.3MB, time=573.60 x[1] = 0.6122 2.252 h = 0.0001 0.004 y2[1] (numeric) = 3.2553499392 4.32116536829 y2[1] (closed_form) = 2.76183735255 3.84704375246 absolute error = 0.6844 relative error = 14.45 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.3384426141 -2.76084475892 y1[1] (closed_form) = 3.93312863143 -2.70138867251 absolute error = 0.4097 relative error = 8.585 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.59 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 = 28.59 Order of pole (three term test) = 32.68 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46502.0MB, alloc=44.3MB, time=574.16 memory used=46548.1MB, alloc=44.3MB, time=574.72 x[1] = 0.6123 2.256 h = 0.003 0.006 y2[1] (numeric) = 3.27388695323 4.33448625819 y2[1] (closed_form) = 2.77305987175 3.86253582025 absolute error = 0.6882 relative error = 14.47 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.35542744616 -2.77433598555 y1[1] (closed_form) = 3.9482710263 -2.71284392966 absolute error = 0.4118 relative error = 8.596 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.19 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 = 38.19 Order of pole (three term test) = 32.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46593.9MB, alloc=44.3MB, time=575.28 memory used=46640.1MB, alloc=44.3MB, time=575.84 x[1] = 0.6153 2.262 h = 0.0001 0.005 y2[1] (numeric) = 3.29251272122 4.34783736406 y2[1] (closed_form) = 2.80128893047 3.87808904471 absolute error = 0.6797 relative error = 14.21 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.3716248248 -2.80705861787 y1[1] (closed_form) = 3.96313142925 -2.74117780503 absolute error = 0.4138 relative error = 8.587 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.19 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 = 17.19 Order of pole (three term test) = 32.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46686.1MB, alloc=44.3MB, time=576.41 x[1] = 0.6154 2.267 h = 0.0001 0.003 y2[1] (numeric) = 3.31122821846 4.36121840891 y2[1] (closed_form) = 2.81542813586 3.89767771929 absolute error = 0.6787 relative error = 14.12 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.39306726543 -2.82400338523 y1[1] (closed_form) = 3.98228997162 -2.75560835439 absolute error = 0.4164 relative error = 8.599 % Correct digits = 1 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) = 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 = 13.98 Order of pole (three term test) = 33.07 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46732.2MB, alloc=44.3MB, time=576.97 memory used=46778.5MB, alloc=44.3MB, time=577.54 x[1] = 0.6155 2.27 h = 0.001 0.001 y2[1] (numeric) = 3.3300339288 4.374629627 y2[1] (closed_form) = 2.82410702873 3.90936572043 absolute error = 0.6873 relative error = 14.25 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.40583896756 -2.83440204803 y1[1] (closed_form) = 3.9937185519 -2.76445800211 absolute error = 0.418 relative error = 8.606 % Correct digits = 1 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) = 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 = 11.04 Order of pole (three term test) = 33.13 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46824.6MB, alloc=44.3MB, time=578.11 memory used=46870.9MB, alloc=44.3MB, time=578.68 x[1] = 0.6165 2.271 h = 0.001 0.003 y2[1] (numeric) = 3.34892997186 4.38807116199 y2[1] (closed_form) = 2.83086911506 3.91059215462 absolute error = 0.7045 relative error = 14.59 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.40688084101 -2.84212287031 y1[1] (closed_form) = 3.99480104389 -2.77119546894 absolute error = 0.4181 relative error = 8.6 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.48 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 = 52.48 Order of pole (three term test) = 33.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=46916.8MB, alloc=44.3MB, time=579.25 memory used=46963.1MB, alloc=44.3MB, time=579.81 x[1] = 0.6175 2.274 h = 0.0001 0.004 y2[1] (numeric) = 3.36791638911 4.40154302148 y2[1] (closed_form) = 2.84320058341 3.91981251202 absolute error = 0.7123 relative error = 14.71 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.41670683906 -2.85659292181 y1[1] (closed_form) = 4.00370961631 -2.78362176308 absolute error = 0.4194 relative error = 8.601 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.88 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 = 29.88 Order of pole (three term test) = 33.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47009.0MB, alloc=44.3MB, time=580.37 x[1] = 0.6176 2.278 h = 0.003 0.006 y2[1] (numeric) = 3.38699331639 4.4150452435 y2[1] (closed_form) = 2.85475977361 3.93557923036 absolute error = 0.7164 relative error = 14.73 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.43400226071 -2.87054354018 y1[1] (closed_form) = 4.01913548201 -2.79541043664 absolute error = 0.4216 relative error = 8.612 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 39.91 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 = 39.91 Order of pole (three term test) = 33.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47054.8MB, alloc=44.3MB, time=580.93 memory used=47101.1MB, alloc=44.3MB, time=581.50 x[1] = 0.6206 2.284 h = 0.0001 0.005 y2[1] (numeric) = 3.4061611353 4.42857788746 y2[1] (closed_form) = 2.88369924671 3.95130945406 absolute error = 0.7076 relative error = 14.47 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.45034340614 -2.90418838498 y1[1] (closed_form) = 4.0341885128 -2.82445603622 absolute error = 0.4237 relative error = 8.604 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.96 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 = 17.96 Order of pole (three term test) = 33.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47147.0MB, alloc=44.3MB, time=582.06 memory used=47193.3MB, alloc=44.3MB, time=582.62 x[1] = 0.6207 2.289 h = 0.0001 0.003 y2[1] (numeric) = 3.42542084091 4.44214066462 y2[1] (closed_form) = 2.89826301712 3.9712459613 absolute error = 0.7069 relative error = 14.38 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.47217861161 -2.92171083717 y1[1] (closed_form) = 4.05370576382 -2.83930703709 absolute error = 0.4265 relative error = 8.618 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.6 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 = 14.6 Order of pole (three term test) = 33.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47239.3MB, alloc=44.3MB, time=583.19 x[1] = 0.6208 2.292 h = 0.001 0.001 y2[1] (numeric) = 3.44477292909 4.45573381156 y2[1] (closed_form) = 2.90720054244 3.98314014607 absolute error = 0.7158 relative error = 14.52 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.48518190678 -2.93246099817 y1[1] (closed_form) = 4.06534706154 -2.84841294434 absolute error = 0.4282 relative error = 8.626 % Correct digits = 1 memory used=47285.8MB, alloc=44.3MB, time=583.76 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 11.53 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 = 11.53 Order of pole (three term test) = 33.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47331.8MB, alloc=44.3MB, time=584.33 x[1] = 0.6218 2.293 h = 0.001 0.003 y2[1] (numeric) = 3.46421752289 4.46935747439 y2[1] (closed_form) = 2.914118286 3.98435417068 absolute error = 0.7334 relative error = 14.86 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.48618996237 -2.94037802879 y1[1] (closed_form) = 4.06642015043 -2.85530735073 absolute error = 0.4283 relative error = 8.62 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.84 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 = 54.84 Order of pole (three term test) = 33.84 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47377.7MB, alloc=44.3MB, time=584.90 memory used=47424.0MB, alloc=44.3MB, time=585.46 x[1] = 0.6228 2.296 h = 0.0001 0.004 y2[1] (numeric) = 3.48375466475 4.48301166066 y2[1] (closed_form) = 2.92677426394 3.99370531867 absolute error = 0.7414 relative error = 14.97 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.49614453006 -2.95527614594 y1[1] (closed_form) = 4.07546679373 -2.86805770628 absolute error = 0.4296 relative error = 8.621 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.22 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 = 31.22 Order of pole (three term test) = 33.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47470.0MB, alloc=44.3MB, time=586.02 memory used=47516.1MB, alloc=44.3MB, time=586.59 x[1] = 0.6229 2.3 h = 0.003 0.006 y2[1] (numeric) = 3.50338449372 4.49669640843 y2[1] (closed_form) = 2.93867907232 4.00975118017 absolute error = 0.7457 relative error = 15 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.5137545798 -2.96969937848 y1[1] (closed_form) = 4.09118041393 -2.88018876856 absolute error = 0.432 relative error = 8.633 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 41.7 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 = 41.7 Order of pole (three term test) = 34.04 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47562.0MB, alloc=44.3MB, time=587.16 x[1] = 0.6259 2.306 h = 0.0001 0.005 y2[1] (numeric) = 3.52310740011 4.51041177619 y2[1] (closed_form) = 2.96834582255 4.02565882568 absolute error = 0.7367 relative error = 14.73 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.53023617468 -3.00428946204 y1[1] (closed_form) = 4.10642616163 -2.90996284553 absolute error = 0.4342 relative error = 8.627 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.77 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 = 18.77 Order of pole (three term test) = 34.3 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47608.0MB, alloc=44.3MB, time=587.72 memory used=47654.2MB, alloc=44.3MB, time=588.28 x[1] = 0.626 2.311 h = 0.0001 0.003 y2[1] (numeric) = 3.5429243992 4.52415746308 y2[1] (closed_form) = 2.98334544747 4.04594885855 absolute error = 0.7361 relative error = 14.64 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.55246928432 -3.0224062304 y1[1] (closed_form) = 4.12630755614 -2.9252456206 absolute error = 0.4371 relative error = 8.642 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.26 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 = 15.26 Order of pole (three term test) = 34.42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47700.1MB, alloc=44.3MB, time=588.84 memory used=47746.6MB, alloc=44.3MB, time=589.42 x[1] = 0.6261 2.314 h = 0.001 0.001 y2[1] (numeric) = 3.56283599911 4.53793370801 y2[1] (closed_form) = 2.992548454 4.0580525654 absolute error = 0.7453 relative error = 14.78 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.56570712618 -3.03351795162 y1[1] (closed_form) = 4.13816475517 -2.93461465391 absolute error = 0.4388 relative error = 8.65 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.05 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 = 12.05 Order of pole (three term test) = 34.49 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47792.5MB, alloc=44.3MB, time=589.98 memory used=47838.8MB, alloc=44.3MB, time=590.56 x[1] = 0.6271 2.315 h = 0.001 0.003 y2[1] (numeric) = 3.58284232645 4.55174065957 y2[1] (closed_form) = 2.99962529186 4.05925312059 absolute error = 0.7633 relative error = 15.12 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.56667912953 -3.04163561751 y1[1] (closed_form) = 4.13922732232 -2.94166939345 absolute error = 0.439 relative error = 8.645 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.31 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 = 57.31 Order of pole (three term test) = 34.56 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47884.6MB, alloc=44.3MB, time=591.12 x[1] = 0.6281 2.318 h = 0.0001 0.004 y2[1] (numeric) = 3.60294342465 4.56557832523 y2[1] (closed_form) = 3.01261373041 4.06873637096 absolute error = 0.7716 relative error = 15.24 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.57676221536 -3.05697292937 y1[1] (closed_form) = 4.14841318746 -2.95475173342 absolute error = 0.4404 relative error = 8.647 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.63 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 = 32.63 Order of pole (three term test) = 34.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=47930.6MB, alloc=44.3MB, time=591.68 memory used=47976.8MB, alloc=44.3MB, time=592.25 x[1] = 0.6282 2.322 h = 0.003 0.006 y2[1] (numeric) = 3.62313943601 4.57944674309 y2[1] (closed_form) = 3.02487332681 4.08506591489 absolute error = 0.7761 relative error = 15.27 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.59469095187 -3.07188231441 y1[1] (closed_form) = 4.16441889718 -2.96723437995 absolute error = 0.4428 relative error = 8.66 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.58 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 = 43.58 Order of pole (three term test) = 34.77 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48022.7MB, alloc=44.3MB, time=592.81 memory used=48068.9MB, alloc=44.3MB, time=593.37 x[1] = 0.6312 2.328 h = 0.0001 0.005 y2[1] (numeric) = 3.64343075978 4.59334597066 y2[1] (closed_form) = 3.05528458987 4.10115131606 absolute error = 0.7669 relative error = 15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.61130948335 -3.10744115851 y1[1] (closed_form) = 4.17985736882 -2.99775406456 absolute error = 0.4452 relative error = 8.655 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.61 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 = 19.61 Order of pole (three term test) = 35.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48114.7MB, alloc=44.3MB, time=593.94 x[1] = 0.6313 2.333 h = 0.0001 0.003 y2[1] (numeric) = 3.66381843182 4.60727569457 y2[1] (closed_form) = 3.07073163997 4.12180062707 absolute error = 0.7664 relative error = 14.91 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.63394566313 -3.12616927202 y1[1] (closed_form) = 4.20010840701 -3.01348021829 absolute error = 0.4482 relative error = 8.671 % Correct digits = 1 memory used=48160.9MB, alloc=44.3MB, time=594.50 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.95 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 = 15.95 Order of pole (three term test) = 35.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48207.0MB, alloc=44.3MB, time=595.07 x[1] = 0.6314 2.336 h = 0.001 0.001 y2[1] (numeric) = 3.68430297278 4.62123615605 y2[1] (closed_form) = 3.08020714636 4.13411722804 absolute error = 0.776 relative error = 15.05 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.64742101793 -3.13765285522 y1[1] (closed_form) = 4.21218472829 -3.02311941454 absolute error = 0.4501 relative error = 8.68 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 12.59 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 = 12.59 Order of pole (three term test) = 35.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48253.1MB, alloc=44.3MB, time=595.64 memory used=48299.3MB, alloc=44.3MB, time=596.20 x[1] = 0.6324 2.337 h = 0.0001 0.004 y2[1] (numeric) = 3.70488451295 4.63522750623 y2[1] (closed_form) = 3.08744658502 4.13530321073 absolute error = 0.7945 relative error = 15.39 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.64835466153 -3.14597567013 y1[1] (closed_form) = 4.21323561284 -3.03033795145 absolute error = 0.4502 relative error = 8.675 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 75.78 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 = 75.78 Order of pole (three term test) = 35.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48345.2MB, alloc=44.3MB, time=596.77 memory used=48391.4MB, alloc=44.3MB, time=597.33 x[1] = 0.6325 2.341 h = 0.003 0.006 y2[1] (numeric) = 3.72556310504 4.64924979542 y2[1] (closed_form) = 3.10001563431 4.15188498863 absolute error = 0.7992 relative error = 15.42 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.66655208422 -3.1613007566 y1[1] (closed_form) = 4.22950059531 -3.04312721717 absolute error = 0.4527 relative error = 8.689 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.26 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 = 45.26 Order of pole (three term test) = 35.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48437.2MB, alloc=44.3MB, time=597.90 x[1] = 0.6355 2.347 h = 0.0001 0.005 y2[1] (numeric) = 3.74633912909 4.66330307825 y2[1] (closed_form) = 3.13107972055 4.1681327478 absolute error = 0.7898 relative error = 15.15 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.68328189857 -3.19768523594 y1[1] (closed_form) = 4.24511406388 -3.07430041286 absolute error = 0.4552 relative error = 8.685 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.37 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 = 20.37 Order of pole (three term test) = 35.75 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48483.1MB, alloc=44.3MB, time=598.46 memory used=48529.2MB, alloc=44.3MB, time=599.02 x[1] = 0.6356 2.352 h = 0.0001 0.003 y2[1] (numeric) = 3.7672136391 4.67738703048 y2[1] (closed_form) = 3.1469170103 4.18910148795 absolute error = 0.7894 relative error = 15.07 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.70625793422 -3.21693611092 y1[1] (closed_form) = 4.26569320812 -3.09041323113 absolute error = 0.4584 relative error = 8.702 % Correct digits = 1 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) = 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 = 16.57 Order of pole (three term test) = 35.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48575.1MB, alloc=44.3MB, time=599.58 memory used=48621.5MB, alloc=44.3MB, time=600.16 x[1] = 0.6357 2.355 h = 0.001 0.001 y2[1] (numeric) = 3.78818716674 4.69150189546 y2[1] (closed_form) = 3.15663023723 4.20160742994 absolute error = 0.7993 relative error = 15.21 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.71993349064 -3.22873763153 y1[1] (closed_form) = 4.27796408543 -3.10028807943 absolute error = 0.4603 relative error = 8.712 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.08 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 = 13.08 Order of pole (three term test) = 35.98 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48667.5MB, alloc=44.3MB, time=600.72 memory used=48713.7MB, alloc=44.3MB, time=601.29 x[1] = 0.6367 2.356 h = 0.001 0.003 y2[1] (numeric) = 3.80925984549 4.70564782658 y2[1] (closed_form) = 3.16401269139 4.20278194686 absolute error = 0.8181 relative error = 15.55 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.72083334767 -3.23723491905 y1[1] (closed_form) = 4.27900595988 -3.10765059541 absolute error = 0.4604 relative error = 8.707 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 62.21 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 = 62.21 Order of pole (three term test) = 36.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48759.7MB, alloc=44.3MB, time=601.85 x[1] = 0.6377 2.359 h = 0.0001 0.004 y2[1] (numeric) = 3.83043172061 4.71982483115 y2[1] (closed_form) = 3.17763994142 4.21251863259 absolute error = 0.8267 relative error = 15.67 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.73115171138 -3.25340716532 y1[1] (closed_form) = 4.28845808499 -3.12137071078 absolute error = 0.462 relative error = 8.71 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.41 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 = 35.41 Order of pole (three term test) = 36.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48805.5MB, alloc=44.3MB, time=602.41 memory used=48851.6MB, alloc=44.3MB, time=602.98 x[1] = 0.6378 2.363 h = 0.003 0.006 y2[1] (numeric) = 3.85170294073 4.73403294732 y2[1] (closed_form) = 3.19058139701 4.2293927791 absolute error = 0.8317 relative error = 15.7 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.74967531063 -3.26924409412 y1[1] (closed_form) = 4.30502347555 -3.13452923039 absolute error = 0.4646 relative error = 8.725 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.3 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 = 47.3 Order of pole (three term test) = 36.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48897.4MB, alloc=44.3MB, time=603.54 memory used=48943.7MB, alloc=44.3MB, time=604.10 x[1] = 0.6408 2.369 h = 0.0001 0.005 y2[1] (numeric) = 3.87307392222 4.74827223073 y2[1] (closed_form) = 3.22242308632 4.24581888182 absolute error = 0.8221 relative error = 15.42 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.76653507045 -3.30664182459 y1[1] (closed_form) = 4.3208296641 -3.16648094202 absolute error = 0.4672 relative error = 8.722 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.29 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 = 21.29 Order of pole (three term test) = 36.63 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=48989.6MB, alloc=44.3MB, time=604.66 x[1] = 0.6409 2.374 h = 0.0001 0.003 y2[1] (numeric) = 3.89454574045 4.76254234395 y2[1] (closed_form) = 3.23873003246 4.2671579084 absolute error = 0.8219 relative error = 15.34 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.78992371388 -3.32653637205 y1[1] (closed_form) = 4.34178900616 -3.18305943739 absolute error = 0.4705 relative error = 8.74 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.31 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 = 17.31 Order of pole (three term test) = 36.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49035.7MB, alloc=44.3MB, time=605.22 memory used=49081.8MB, alloc=44.3MB, time=605.79 x[1] = 0.641 2.377 h = 0.001 0.001 y2[1] (numeric) = 3.91611894022 4.77684353264 y2[1] (closed_form) = 3.24872924415 4.27988319678 absolute error = 0.8321 relative error = 15.49 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.80384225251 -3.33872931273 y1[1] (closed_form) = 4.354285186 -3.19321797012 absolute error = 0.4725 relative error = 8.751 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 13.67 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 = 13.67 Order of pole (three term test) = 36.89 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49127.7MB, alloc=44.3MB, time=606.35 memory used=49174.0MB, alloc=44.3MB, time=606.92 x[1] = 0.642 2.378 h = 0.001 0.003 y2[1] (numeric) = 3.9377936588 4.7911759528 y2[1] (closed_form) = 3.25628102758 4.28104101275 absolute error = 0.8513 relative error = 15.83 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.80469931181 -3.34744026771 y1[1] (closed_form) = 4.35531314422 -3.20075093719 absolute error = 0.4727 relative error = 8.746 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 65.01 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 = 65.01 Order of pole (three term test) = 36.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49219.9MB, alloc=44.3MB, time=607.48 memory used=49266.2MB, alloc=44.3MB, time=608.05 x[1] = 0.643 2.381 h = 0.0001 0.004 y2[1] (numeric) = 3.95956994253 4.80553961164 y2[1] (closed_form) = 3.27026449028 4.29091355576 absolute error = 0.8602 relative error = 15.94 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.81514570401 -3.36408464288 y1[1] (closed_form) = 4.36490780396 -3.21482671857 absolute error = 0.4743 relative error = 8.75 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.01 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 = 37.01 Order of pole (three term test) = 37.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49312.1MB, alloc=44.3MB, time=608.61 x[1] = 0.6431 2.385 h = 0.003 0.006 y2[1] (numeric) = 3.98144794349 4.81993454728 y2[1] (closed_form) = 3.28358818782 4.30808474599 absolute error = 0.8654 relative error = 15.98 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.83399959183 -3.38044791816 y1[1] (closed_form) = 4.38177808635 -3.22836435468 absolute error = 0.4771 relative error = 8.766 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 49.43 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 = 49.43 Order of pole (three term test) = 37.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49358.0MB, alloc=44.3MB, time=609.16 memory used=49404.2MB, alloc=44.3MB, time=609.73 x[1] = 0.6461 2.391 h = 0.0001 0.005 y2[1] (numeric) = 4.00342808758 4.83436081419 y2[1] (closed_form) = 3.3162258284 4.32468925527 absolute error = 0.8556 relative error = 15.7 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.85098517397 -3.41888393018 y1[1] (closed_form) = 4.39777674958 -3.26111283605 absolute error = 0.4799 relative error = 8.765 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.24 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 = 22.24 Order of pole (three term test) = 37.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49450.1MB, alloc=44.3MB, time=610.28 memory used=49496.3MB, alloc=44.3MB, time=610.85 x[1] = 0.6462 2.396 h = 0.0001 0.003 y2[1] (numeric) = 4.02551147189 4.84881806133 y2[1] (closed_form) = 3.33301484229 4.34640449415 absolute error = 0.8556 relative error = 15.62 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.87479166211 -3.43944039458 y1[1] (closed_form) = 4.41912197889 -3.27816945511 absolute error = 0.4834 relative error = 8.785 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.09 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 = 18.09 Order of pole (three term test) = 37.76 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49542.2MB, alloc=44.3MB, time=611.42 memory used=49588.6MB, alloc=44.3MB, time=611.99 x[1] = 0.6463 2.399 h = 0.001 0.001 y2[1] (numeric) = 4.04769865463 4.86330653663 y2[1] (closed_form) = 3.34330756538 4.35935259868 absolute error = 0.8661 relative error = 15.77 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.88895618153 -3.45203578976 y1[1] (closed_form) = 4.43184678939 -3.28861921811 absolute error = 0.4854 relative error = 8.796 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.28 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 = 14.28 Order of pole (three term test) = 37.87 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49634.5MB, alloc=44.3MB, time=612.55 x[1] = 0.6473 2.4 h = 0.001 0.003 y2[1] (numeric) = 4.06998977702 4.87782639872 y2[1] (closed_form) = 3.35103239112 4.36049248037 absolute error = 0.8857 relative error = 16.11 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.88976790983 -3.46096518917 y1[1] (closed_form) = 4.43285954324 -3.29632631046 absolute error = 0.4857 relative error = 8.792 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.93 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 = 67.93 Order of pole (three term test) = 37.95 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49680.4MB, alloc=44.3MB, time=613.11 memory used=49726.8MB, alloc=44.3MB, time=613.68 x[1] = 0.6483 2.403 h = 0.0001 0.004 y2[1] (numeric) = 4.09238488642 4.89237765472 y2[1] (closed_form) = 3.36538074432 4.37050212057 absolute error = 0.8949 relative error = 16.22 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.9003420294 -3.47809382456 y1[1] (closed_form) = 4.4425978293 -3.31076641297 absolute error = 0.4874 relative error = 8.796 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.67 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 = 38.67 Order of pole (three term test) = 38.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49772.6MB, alloc=44.3MB, time=614.24 memory used=49818.7MB, alloc=44.3MB, time=614.80 x[1] = 0.6484 2.407 h = 0.003 0.006 y2[1] (numeric) = 4.11488413852 4.90696034271 y2[1] (closed_form) = 3.37909676302 4.38797507595 absolute error = 0.9004 relative error = 16.26 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 4.91953033231 -3.4949982945 y1[1] (closed_form) = 4.45977753786 -3.32469327214 absolute error = 0.4903 relative error = 8.814 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 51.65 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 = 51.65 Order of pole (three term test) = 38.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49864.7MB, alloc=44.3MB, time=615.36 x[1] = 0.6514 2.413 h = 0.0001 0.005 y2[1] (numeric) = 4.1374879689 4.92157451591 y2[1] (closed_form) = 3.41254910758 4.40475795047 absolute error = 0.8903 relative error = 15.98 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 4.93663738936 -3.53449815273 y1[1] (closed_form) = 4.47596833239 -3.3582571852 absolute error = 0.4932 relative error = 8.814 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.24 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 = 23.24 Order of pole (three term test) = 38.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=49910.7MB, alloc=44.3MB, time=615.92 memory used=49956.7MB, alloc=44.3MB, time=616.48 x[1] = 0.6515 2.418 h = 0.0001 0.003 y2[1] (numeric) = 4.1601974968 4.93621980924 y2[1] (closed_form) = 3.42983290809 4.42685538664 absolute error = 0.8904 relative error = 15.9 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 4.9608669788 -3.55573521164 y1[1] (closed_form) = 4.49770520283 -3.37580468256 absolute error = 0.4969 relative error = 8.836 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.9 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 = 18.9 Order of pole (three term test) = 38.81 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50002.5MB, alloc=44.3MB, time=617.04 memory used=50048.8MB, alloc=44.3MB, time=617.62 x[1] = 0.6516 2.421 h = 0.001 0.001 y2[1] (numeric) = 4.18301329418 4.95089647289 y2[1] (closed_form) = 3.44042685499 4.44002981021 absolute error = 0.9013 relative error = 16.05 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 4.97528048569 -3.56874435678 y1[1] (closed_form) = 4.51066200847 -3.38655340776 absolute error = 0.4991 relative error = 8.848 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 14.93 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 = 14.93 Order of pole (three term test) = 38.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50094.9MB, alloc=44.3MB, time=618.18 memory used=50141.2MB, alloc=44.3MB, time=618.76 x[1] = 0.6526 2.422 h = 0.001 0.003 y2[1] (numeric) = 4.20593550626 4.96560466818 y2[1] (closed_form) = 3.44832851081 4.44115047575 absolute error = 0.9214 relative error = 16.39 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 4.9760442681 -3.57789707026 y1[1] (closed_form) = 4.51165822224 -3.39443837542 absolute error = 0.4993 relative error = 8.844 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.99 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 = 70.99 Order of pole (three term test) = 39.02 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50187.1MB, alloc=44.3MB, time=619.32 x[1] = 0.6536 2.425 h = 0.0001 0.004 y2[1] (numeric) = 4.22896418151 4.98034440211 y2[1] (closed_form) = 3.46305063068 4.45129843048 absolute error = 0.9309 relative error = 16.51 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 4.98674574286 -3.59552236506 y1[1] (closed_form) = 4.52154120685 -3.40925165377 absolute error = 0.5011 relative error = 8.849 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.41 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 = 40.41 Order of pole (three term test) = 39.18 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50233.0MB, alloc=44.3MB, time=619.88 memory used=50279.1MB, alloc=44.3MB, time=620.45 x[1] = 0.6537 2.429 h = 0.003 0.006 y2[1] (numeric) = 4.25209947925 4.9951157127 y2[1] (closed_form) = 3.47716929898 4.46907791851 absolute error = 0.9366 relative error = 16.54 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.00627260024 -3.61298322955 y1[1] (closed_form) = 4.53903492619 -3.42357809219 absolute error = 0.5042 relative error = 8.868 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 53.97 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 = 53.97 Order of pole (three term test) = 39.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50325.0MB, alloc=44.3MB, time=621.01 memory used=50371.2MB, alloc=44.3MB, time=621.57 x[1] = 0.6567 2.435 h = 0.0001 0.005 y2[1] (numeric) = 4.27534184497 5.00991865186 y2[1] (closed_form) = 3.51145551328 4.48603900829 absolute error = 0.9263 relative error = 16.26 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.02349655254 -3.65357304341 y1[1] (closed_form) = 4.55541740609 -3.45797651547 absolute error = 0.5073 relative error = 8.87 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.29 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 = 24.29 Order of pole (three term test) = 39.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50417.0MB, alloc=44.3MB, time=622.14 memory used=50463.2MB, alloc=44.3MB, time=622.70 x[1] = 0.6568 2.44 h = 0.0001 0.003 y2[1] (numeric) = 4.29869242052 5.02475284003 y2[1] (closed_form) = 3.529247134 4.50852468558 absolute error = 0.9266 relative error = 16.18 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.04815451742 -3.67550981712 y1[1] (closed_form) = 4.5775517356 -3.47602796084 absolute error = 0.5111 relative error = 8.893 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.75 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 = 19.75 Order of pole (three term test) = 39.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50509.3MB, alloc=44.3MB, time=623.27 x[1] = 0.6569 2.443 h = 0.001 0.001 y2[1] (numeric) = 4.32215179188 5.03961852964 y2[1] (closed_form) = 3.54015020724 4.52192896401 absolute error = 0.9378 relative error = 16.33 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.06282002527 -3.68894427452 y1[1] (closed_form) = 4.59074393688 -3.48708357059 absolute error = 0.5134 relative error = 8.906 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 15.6 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 = 15.6 Order of pole (three term test) = 40.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50555.3MB, alloc=44.3MB, time=623.83 memory used=50601.7MB, alloc=44.3MB, time=624.40 x[1] = 0.6579 2.444 h = 0.0001 0.004 y2[1] (numeric) = 4.3457201084 5.05451588474 y2[1] (closed_form) = 3.54823255705 4.52302908153 absolute error = 0.9584 relative error = 16.67 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.06353316296 -3.69832526596 y1[1] (closed_form) = 4.59172222586 -3.49515024083 absolute error = 0.5137 relative error = 8.902 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 93.86 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 = 93.86 Order of pole (three term test) = 40.16 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50647.7MB, alloc=44.3MB, time=624.96 memory used=50693.6MB, alloc=44.3MB, time=625.52 x[1] = 0.658 2.448 h = 0.003 0.006 y2[1] (numeric) = 4.36939743018 5.06944495967 y2[1] (closed_form) = 3.56270254849 4.54108124387 absolute error = 0.9643 relative error = 16.71 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.08334531908 -3.71626166245 y1[1] (closed_form) = 4.60949487706 -3.50982529582 absolute error = 0.5169 relative error = 8.921 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 56.06 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 = 56.06 Order of pole (three term test) = 40.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50739.5MB, alloc=44.3MB, time=626.08 x[1] = 0.661 2.454 h = 0.0001 0.005 y2[1] (numeric) = 4.39318418131 5.08440580371 y2[1] (closed_form) = 3.59772008088 4.55820578055 absolute error = 0.9538 relative error = 16.42 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.10066301068 -3.75778012055 y1[1] (closed_form) = 4.62605217232 -3.54495536553 absolute error = 0.5201 relative error = 8.925 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.23 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 = 25.23 Order of pole (three term test) = 40.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50785.6MB, alloc=44.3MB, time=626.64 memory used=50831.6MB, alloc=44.3MB, time=627.21 x[1] = 0.6611 2.459 h = 0.0001 0.003 y2[1] (numeric) = 4.41708152355 5.09939802472 y2[1] (closed_form) = 3.61595477519 4.58103679374 absolute error = 0.9542 relative error = 16.35 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.12568199479 -3.78031492848 y1[1] (closed_form) = 4.64853954973 -3.56344647442 absolute error = 0.5241 relative error = 8.948 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.52 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 = 20.52 Order of pole (three term test) = 40.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50877.6MB, alloc=44.3MB, time=627.77 memory used=50924.1MB, alloc=44.3MB, time=628.34 x[1] = 0.6612 2.462 h = 0.001 0.001 y2[1] (numeric) = 4.4410900552 5.11442187721 y2[1] (closed_form) = 3.62712761469 4.59464559397 absolute error = 0.9658 relative error = 16.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.14055980905 -3.79411284875 y1[1] (closed_form) = 4.66194090971 -3.57476987297 absolute error = 0.5265 relative error = 8.962 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.2 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 = 16.2 Order of pole (three term test) = 41.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=50970.0MB, alloc=44.3MB, time=628.90 memory used=51016.3MB, alloc=44.3MB, time=629.48 x[1] = 0.6622 2.463 h = 0.001 0.003 y2[1] (numeric) = 4.46520992922 5.12947752765 y2[1] (closed_form) = 3.63536892048 4.59572913514 absolute error = 0.9867 relative error = 16.84 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.14122861539 -3.80368793652 y1[1] (closed_form) = 4.66290485018 -3.58299630844 absolute error = 0.5268 relative error = 8.958 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 77.05 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 = 77.05 Order of pole (three term test) = 41.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51062.3MB, alloc=44.3MB, time=630.04 x[1] = 0.6632 2.466 h = 0.0001 0.004 y2[1] (numeric) = 4.48944119617 5.14456498283 y2[1] (closed_form) = 3.65080917389 4.60614232864 absolute error = 0.9966 relative error = 16.96 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.15216235493 -3.82225690395 y1[1] (closed_form) = 4.67306456932 -3.59852649588 absolute error = 0.5288 relative error = 8.965 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 43.86 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 = 43.86 Order of pole (three term test) = 41.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51108.2MB, alloc=44.3MB, time=630.60 memory used=51154.2MB, alloc=44.3MB, time=631.17 x[1] = 0.6633 2.47 h = 0.003 0.006 y2[1] (numeric) = 4.51378402238 5.15968428066 y2[1] (closed_form) = 3.6657016591 4.62451014697 absolute error = 1.003 relative error = 16.99 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.17232068249 -3.84077852936 y1[1] (closed_form) = 4.69116002563 -3.61362102885 absolute error = 0.5321 relative error = 8.986 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 58.58 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 = 58.58 Order of pole (three term test) = 41.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51200.1MB, alloc=44.3MB, time=631.73 memory used=51246.5MB, alloc=44.3MB, time=632.30 x[1] = 0.6663 2.476 h = 0.0001 0.005 y2[1] (numeric) = 4.53823887237 5.17483547047 y2[1] (closed_form) = 3.70158985853 4.64181255524 absolute error = 0.992 relative error = 16.71 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.18974621971 -3.88343631345 y1[1] (closed_form) = 4.70790812678 -3.64962225621 absolute error = 0.5356 relative error = 8.991 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.37 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 = 26.37 Order of pole (three term test) = 42 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51292.3MB, alloc=44.3MB, time=632.85 x[1] = 0.6664 2.481 h = 0.0001 0.003 y2[1] (numeric) = 4.56280693134 5.1900181449 y2[1] (closed_form) = 3.72035741483 4.66504337581 absolute error = 0.9926 relative error = 16.64 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.21520328927 -3.90670712303 y1[1] (closed_form) = 4.73080412314 -3.66864242567 absolute error = 0.5397 relative error = 9.016 % Correct digits = 1 memory used=51338.5MB, alloc=44.3MB, time=633.42 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.44 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 = 21.44 Order of pole (three term test) = 42.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51384.6MB, alloc=44.3MB, time=633.98 x[1] = 0.6665 2.484 h = 0.001 0.001 y2[1] (numeric) = 4.58748881228 5.20523256067 y2[1] (closed_form) = 3.73185456364 4.67888879678 absolute error = 1.005 relative error = 16.79 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.23033864352 -3.92095230043 y1[1] (closed_form) = 4.74444740117 -3.68028793084 absolute error = 0.5422 relative error = 9.03 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 16.93 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 = 16.93 Order of pole (three term test) = 42.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51430.5MB, alloc=44.3MB, time=634.54 memory used=51476.9MB, alloc=44.3MB, time=635.12 x[1] = 0.6675 2.485 h = 0.001 0.003 y2[1] (numeric) = 4.61228467247 5.22047888705 y2[1] (closed_form) = 3.74028397821 4.67994922159 absolute error = 1.026 relative error = 17.12 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.23095161934 -3.93076503074 y1[1] (closed_form) = 4.74539075231 -3.68870341896 absolute error = 0.5426 relative error = 9.027 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 80.52 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 = 80.52 Order of pole (three term test) = 42.5 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51522.8MB, alloc=44.3MB, time=635.68 memory used=51569.1MB, alloc=44.3MB, time=636.25 x[1] = 0.6685 2.488 h = 0.0001 0.004 y2[1] (numeric) = 4.63719456361 5.23575713067 y2[1] (closed_form) = 3.75612451186 4.69050418762 absolute error = 1.036 relative error = 17.24 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.24201123528 -3.94986733642 y1[1] (closed_form) = 4.75569822927 -3.70463324263 absolute error = 0.5446 relative error = 9.035 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 45.84 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 = 45.84 Order of pole (three term test) = 42.69 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51615.0MB, alloc=44.3MB, time=636.81 x[1] = 0.6686 2.492 h = 0.003 0.006 y2[1] (numeric) = 4.66221865594 5.25106732936 y2[1] (closed_form) = 3.77145056436 4.70919256305 absolute error = 1.043 relative error = 17.28 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.26251990381 -3.96899046571 y1[1] (closed_form) = 4.7741212205 -3.7201583557 absolute error = 0.5481 relative error = 9.056 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.22 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 = 61.22 Order of pole (three term test) = 42.9 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51660.7MB, alloc=44.3MB, time=637.37 memory used=51706.9MB, alloc=44.3MB, time=637.94 x[1] = 0.6716 2.498 h = 0.0001 0.005 y2[1] (numeric) = 4.68735742449 5.26640953087 y2[1] (closed_form) = 3.80822982829 4.7266723617 absolute error = 1.032 relative error = 17 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.2800479832 -4.01281534367 y1[1] (closed_form) = 4.79105936726 -3.75705106045 absolute error = 0.5518 relative error = 9.064 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.55 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 = 27.55 Order of pole (three term test) = 43.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51752.7MB, alloc=44.3MB, time=638.50 memory used=51798.8MB, alloc=44.3MB, time=639.07 x[1] = 0.6717 2.503 h = 0.0001 0.003 y2[1] (numeric) = 4.71261207834 5.28178331209 y2[1] (closed_form) = 3.82754422098 4.7503092042 absolute error = 1.032 relative error = 16.92 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.30594845462 -4.03684262833 y1[1] (closed_form) = 4.81436998555 -3.77661430197 absolute error = 0.5562 relative error = 9.09 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.4 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 = 22.4 Order of pole (three term test) = 43.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51844.8MB, alloc=44.3MB, time=639.64 memory used=51891.1MB, alloc=44.3MB, time=640.21 x[1] = 0.6718 2.506 h = 0.001 0.001 y2[1] (numeric) = 4.73798324545 5.29718893192 y2[1] (closed_form) = 3.8393741499 4.76439487701 absolute error = 1.045 relative error = 17.07 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.3213443762 -4.0515474405 y1[1] (closed_form) = 4.82825868595 -3.78859040506 absolute error = 0.5588 relative error = 9.105 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 17.69 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 = 17.69 Order of pole (three term test) = 43.78 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51937.2MB, alloc=44.3MB, time=640.78 x[1] = 0.6728 2.507 h = 0.001 0.003 y2[1] (numeric) = 4.76347108753 5.31262656246 y2[1] (closed_form) = 3.84799576374 4.76543070305 absolute error = 1.067 relative error = 17.41 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.32189856384 -4.06160306303 y1[1] (closed_form) = 4.82917991522 -3.79719900265 absolute error = 0.5592 relative error = 9.102 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 84.14 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 = 84.14 Order of pole (three term test) = 43.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=51983.2MB, alloc=44.3MB, time=641.34 memory used=52029.4MB, alloc=44.3MB, time=641.91 x[1] = 0.6738 2.51 h = 0.0001 0.004 y2[1] (numeric) = 4.7890756575 5.32809621021 y2[1] (closed_form) = 3.86424626128 4.77612855955 absolute error = 1.077 relative error = 17.53 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.33308337636 -4.08125221266 y1[1] (closed_form) = 4.8396361343 -3.8135381292 absolute error = 0.5614 relative error = 9.111 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.9 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 = 47.9 Order of pole (three term test) = 44.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52075.2MB, alloc=44.3MB, time=642.47 memory used=52121.4MB, alloc=44.3MB, time=643.04 x[1] = 0.6739 2.514 h = 0.003 0.006 y2[1] (numeric) = 4.81479712953 5.34359791284 y2[1] (closed_form) = 3.88001722702 4.79514243824 absolute error = 1.084 relative error = 17.57 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.35394656122 -4.10099350367 y1[1] (closed_form) = 4.85839143919 -3.8295051972 absolute error = 0.565 relative error = 9.134 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 63.97 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 = 63.97 Order of pole (three term test) = 44.31 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52167.2MB, alloc=44.3MB, time=643.60 x[1] = 0.6769 2.52 h = 0.0001 0.005 y2[1] (numeric) = 4.84063598945 5.35913171649 y2[1] (closed_form) = 3.91770840057 4.81279901914 absolute error = 1.073 relative error = 17.28 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.371571614 -4.14601383051 y1[1] (closed_form) = 4.87551875 -3.86731014983 absolute error = 0.569 relative error = 9.143 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.79 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 = 28.79 Order of pole (three term test) = 44.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52213.3MB, alloc=44.3MB, time=644.16 memory used=52259.3MB, alloc=44.3MB, time=644.72 x[1] = 0.677 2.525 h = 0.0001 0.003 y2[1] (numeric) = 4.86659347061 5.37469718179 y2[1] (closed_form) = 3.93758394804 4.83684815568 absolute error = 1.073 relative error = 17.21 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.39792081255 -4.17081854573 y1[1] (closed_form) = 4.89925005558 -3.88743081918 absolute error = 0.5736 relative error = 9.171 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.41 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 = 23.41 Order of pole (three term test) = 45.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52305.2MB, alloc=44.3MB, time=645.28 memory used=52351.4MB, alloc=44.3MB, time=645.85 x[1] = 0.6771 2.528 h = 0.001 0.001 y2[1] (numeric) = 4.89267021634 5.39029456979 y2[1] (closed_form) = 3.94975533565 4.85117774336 absolute error = 1.086 relative error = 17.36 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.41358032997 -4.18599566073 y1[1] (closed_form) = 4.91338771749 -3.89974621946 absolute error = 0.5763 relative error = 9.187 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 18.49 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 = 18.49 Order of pole (three term test) = 45.25 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52397.5MB, alloc=44.3MB, time=646.42 memory used=52443.9MB, alloc=44.3MB, time=646.99 x[1] = 0.6781 2.529 h = 0.001 0.003 y2[1] (numeric) = 4.91886639289 5.40592405549 y2[1] (closed_form) = 3.95857332111 4.85218743216 absolute error = 1.109 relative error = 17.7 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.41407267826 -4.19629952572 y1[1] (closed_form) = 4.91428523721 -3.90855206623 absolute error = 0.5767 relative error = 9.184 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 87.92 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 = 87.92 Order of pole (three term test) = 45.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52489.9MB, alloc=44.3MB, time=647.55 x[1] = 0.6791 2.532 h = 0.0001 0.004 y2[1] (numeric) = 4.94518205438 5.42158564522 y2[1] (closed_form) = 3.97524368644 4.86302926663 absolute error = 1.119 relative error = 17.82 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.42538192053 -4.21650932068 y1[1] (closed_form) = 4.92489115507 -3.92531038362 absolute error = 0.579 relative error = 9.194 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.05 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 = 50.05 Order of pole (three term test) = 45.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52535.8MB, alloc=44.3MB, time=648.11 memory used=52581.9MB, alloc=44.3MB, time=648.68 x[1] = 0.6792 2.536 h = 0.003 0.006 y2[1] (numeric) = 4.97161737905 5.4372793765 y2[1] (closed_form) = 3.99147119016 4.88237363938 absolute error = 1.126 relative error = 17.86 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.44660380085 -4.2368858226 y1[1] (closed_form) = 4.94398360079 -3.94173106036 absolute error = 0.5829 relative error = 9.218 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 66.85 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 = 66.85 Order of pole (three term test) = 45.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52627.7MB, alloc=44.3MB, time=649.24 memory used=52673.9MB, alloc=44.3MB, time=649.80 x[1] = 0.6822 2.542 h = 0.0001 0.005 y2[1] (numeric) = 4.99817286372 5.4530052937 y2[1] (closed_form) = 4.03009557541 4.9002062623 absolute error = 1.115 relative error = 17.57 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.46431998372 -4.28313055197 y1[1] (closed_form) = 4.9612990676 -3.9804694914 absolute error = 0.5871 relative error = 9.229 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.09 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 = 30.09 Order of pole (three term test) = 46.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52719.8MB, alloc=44.3MB, time=650.37 memory used=52766.0MB, alloc=44.3MB, time=650.93 x[1] = 0.6823 2.547 h = 0.0001 0.003 y2[1] (numeric) = 5.02484976652 5.46876294078 y2[1] (closed_form) = 4.05054694806 4.9246740221 absolute error = 1.116 relative error = 17.5 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.49112324095 -4.30873414591 y1[1] (closed_form) = 4.9854571876 -4.00116229662 absolute error = 0.5919 relative error = 9.259 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.47 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 = 24.47 Order of pole (three term test) = 46.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52812.0MB, alloc=44.3MB, time=651.50 x[1] = 0.6824 2.55 h = 0.001 0.001 y2[1] (numeric) = 5.05164874644 5.48455258088 y2[1] (closed_form) = 4.06306868549 4.93925121926 absolute error = 1.129 relative error = 17.65 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.50704938229 -4.32439652863 y1[1] (closed_form) = 4.99984738453 -4.01382590613 absolute error = 0.5947 relative error = 9.276 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 19.32 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 = 19.32 Order of pole (three term test) = 46.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52858.0MB, alloc=44.3MB, time=652.06 memory used=52904.3MB, alloc=44.3MB, time=652.63 x[1] = 0.6834 2.551 h = 0.0001 0.004 y2[1] (numeric) = 5.07856997444 5.50037439192 y2[1] (closed_form) = 4.07208729836 4.94023317466 absolute error = 1.152 relative error = 17.99 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.50747674393 -4.33495408861 y1[1] (closed_form) = 5.00071955024 -4.02283322617 absolute error = 0.5952 relative error = 9.273 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 116.3 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 = 116.3 Order of pole (three term test) = 46.94 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=52950.1MB, alloc=44.3MB, time=653.19 memory used=52996.3MB, alloc=44.3MB, time=653.76 x[1] = 0.6835 2.555 h = 0.003 0.006 y2[1] (numeric) = 5.10561351895 5.51622843253 y2[1] (closed_form) = 4.08871328253 4.95987168794 absolute error = 1.159 relative error = 18.03 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.52900073065 -4.35587324466 y1[1] (closed_form) = 5.02011169522 -4.03964980887 absolute error = 0.5991 relative error = 9.298 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 69.44 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 = 69.44 Order of pole (three term test) = 47.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53042.2MB, alloc=44.3MB, time=654.32 x[1] = 0.6865 2.561 h = 0.0001 0.005 y2[1] (numeric) = 5.13277985294 5.53211474486 y2[1] (closed_form) = 4.12815627694 4.97786661488 absolute error = 1.147 relative error = 17.74 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.54678818497 -4.40316086984 y1[1] (closed_form) = 5.03759968511 -4.07920688354 absolute error = 0.6035 relative error = 9.31 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.25 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 = 31.25 Order of pole (three term test) = 47.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53088.3MB, alloc=44.3MB, time=654.88 memory used=53134.5MB, alloc=44.3MB, time=655.44 x[1] = 0.6866 2.566 h = 0.0001 0.003 y2[1] (numeric) = 5.16007025633 5.54803285827 y2[1] (closed_form) = 4.14911023287 5.00270692683 absolute error = 1.149 relative error = 17.67 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.57397389924 -4.42944695034 y1[1] (closed_form) = 5.0621372063 -4.10039903231 absolute error = 0.6085 relative error = 9.34 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.41 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 = 25.41 Order of pole (three term test) = 48.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53180.3MB, alloc=44.3MB, time=656.00 memory used=53226.8MB, alloc=44.3MB, time=656.57 x[1] = 0.6867 2.569 h = 0.001 0.001 y2[1] (numeric) = 5.18748540194 5.56398303792 y2[1] (closed_form) = 4.16193781543 5.01750456186 absolute error = 1.162 relative error = 17.83 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.59012453829 -4.44552385313 y1[1] (closed_form) = 5.07675196083 -4.11336660451 absolute error = 0.6115 relative error = 9.358 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.07 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 = 20.07 Order of pole (three term test) = 48.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53272.9MB, alloc=44.3MB, time=657.14 memory used=53319.4MB, alloc=44.3MB, time=657.71 x[1] = 0.6877 2.57 h = 0.001 0.003 y2[1] (numeric) = 5.21502546476 5.57996546432 y2[1] (closed_form) = 4.17113295182 5.01846378221 absolute error = 1.185 relative error = 18.16 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.59049526483 -4.45629706972 y1[1] (closed_form) = 5.07760341115 -4.12255112393 absolute error = 0.6119 relative error = 9.356 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 95.44 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 = 95.44 Order of pole (three term test) = 48.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53365.3MB, alloc=44.3MB, time=658.27 x[1] = 0.6887 2.573 h = 0.0001 0.004 y2[1] (numeric) = 5.24269050122 5.59598014352 y2[1] (closed_form) = 4.18860998293 5.02958159913 absolute error = 1.197 relative error = 18.28 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.60203032762 -4.47757158252 y1[1] (closed_form) = 5.08849560928 -4.14011474387 absolute error = 0.6145 relative error = 9.367 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.33 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 = 54.33 Order of pole (three term test) = 48.61 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53411.3MB, alloc=44.3MB, time=658.83 memory used=53457.4MB, alloc=44.3MB, time=659.39 x[1] = 0.6888 2.577 h = 0.003 0.006 y2[1] (numeric) = 5.27048069738 5.61202711271 y2[1] (closed_form) = 4.20571483943 5.04956015707 absolute error = 1.204 relative error = 18.32 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.62392067382 -4.49915828325 y1[1] (closed_form) = 5.1082341514 -4.15740732624 absolute error = 0.6186 relative error = 9.393 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 72.56 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 = 72.56 Order of pole (three term test) = 48.88 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53503.3MB, alloc=44.3MB, time=659.95 memory used=53549.4MB, alloc=44.3MB, time=660.52 x[1] = 0.6918 2.583 h = 0.0001 0.005 y2[1] (numeric) = 5.29839657118 5.62810641293 y2[1] (closed_form) = 4.24613194566 5.06772964592 absolute error = 1.192 relative error = 18.03 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.64178777404 -4.54772504417 y1[1] (closed_form) = 5.12590833246 -4.19793865708 absolute error = 0.6233 relative error = 9.407 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.66 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 = 32.66 Order of pole (three term test) = 49.45 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53595.3MB, alloc=44.3MB, time=661.08 memory used=53641.5MB, alloc=44.3MB, time=661.64 x[1] = 0.6919 2.588 h = 0.0001 0.003 y2[1] (numeric) = 5.32643942826 5.64421755597 y2[1] (closed_form) = 4.26768991294 5.09300069347 absolute error = 1.194 relative error = 17.96 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.66943732993 -4.57485069699 y1[1] (closed_form) = 5.15088441702 -4.21973120078 absolute error = 0.6285 relative error = 9.439 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 26.56 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 = 26.56 Order of pole (three term test) = 49.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53687.4MB, alloc=44.3MB, time=662.21 x[1] = 0.692 2.591 h = 0.001 0.001 y2[1] (numeric) = 5.35460995779 5.66036080902 y2[1] (closed_form) = 4.28088492741 5.10805300755 absolute error = 1.207 relative error = 18.12 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.68586013801 -4.59143746777 y1[1] (closed_form) = 5.16575855835 -4.23306410499 absolute error = 0.6316 relative error = 9.457 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 20.97 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 = 20.97 Order of pole (three term test) = 50 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53733.4MB, alloc=44.3MB, time=662.78 memory used=53779.7MB, alloc=44.3MB, time=663.35 x[1] = 0.693 2.592 h = 0.001 0.003 y2[1] (numeric) = 5.38290833968 5.67653635562 y2[1] (closed_form) = 4.29028885844 5.10898141798 absolute error = 1.231 relative error = 18.46 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.68615983541 -4.60247466215 y1[1] (closed_form) = 5.16658149024 -4.24245820896 absolute error = 0.6321 relative error = 9.455 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 99.73 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 = 99.73 Order of pole (three term test) = 50.12 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53825.6MB, alloc=44.3MB, time=663.91 memory used=53871.9MB, alloc=44.3MB, time=664.48 x[1] = 0.694 2.595 h = 0.0001 0.004 y2[1] (numeric) = 5.41133463162 5.69274420161 y2[1] (closed_form) = 4.30821533779 5.12024626641 absolute error = 1.243 relative error = 18.57 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.69781663735 -4.6243506322 y1[1] (closed_form) = 5.17762608131 -4.26047056157 absolute error = 0.6348 relative error = 9.468 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 56.77 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 = 56.77 Order of pole (three term test) = 50.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53917.7MB, alloc=44.3MB, time=665.05 x[1] = 0.6941 2.599 h = 0.003 0.006 y2[1] (numeric) = 5.43988902402 5.70898438397 y2[1] (closed_form) = 4.32581152448 5.14056998853 absolute error = 1.251 relative error = 18.62 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.7200775236 -4.64662312293 y1[1] (closed_form) = 5.19771598689 -4.27825163107 absolute error = 0.6392 relative error = 9.495 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 75.83 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 = 75.83 Order of pole (three term test) = 50.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=53963.5MB, alloc=44.3MB, time=665.60 memory used=54009.8MB, alloc=44.3MB, time=666.17 x[1] = 0.6971 2.605 h = 0.0001 0.005 y2[1] (numeric) = 5.46857204648 5.72525694171 y2[1] (closed_form) = 4.36722540705 5.15891289718 absolute error = 1.238 relative error = 18.32 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.73801757224 -4.69649979547 y1[1] (closed_form) = 5.21557496455 -4.31977981918 absolute error = 0.6441 relative error = 9.511 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.13 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 = 34.13 Order of pole (three term test) = 51.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54055.8MB, alloc=44.3MB, time=666.73 memory used=54102.0MB, alloc=44.3MB, time=667.33 x[1] = 0.6972 2.61 h = 0.0001 0.003 y2[1] (numeric) = 5.49738503079 5.74156136843 y2[1] (closed_form) = 4.38940310811 5.18462117427 absolute error = 1.24 relative error = 18.25 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.76613630795 -4.72448797446 y1[1] (closed_form) = 5.24099591723 -4.34218851839 absolute error = 0.6496 relative error = 9.544 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.75 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 = 27.75 Order of pole (three term test) = 51.64 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54148.0MB, alloc=44.3MB, time=667.89 memory used=54194.3MB, alloc=44.3MB, time=668.46 x[1] = 0.6973 2.613 h = 0.001 0.001 y2[1] (numeric) = 5.52632868285 5.75789793336 y2[1] (closed_form) = 4.40297508086 5.19993195279 absolute error = 1.254 relative error = 18.41 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.78283430424 -4.74159848502 y1[1] (closed_form) = 5.25613311736 -4.3558963023 absolute error = 0.6528 relative error = 9.563 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 21.91 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 = 21.91 Order of pole (three term test) = 51.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54240.4MB, alloc=44.3MB, time=669.03 x[1] = 0.6983 2.614 h = 0.001 0.003 y2[1] (numeric) = 5.55540318761 5.77426682306 y2[1] (closed_form) = 4.41259231051 5.20082778343 absolute error = 1.279 relative error = 18.75 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.78305952889 -4.75290541973 y1[1] (closed_form) = 5.25692571513 -4.36550446573 absolute error = 0.6534 relative error = 9.562 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 104.2 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 = 104.2 Order of pole (three term test) = 51.99 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54286.4MB, alloc=44.3MB, time=669.60 memory used=54332.6MB, alloc=44.3MB, time=670.16 x[1] = 0.6993 2.617 h = 0.0001 0.004 y2[1] (numeric) = 5.58460860406 5.79066804319 y2[1] (closed_form) = 4.43097903838 5.21224061848 absolute error = 1.291 relative error = 18.86 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.79483692813 -4.77539786941 y1[1] (closed_form) = 5.26812353383 -4.38397633904 absolute error = 0.6562 relative error = 9.575 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 59.33 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 = 59.33 Order of pole (three term test) = 52.27 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54378.5MB, alloc=44.3MB, time=670.72 memory used=54424.7MB, alloc=44.3MB, time=671.29 x[1] = 0.6994 2.621 h = 0.003 0.006 y2[1] (numeric) = 5.61394512701 5.80710163046 y2[1] (closed_form) = 4.4490793176 5.23291466709 absolute error = 1.299 relative error = 18.91 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.81747253006 -4.79837482134 y1[1] (closed_form) = 5.28856981546 -4.4022586878 absolute error = 0.6608 relative error = 9.603 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 79.24 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 = 79.24 Order of pole (three term test) = 52.57 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54470.4MB, alloc=44.3MB, time=671.85 x[1] = 0.7024 2.627 h = 0.0001 0.005 y2[1] (numeric) = 5.64341329804 5.82356762176 y2[1] (closed_form) = 4.49151313593 5.25142970004 absolute error = 1.286 relative error = 18.61 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.8354785172 -4.84959282631 y1[1] (closed_form) = 5.30661204693 -4.44480683185 absolute error = 0.666 relative error = 9.621 % Correct digits = 1 memory used=54516.6MB, alloc=44.3MB, time=672.42 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.66 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 = 35.66 Order of pole (three term test) = 53.2 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54562.6MB, alloc=44.3MB, time=673.00 x[1] = 0.7025 2.632 h = 0.0001 0.003 y2[1] (numeric) = 5.67301447551 5.84006549197 y2[1] (closed_form) = 4.51432667772 5.27758175544 absolute error = 1.288 relative error = 18.55 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.86407176641 -4.87846702151 y1[1] (closed_form) = 5.33248423162 -4.46784783182 absolute error = 0.6717 relative error = 9.655 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29 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 = 29 Order of pole (three term test) = 53.59 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54608.5MB, alloc=44.3MB, time=673.55 memory used=54654.9MB, alloc=44.3MB, time=674.13 x[1] = 0.7026 2.635 h = 0.001 0.001 y2[1] (numeric) = 5.7027493825 5.85659551229 y2[1] (closed_form) = 4.52828536726 5.29315481371 absolute error = 1.303 relative error = 18.7 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.88104796276 -4.89611546661 y1[1] (closed_form) = 5.34788819504 -4.48194027538 absolute error = 0.6751 relative error = 9.676 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 22.9 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 = 22.9 Order of pole (three term test) = 53.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54700.9MB, alloc=44.3MB, time=674.70 memory used=54747.2MB, alloc=44.3MB, time=675.28 x[1] = 0.7036 2.636 h = 0.001 0.003 y2[1] (numeric) = 5.73261820907 5.87315787237 y2[1] (closed_form) = 4.53812048918 5.29401623007 absolute error = 1.327 relative error = 19.04 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 5.88119516413 -4.90769801324 y1[1] (closed_form) = 5.34864857927 -4.49176706371 absolute error = 0.6757 relative error = 9.675 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 108.9 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 = 108.9 Order of pole (three term test) = 53.97 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54793.1MB, alloc=44.3MB, time=675.84 x[1] = 0.7046 2.639 h = 0.0001 0.004 y2[1] (numeric) = 5.76262101556 5.88975257766 y2[1] (closed_form) = 4.55697851016 5.30557796701 absolute error = 1.34 relative error = 19.16 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.89309191328 -4.93082229109 y1[1] (closed_form) = 5.36000042297 -4.510709491 absolute error = 0.6787 relative error = 9.689 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 61.99 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 = 61.99 Order of pole (three term test) = 54.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54839.0MB, alloc=44.3MB, time=676.40 memory used=54885.1MB, alloc=44.3MB, time=676.96 x[1] = 0.7047 2.643 h = 0.003 0.006 y2[1] (numeric) = 5.79275800131 5.90637966459 y2[1] (closed_form) = 4.5755959558 5.32660754657 absolute error = 1.348 relative error = 19.2 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 5.9161063991 -4.95452281069 y1[1] (closed_form) = 5.3808081388 -4.52950622277 absolute error = 0.6835 relative error = 9.718 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 82.8 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 = 82.8 Order of pole (three term test) = 54.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=54930.8MB, alloc=44.3MB, time=677.52 memory used=54977.2MB, alloc=44.3MB, time=678.09 x[1] = 0.7077 2.649 h = 0.0001 0.005 y2[1] (numeric) = 5.82302972008 5.92303916779 y2[1] (closed_form) = 4.61907337448 5.34529324893 absolute error = 1.335 relative error = 18.9 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 5.93417099181 -5.00711422638 y1[1] (closed_form) = 5.39903192696 -4.57309792921 absolute error = 0.689 relative error = 9.738 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.26 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 = 37.26 Order of pole (three term test) = 55.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55023.0MB, alloc=44.3MB, time=678.65 memory used=55069.1MB, alloc=44.3MB, time=679.21 x[1] = 0.7078 2.654 h = 0.0001 0.003 y2[1] (numeric) = 5.85343755734 5.93973054289 y2[1] (closed_form) = 4.64253925732 5.37189568543 absolute error = 1.337 relative error = 18.84 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 5.96324408056 -5.03689847586 y1[1] (closed_form) = 5.42536176581 -4.5967877687 absolute error = 0.695 relative error = 9.774 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.3 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 = 30.3 Order of pole (three term test) = 55.66 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55115.1MB, alloc=44.3MB, time=679.78 x[1] = 0.7079 2.657 h = 0.001 0.001 y2[1] (numeric) = 5.8839822537 5.95645406301 y2[1] (closed_form) = 4.65689465966 5.38773486814 absolute error = 1.352 relative error = 18.99 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 5.98050147955 -5.05509938029 y1[1] (closed_form) = 5.44103622892 -4.61127488947 absolute error = 0.6986 relative error = 9.795 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 23.93 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 = 23.93 Order of pole (three term test) = 55.91 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55161.1MB, alloc=44.3MB, time=680.34 memory used=55207.4MB, alloc=44.3MB, time=680.91 x[1] = 0.7089 2.658 h = 0.0001 0.004 y2[1] (numeric) = 5.9146640045 5.97320992092 y2[1] (closed_form) = 4.66695235879 5.38855996923 absolute error = 1.378 relative error = 19.33 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 5.98056699714 -5.06696352129 y1[1] (closed_form) = 5.44176245451 -4.62132496028 absolute error = 0.6992 relative error = 9.794 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 144 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 = 144 Order of pole (three term test) = 56.05 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55253.1MB, alloc=44.3MB, time=681.48 memory used=55299.2MB, alloc=44.3MB, time=682.04 x[1] = 0.709 2.662 h = 0.003 0.006 y2[1] (numeric) = 5.94548288759 5.98999817981 y2[1] (closed_form) = 4.6860213562 5.40990615561 absolute error = 1.387 relative error = 19.37 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.0039003963 -5.09128192946 y1[1] (closed_form) = 5.4628917112 -4.64057080396 absolute error = 0.7042 relative error = 9.824 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 86.01 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 = 86.01 Order of pole (three term test) = 56.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55344.9MB, alloc=44.3MB, time=682.60 x[1] = 0.712 2.668 h = 0.0001 0.005 y2[1] (numeric) = 5.97643943014 6.00681887254 y2[1] (closed_form) = 4.73041440826 5.42875029776 absolute error = 1.374 relative error = 19.08 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.02200798251 -5.14504284479 y1[1] (closed_form) = 5.48128311905 -4.68507794062 absolute error = 0.7099 relative error = 9.845 % Correct digits = 1 memory used=55390.9MB, alloc=44.3MB, time=683.16 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.71 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 = 38.71 Order of pole (three term test) = 57.08 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55437.0MB, alloc=44.3MB, time=683.74 x[1] = 0.7121 2.673 h = 0.0001 0.003 y2[1] (numeric) = 6.00753504155 6.02367143792 y2[1] (closed_form) = 4.75444985165 5.45575378092 absolute error = 1.376 relative error = 19.01 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.05148499743 -5.17560424706 y1[1] (closed_form) = 5.50802008238 -4.70933427373 absolute error = 0.7161 relative error = 9.881 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 31.48 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 = 31.48 Order of pole (three term test) = 57.52 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55482.9MB, alloc=44.3MB, time=684.30 memory used=55529.3MB, alloc=44.3MB, time=684.87 x[1] = 0.7122 2.676 h = 0.001 0.001 y2[1] (numeric) = 6.03877047779 6.04055615092 y2[1] (closed_form) = 4.76915168808 5.47183002762 absolute error = 1.391 relative error = 19.17 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.06897901662 -5.19427688145 y1[1] (closed_form) = 5.52393526683 -4.72416604332 absolute error = 0.7198 relative error = 9.903 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 24.86 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 = 24.86 Order of pole (three term test) = 57.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55575.3MB, alloc=44.3MB, time=685.43 memory used=55621.6MB, alloc=44.3MB, time=686.00 x[1] = 0.7132 2.677 h = 0.001 0.003 y2[1] (numeric) = 6.07014593883 6.05747320712 y2[1] (closed_form) = 4.77940526148 5.47262502427 absolute error = 1.417 relative error = 19.5 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.06897358207 -5.20638033997 y1[1] (closed_form) = 5.52463321759 -4.73441254921 absolute error = 0.7205 relative error = 9.902 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 118.2 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 = 118.2 Order of pole (three term test) = 57.93 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55667.5MB, alloc=44.3MB, time=686.56 x[1] = 0.7142 2.68 h = 0.0001 0.004 y2[1] (numeric) = 6.10166148758 6.07442261154 y2[1] (closed_form) = 4.79916870601 5.48447205971 absolute error = 1.43 relative error = 19.62 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.08108552568 -5.23070396128 y1[1] (closed_form) = 5.53627957839 -4.75425893965 absolute error = 0.7237 relative error = 9.918 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 67.29 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 = 67.29 Order of pole (three term test) = 58.26 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55713.3MB, alloc=44.3MB, time=687.12 memory used=55759.4MB, alloc=44.3MB, time=687.68 x[1] = 0.7143 2.684 h = 0.003 0.006 y2[1] (numeric) = 6.13331733204 6.09140440009 y2[1] (closed_form) = 4.81877998797 5.50618373601 absolute error = 1.439 relative error = 19.67 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.1048054211 -5.25578216319 y1[1] (closed_form) = 5.55777996522 -4.77404434203 absolute error = 0.7289 relative error = 9.949 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 89.88 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 = 89.88 Order of pole (three term test) = 58.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55805.2MB, alloc=44.3MB, time=688.24 memory used=55851.4MB, alloc=44.3MB, time=688.81 x[1] = 0.7173 2.69 h = 0.0001 0.005 y2[1] (numeric) = 6.1651140494 6.10841860307 y2[1] (closed_form) = 4.86426207717 5.5251956914 absolute error = 1.426 relative error = 19.37 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.12295726238 -5.31097711303 y1[1] (closed_form) = 5.57634963541 -4.81964037906 absolute error = 0.735 relative error = 9.972 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.45 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 = 40.45 Order of pole (three term test) = 59.34 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55897.2MB, alloc=44.3MB, time=689.36 memory used=55943.5MB, alloc=44.3MB, time=689.93 x[1] = 0.7174 2.695 h = 0.0001 0.003 y2[1] (numeric) = 6.19705307716 6.12546463904 y2[1] (closed_form) = 4.88898156298 5.55266219087 absolute error = 1.428 relative error = 19.3 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.15292385004 -5.34249416523 y1[1] (closed_form) = 5.60355656335 -4.84457732686 absolute error = 0.7414 relative error = 10.01 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.89 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 = 32.89 Order of pole (three term test) = 59.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=55989.4MB, alloc=44.3MB, time=690.50 x[1] = 0.7175 2.698 h = 0.001 0.001 y2[1] (numeric) = 6.22913518962 6.14254278479 y2[1] (closed_form) = 4.90409931665 5.56901191832 absolute error = 1.444 relative error = 19.46 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.17070454489 -5.36174681192 y1[1] (closed_form) = 5.6197494091 -4.85982301965 absolute error = 0.7453 relative error = 10.03 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 25.97 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 = 25.97 Order of pole (three term test) = 60.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56035.3MB, alloc=44.3MB, time=691.06 memory used=56081.6MB, alloc=44.3MB, time=691.63 x[1] = 0.7185 2.699 h = 0.001 0.003 y2[1] (numeric) = 6.26136059225 6.15965323912 y2[1] (closed_form) = 4.91458445834 5.56976693711 absolute error = 1.47 relative error = 19.79 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.17061040426 -5.37414314318 y1[1] (closed_form) = 5.62040945839 -4.87030175086 absolute error = 0.746 relative error = 10.03 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 123.5 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 = 123.5 Order of pole (three term test) = 60.24 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56127.7MB, alloc=44.3MB, time=692.19 memory used=56173.9MB, alloc=44.3MB, time=692.76 x[1] = 0.7195 2.702 h = 0.0001 0.004 y2[1] (numeric) = 6.29372934938 6.17679600682 y2[1] (closed_form) = 4.93485217969 5.5817653948 absolute error = 1.483 relative error = 19.91 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.18283753704 -5.39914396417 y1[1] (closed_form) = 5.63221204088 -4.89065165251 absolute error = 0.7495 relative error = 10.05 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 70.32 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 = 70.32 Order of pole (three term test) = 60.58 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56219.8MB, alloc=44.3MB, time=693.32 x[1] = 0.7196 2.706 h = 0.003 0.006 y2[1] (numeric) = 6.32624167384 6.19397112339 y2[1] (closed_form) = 4.95501975098 5.60384788617 absolute error = 1.493 relative error = 19.96 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.20694806313 -5.4250023964 y1[1] (closed_form) = 5.65408874605 -4.91099064848 absolute error = 0.7549 relative error = 10.08 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 93.92 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 = 93.92 Order of pole (three term test) = 60.96 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56265.8MB, alloc=44.3MB, time=693.88 memory used=56311.9MB, alloc=44.3MB, time=694.44 x[1] = 0.7226 2.712 h = 0.0001 0.005 y2[1] (numeric) = 6.35889815576 6.2111786166 y2[1] (closed_form) = 5.00161604755 5.62302571555 absolute error = 1.479 relative error = 19.66 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.2251358228 -5.48166546005 y1[1] (closed_form) = 5.67283451111 -4.95770070494 absolute error = 0.7613 relative error = 10.1 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.27 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 = 42.27 Order of pole (three term test) = 61.72 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56357.8MB, alloc=44.3MB, time=695.00 memory used=56404.1MB, alloc=44.3MB, time=695.57 x[1] = 0.7227 2.717 h = 0.0001 0.003 y2[1] (numeric) = 6.39170026122 6.22841788404 y2[1] (closed_form) = 5.02703725163 5.65096198892 absolute error = 1.482 relative error = 19.59 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.25559727209 -5.51416387475 y1[1] (closed_form) = 5.70051799219 -4.98333598188 absolute error = 0.768 relative error = 10.14 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 34.37 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 = 34.37 Order of pole (three term test) = 62.21 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56450.2MB, alloc=44.3MB, time=696.14 memory used=56496.6MB, alloc=44.3MB, time=696.71 x[1] = 0.7228 2.72 h = 0.001 0.001 y2[1] (numeric) = 6.42464878322 6.24568920431 y2[1] (closed_form) = 5.04258162813 5.6675891256 absolute error = 1.498 relative error = 19.75 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.27366760844 -5.53401206676 y1[1] (closed_form) = 5.71699232636 -4.99900632519 absolute error = 0.7721 relative error = 10.17 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 27.14 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 = 27.14 Order of pole (three term test) = 62.51 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56542.5MB, alloc=44.3MB, time=697.28 x[1] = 0.7238 2.721 h = 0.001 0.003 y2[1] (numeric) = 6.45774393291 6.26299277943 y2[1] (closed_form) = 5.05330329461 5.66830206545 absolute error = 1.525 relative error = 20.08 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.27348076261 -5.5467075892 y1[1] (closed_form) = 5.71761233128 -5.00972221315 absolute error = 0.7729 relative error = 10.17 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 129.1 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 = 129.1 Order of pole (three term test) = 62.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56588.4MB, alloc=44.3MB, time=697.84 memory used=56634.7MB, alloc=44.3MB, time=698.41 x[1] = 0.7248 2.724 h = 0.0001 0.004 y2[1] (numeric) = 6.49098577607 6.28032861396 y2[1] (closed_form) = 5.07408733153 5.68045268896 absolute error = 1.539 relative error = 20.2 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.28582138401 -5.57240230508 y1[1] (closed_form) = 5.72957177056 -5.03058765657 absolute error = 0.7765 relative error = 10.18 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 73.48 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 = 73.48 Order of pole (three term test) = 63.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56680.7MB, alloc=44.3MB, time=698.97 memory used=56726.7MB, alloc=44.3MB, time=699.53 x[1] = 0.7249 2.728 h = 0.003 0.006 y2[1] (numeric) = 6.52437453044 6.29769674299 y2[1] (closed_form) = 5.09482553705 5.70291135989 absolute error = 1.548 relative error = 20.25 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.31032665713 -5.59906187766 y1[1] (closed_form) = 5.75183002475 -5.05149462117 absolute error = 0.7821 relative error = 10.22 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 98.15 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 = 98.15 Order of pole (three term test) = 63.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56772.6MB, alloc=44.3MB, time=700.09 memory used=56818.9MB, alloc=44.3MB, time=700.66 x[1] = 0.7279 2.734 h = 0.0001 0.005 y2[1] (numeric) = 6.55791079937 6.31509719158 y2[1] (closed_form) = 5.14256175792 5.72225293979 absolute error = 1.534 relative error = 19.95 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.32854163201 -5.65722784244 y1[1] (closed_form) = 5.77074953768 -5.09934436508 absolute error = 0.7889 relative error = 10.24 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.17 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 = 44.17 Order of pole (three term test) = 64.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56864.7MB, alloc=44.3MB, time=701.22 x[1] = 0.728 2.739 h = 0.0001 0.003 y2[1] (numeric) = 6.59159607807 6.33252933578 y2[1] (closed_form) = 5.1687027856 5.75066579516 absolute error = 1.537 relative error = 19.88 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.35950321101 -5.69073392838 y1[1] (closed_form) = 5.79891621483 -5.12569611516 absolute error = 0.7959 relative error = 10.28 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.92 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 = 35.92 Order of pole (three term test) = 64.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=56910.6MB, alloc=44.3MB, time=701.78 memory used=56957.0MB, alloc=44.3MB, time=702.35 x[1] = 0.7281 2.742 h = 0.001 0.001 y2[1] (numeric) = 6.62543117866 6.34999345589 y2[1] (closed_form) = 5.1846847497 5.76757429654 absolute error = 1.554 relative error = 20.04 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.37786613705 -5.71119355764 y1[1] (closed_form) = 5.81567589384 -5.14180209556 absolute error = 0.8002 relative error = 10.31 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 28.36 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 = 28.36 Order of pole (three term test) = 65.06 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57003.0MB, alloc=44.3MB, time=702.91 memory used=57049.2MB, alloc=44.3MB, time=703.49 x[1] = 0.7291 2.743 h = 0.001 0.003 y2[1] (numeric) = 6.65941631809 6.36748975726 y2[1] (closed_form) = 5.19564799549 5.768242982 absolute error = 1.582 relative error = 20.37 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.37758246474 -5.72419470781 y1[1] (closed_form) = 5.81625363793 -5.15276017047 absolute error = 0.801 relative error = 10.31 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 134.9 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 = 134.9 Order of pole (three term test) = 65.23 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57095.0MB, alloc=44.3MB, time=704.05 x[1] = 0.7301 2.746 h = 0.0001 0.004 y2[1] (numeric) = 6.69355156364 6.38501824415 y2[1] (closed_form) = 5.21696065765 5.78054646388 absolute error = 1.596 relative error = 20.49 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.39003474727 -5.7506003734 y1[1] (closed_form) = 5.8283705204 -5.17415345786 absolute error = 0.8048 relative error = 10.33 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 76.79 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 = 76.79 Order of pole (three term test) = 65.6 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57141.0MB, alloc=44.3MB, time=704.60 memory used=57187.2MB, alloc=44.3MB, time=705.17 x[1] = 0.7302 2.75 h = 0.003 0.006 y2[1] (numeric) = 6.72783713805 6.40257895123 y2[1] (closed_form) = 5.23828419016 5.80338671727 absolute error = 1.606 relative error = 20.54 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.4149388627 -5.77808248023 y1[1] (closed_form) = 5.85101559577 -5.19564311407 absolute error = 0.8107 relative error = 10.36 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 102.6 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 = 102.6 Order of pole (three term test) = 66.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57233.0MB, alloc=44.3MB, time=705.73 memory used=57279.2MB, alloc=44.3MB, time=706.29 x[1] = 0.7332 2.756 h = 0.0001 0.005 y2[1] (numeric) = 6.76227365821 6.42017190073 y2[1] (closed_form) = 5.28718661017 5.82288973302 absolute error = 1.591 relative error = 20.23 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.43317197104 -5.83778685509 y1[1] (closed_form) = 5.87010632302 -5.24465877359 absolute error = 0.8178 relative error = 10.39 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.16 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 = 46.16 Order of pole (three term test) = 66.86 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57325.1MB, alloc=44.3MB, time=706.85 memory used=57371.4MB, alloc=44.3MB, time=707.42 x[1] = 0.7333 2.761 h = 0.0001 0.003 y2[1] (numeric) = 6.79686264896 6.43779644649 y2[1] (closed_form) = 5.31406600613 5.8517860279 absolute error = 1.594 relative error = 20.17 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.46463892319 -5.87232753024 y1[1] (closed_form) = 5.89876289237 -5.27174558012 absolute error = 0.8252 relative error = 10.43 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 37.53 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 = 37.53 Order of pole (three term test) = 67.41 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57417.3MB, alloc=44.3MB, time=707.98 x[1] = 0.7334 2.764 h = 0.001 0.001 y2[1] (numeric) = 6.83160494198 6.4554528705 y2[1] (closed_form) = 5.33049678774 5.86897987568 absolute error = 1.612 relative error = 20.33 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.48329736705 -5.89341485546 y1[1] (closed_form) = 5.91581180114 -5.28829844935 absolute error = 0.8296 relative error = 10.45 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 29.64 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 = 29.64 Order of pole (three term test) = 67.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57463.5MB, alloc=44.3MB, time=708.56 memory used=57509.7MB, alloc=44.3MB, time=709.13 x[1] = 0.7344 2.765 h = 0.0001 0.004 y2[1] (numeric) = 6.86650076019 6.47314138144 y2[1] (closed_form) = 5.34170676718 5.8696020548 absolute error = 1.64 relative error = 20.66 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.48291262145 -5.90672818996 y1[1] (closed_form) = 5.91634499219 -5.299503842 absolute error = 0.8305 relative error = 10.46 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 178.4 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 = 178.4 Order of pole (three term test) = 67.92 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57555.6MB, alloc=44.3MB, time=709.69 memory used=57601.8MB, alloc=44.3MB, time=710.26 x[1] = 0.7345 2.769 h = 0.003 0.006 y2[1] (numeric) = 6.90155019201 6.49086204726 y2[1] (closed_form) = 5.36354153305 5.89278233398 absolute error = 1.65 relative error = 20.71 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.50815221628 -5.93491244053 y1[1] (closed_form) = 5.93933446939 -5.32150242698 absolute error = 0.8366 relative error = 10.49 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 106.5 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 = 106.5 Order of pole (three term test) = 68.37 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57647.7MB, alloc=44.3MB, time=710.82 memory used=57693.9MB, alloc=44.3MB, time=711.39 x[1] = 0.7375 2.775 h = 0.0001 0.005 y2[1] (numeric) = 6.93675382474 6.50861488903 y2[1] (closed_form) = 5.41346737115 5.91243663179 absolute error = 1.636 relative error = 20.41 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.5263932139 -5.99592648255 y1[1] (closed_form) = 5.95858471973 -5.3715411118 absolute error = 0.844 relative error = 10.52 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 47.94 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 = 47.94 Order of pole (three term test) = 69.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57739.9MB, alloc=44.3MB, time=711.94 x[1] = 0.7376 2.78 h = 0.0001 0.003 y2[1] (numeric) = 6.97211320935 6.52639924126 y2[1] (closed_form) = 5.44099165205 5.94176368786 absolute error = 1.639 relative error = 20.34 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.55828529403 -6.03135033544 y1[1] (closed_form) = 5.98767743931 -5.39926990921 absolute error = 0.8515 relative error = 10.56 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 38.99 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 = 38.99 Order of pole (three term test) = 69.8 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57785.7MB, alloc=44.3MB, time=712.50 memory used=57832.0MB, alloc=44.3MB, time=713.07 x[1] = 0.7377 2.783 h = 0.001 0.001 y2[1] (numeric) = 7.00762919471 6.54421538754 y2[1] (closed_form) = 5.45781449624 5.95921189356 absolute error = 1.657 relative error = 20.5 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.57719222217 -6.05297344032 y1[1] (closed_form) = 6.00498395025 -5.41621315365 absolute error = 0.8561 relative error = 10.59 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 30.79 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 = 30.79 Order of pole (three term test) = 70.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57877.9MB, alloc=44.3MB, time=713.64 memory used=57924.2MB, alloc=44.3MB, time=714.20 x[1] = 0.7387 2.784 h = 0.001 0.003 y2[1] (numeric) = 7.04330200893 6.56206353953 y2[1] (closed_form) = 5.46924165275 5.95979520273 absolute error = 1.685 relative error = 20.84 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.57671990644 -6.06655202965 y1[1] (closed_form) = 6.00547992763 -5.42763618519 absolute error = 0.857 relative error = 10.59 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 146.4 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 = 146.4 Order of pole (three term test) = 70.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=57970.2MB, alloc=44.3MB, time=714.77 x[1] = 0.7397 2.787 h = 0.0001 0.004 y2[1] (numeric) = 7.07913172215 6.57994370098 y2[1] (closed_form) = 5.49156983992 5.97239143227 absolute error = 1.7 relative error = 20.95 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.58937170552 -6.09430664195 y1[1] (closed_form) = 6.01789780476 -5.4500434746 absolute error = 0.8612 relative error = 10.61 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 83.35 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 = 83.35 Order of pole (three term test) = 70.74 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58016.2MB, alloc=44.3MB, time=715.38 memory used=58062.4MB, alloc=44.3MB, time=715.94 x[1] = 0.7398 2.791 h = 0.003 0.006 y2[1] (numeric) = 7.11511856675 6.59785590572 y2[1] (closed_form) = 5.51401816056 5.99596363155 absolute error = 1.71 relative error = 21 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.61501758281 -6.12335397981 y1[1] (closed_form) = 6.04128420583 -5.47265303667 absolute error = 0.8675 relative error = 10.64 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 111.3 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 = 111.3 Order of pole (three term test) = 71.22 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58108.3MB, alloc=44.3MB, time=716.50 memory used=58154.6MB, alloc=44.3MB, time=717.07 x[1] = 0.7428 2.797 h = 0.0001 0.005 y2[1] (numeric) = 7.15126318556 6.61580017051 y2[1] (closed_form) = 5.56516064664 6.01577485375 absolute error = 1.696 relative error = 20.69 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.6332590022 -6.18597352199 y1[1] (closed_form) = 6.06070076316 -5.52390800724 absolute error = 0.8753 relative error = 10.67 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 50.1 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 = 50.1 Order of pole (three term test) = 72.11 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58200.4MB, alloc=44.3MB, time=717.63 memory used=58246.7MB, alloc=44.3MB, time=718.19 x[1] = 0.7429 2.802 h = 0.0001 0.003 y2[1] (numeric) = 7.18756716032 6.63377580653 y2[1] (closed_form) = 5.593458924 6.04559847064 absolute error = 1.699 relative error = 20.63 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.66566598888 -6.22248300975 y1[1] (closed_form) = 6.09029620623 -5.55240756302 absolute error = 0.8832 relative error = 10.72 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 40.74 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 = 40.74 Order of pole (three term test) = 72.73 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58292.7MB, alloc=44.3MB, time=718.76 x[1] = 0.743 2.805 h = 0.001 0.001 y2[1] (numeric) = 7.22403136029 6.65178309893 y2[1] (closed_form) = 5.61075216025 6.06333964027 absolute error = 1.717 relative error = 20.79 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.68487374069 -6.24476464511 y1[1] (closed_form) = 6.10789939053 -5.56981931263 absolute error = 0.8879 relative error = 10.74 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 32.17 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 = 32.17 Order of pole (three term test) = 73.1 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58338.6MB, alloc=44.3MB, time=719.33 memory used=58385.0MB, alloc=44.3MB, time=719.90 x[1] = 0.744 2.806 h = 0.001 0.003 y2[1] (numeric) = 7.26065601985 6.66982226279 y2[1] (closed_form) = 5.62243594247 6.0638721057 absolute error = 1.747 relative error = 21.12 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.6842922104 -6.25866777545 y1[1] (closed_form) = 6.1083464043 -5.58149951248 absolute error = 0.889 relative error = 10.74 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 153 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 = 153 Order of pole (three term test) = 73.28 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58430.9MB, alloc=44.3MB, time=720.47 memory used=58477.4MB, alloc=44.3MB, time=721.04 x[1] = 0.745 2.809 h = 0.0001 0.004 y2[1] (numeric) = 7.29744121068 6.68789330154 y2[1] (closed_form) = 5.64532951202 6.0766230277 absolute error = 1.762 relative error = 21.24 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.69704974055 -6.28718373626 y1[1] (closed_form) = 6.12092326737 -5.60447138662 absolute error = 0.8933 relative error = 10.76 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 87.1 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 = 87.1 Order of pole (three term test) = 73.71 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58523.2MB, alloc=44.3MB, time=721.60 x[1] = 0.7451 2.813 h = 0.003 0.006 y2[1] (numeric) = 7.33438717052 6.70599624847 y2[1] (closed_form) = 5.66840711958 6.10059265885 absolute error = 1.773 relative error = 21.29 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.7231059189 -6.31711703359 y1[1] (closed_form) = 6.14471198176 -5.62770768812 absolute error = 0.8999 relative error = 10.8 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 116.3 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 = 116.3 Order of pole (three term test) = 74.21 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58569.3MB, alloc=44.3MB, time=722.18 memory used=58615.3MB, alloc=44.3MB, time=722.75 x[1] = 0.7481 2.819 h = 0.0001 0.005 y2[1] (numeric) = 7.37149455656 6.72413111713 y2[1] (closed_form) = 5.72079419099 6.12055791047 absolute error = 1.758 relative error = 20.98 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.74133750318 -6.38137978083 y1[1] (closed_form) = 6.16429174495 -5.68020684104 absolute error = 0.9081 relative error = 10.83 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 52.35 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 = 52.35 Order of pole (three term test) = 75.15 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58661.2MB, alloc=44.3MB, time=723.31 memory used=58707.4MB, alloc=44.3MB, time=723.87 x[1] = 0.7482 2.824 h = 0.0001 0.003 y2[1] (numeric) = 7.40876498174 6.74229719459 y2[1] (closed_form) = 5.74988632203 6.1508850858 absolute error = 1.761 relative error = 20.92 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.77426454934 -6.41900368265 y1[1] (closed_form) = 6.19439675816 -5.70949705097 absolute error = 0.9163 relative error = 10.88 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 42.57 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 = 42.57 Order of pole (three term test) = 75.79 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58753.3MB, alloc=44.3MB, time=724.44 memory used=58799.6MB, alloc=44.3MB, time=725.01 x[1] = 0.7483 2.827 h = 0.001 0.001 y2[1] (numeric) = 7.44619933621 6.76049476749 y2[1] (closed_form) = 5.76766197228 6.16892327487 absolute error = 1.78 relative error = 21.07 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.79377598252 -6.44196122743 y1[1] (closed_form) = 6.21230058077 -5.72738934953 absolute error = 0.9213 relative error = 10.9 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 33.62 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 = 33.62 Order of pole (three term test) = 76.19 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58845.7MB, alloc=44.3MB, time=725.57 x[1] = 0.7493 2.828 h = 0.001 0.003 y2[1] (numeric) = 7.48379786074 6.77872405437 y2[1] (closed_form) = 5.7796078313 6.16940241445 absolute error = 1.81 relative error = 21.41 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.79308060437 -6.45619581911 y1[1] (closed_form) = 6.2126961107 -5.73933214721 absolute error = 0.9224 relative error = 10.91 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 159.9 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 = 159.9 Order of pole (three term test) = 76.38 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58891.6MB, alloc=44.3MB, time=726.13 memory used=58937.8MB, alloc=44.3MB, time=726.70 x[1] = 0.7503 2.831 h = 0.0001 0.004 y2[1] (numeric) = 7.52156062863 6.79698505833 y2[1] (closed_form) = 5.80308019466 6.18230850318 absolute error = 1.825 relative error = 21.52 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.80594149456 -6.48549166768 y1[1] (closed_form) = 6.22543233635 -5.76288201264 absolute error = 0.9269 relative error = 10.93 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 91.02 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 = 91.02 Order of pole (three term test) = 76.83 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=58983.7MB, alloc=44.3MB, time=727.26 memory used=59029.7MB, alloc=44.3MB, time=727.82 x[1] = 0.7504 2.835 h = 0.003 0.006 y2[1] (numeric) = 7.55948788306 6.81527781207 y2[1] (closed_form) = 5.8268032009 6.20668111238 absolute error = 1.836 relative error = 21.57 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.83241195863 -6.51633432269 y1[1] (closed_form) = 6.24962879076 -5.78676119548 absolute error = 0.9338 relative error = 10.96 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 121.6 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 = 121.6 Order of pole (three term test) = 77.36 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59075.5MB, alloc=44.3MB, time=728.38 memory used=59121.7MB, alloc=44.3MB, time=728.95 x[1] = 0.7534 2.841 h = 0.0001 0.005 y2[1] (numeric) = 7.59758029587 6.83360232579 y2[1] (closed_form) = 5.88046339835 6.22679727845 absolute error = 1.821 relative error = 21.26 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.85062302258 -6.58227875662 y1[1] (closed_form) = 6.26936844293 -5.84053303266 absolute error = 0.9424 relative error = 11 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 54.71 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 = 54.71 Order of pole (three term test) = 78.33 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59167.7MB, alloc=44.3MB, time=729.51 x[1] = 0.7535 2.846 h = 0.0001 0.003 y2[1] (numeric) = 7.63583951182 6.85195786177 y2[1] (closed_form) = 5.91036971968 6.25763505427 absolute error = 1.825 relative error = 21.2 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.88407524052 -6.62104651413 y1[1] (closed_form) = 6.29998992085 -5.87063427183 absolute error = 0.9509 relative error = 11.04 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 44.49 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 = 44.49 Order of pole (three term test) = 79.01 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59213.4MB, alloc=44.3MB, time=730.07 memory used=59259.8MB, alloc=44.3MB, time=730.65 x[1] = 0.7536 2.849 h = 0.001 0.001 y2[1] (numeric) = 7.67426644238 6.87034470802 y2[1] (closed_form) = 5.92864009507 6.2759743412 absolute error = 1.844 relative error = 21.36 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 6.90389318261 -6.64469774595 y1[1] (closed_form) = 6.31819837173 -5.88901945234 absolute error = 0.9561 relative error = 11.07 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 35.13 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 = 35.13 Order of pole (three term test) = 79.43 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59305.7MB, alloc=44.3MB, time=731.22 memory used=59352.0MB, alloc=44.3MB, time=731.79 x[1] = 0.7546 2.85 h = 0.001 0.003 y2[1] (numeric) = 7.71286133489 6.8887630866 y2[1] (closed_form) = 5.94085358901 6.27639758741 absolute error = 1.875 relative error = 21.69 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 6.90307918398 -6.65927084711 y1[1] (closed_form) = 6.31853981289 -5.90123038509 absolute error = 0.9572 relative error = 11.07 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 167.1 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 = 167.1 Order of pole (three term test) = 79.62 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59397.8MB, alloc=44.3MB, time=732.35 x[1] = 0.7556 2.853 h = 0.0001 0.004 y2[1] (numeric) = 7.75162426428 6.90721300028 y2[1] (closed_form) = 5.9649184577 6.28945925286 absolute error = 1.89 relative error = 21.81 % Correct digits = 1 h = 0.0001 0.004 y1[1] (numeric) = 6.91604091145 -6.6893655189 y1[1] (closed_form) = 6.3314357156 -5.92537194904 absolute error = 0.962 relative error = 11.09 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 95.11 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 = 95.11 Order of pole (three term test) = 80.09 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59444.0MB, alloc=44.3MB, time=732.92 memory used=59490.1MB, alloc=44.3MB, time=733.48 x[1] = 0.7557 2.857 h = 0.003 0.006 y2[1] (numeric) = 7.79055547933 6.92569448112 y2[1] (closed_form) = 5.9893033626 6.31424041951 absolute error = 1.902 relative error = 21.86 % Correct digits = 1 h = 0.003 0.006 y1[1] (numeric) = 6.94292960826 -6.72114146734 y1[1] (closed_form) = 6.3560453727 -5.94991054332 absolute error = 0.9691 relative error = 11.13 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 127 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 = 127 Order of pole (three term test) = 80.65 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59535.8MB, alloc=44.3MB, time=734.03 memory used=59582.1MB, alloc=44.3MB, time=734.60 x[1] = 0.7587 2.863 h = 0.0001 0.005 y2[1] (numeric) = 7.82965566681 6.94420753582 y2[1] (closed_form) = 6.04426584244 6.33450415695 absolute error = 1.887 relative error = 21.55 % Correct digits = 1 h = 0.0001 0.005 y1[1] (numeric) = 6.96110902446 -6.78880686112 y1[1] (closed_form) = 6.37594137307 -6.0049841842 absolute error = 0.9782 relative error = 11.17 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 57.17 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 = 57.17 Order of pole (three term test) = 81.67 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59628.0MB, alloc=44.3MB, time=735.16 memory used=59674.2MB, alloc=44.3MB, time=735.72 x[1] = 0.7588 2.868 h = 0.0001 0.003 y2[1] (numeric) = 7.86892650387 6.96275140111 y2[1] (closed_form) = 6.07500718095 6.36585961822 absolute error = 1.891 relative error = 21.49 % Correct digits = 1 h = 0.0001 0.003 y1[1] (numeric) = 6.99509148128 -6.82874859287 y1[1] (closed_form) = 6.40708625658 -6.03591731793 absolute error = 0.9871 relative error = 11.21 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 46.49 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 = 46.49 Order of pole (three term test) = 82.39 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59720.2MB, alloc=44.3MB, time=736.29 x[1] = 0.7589 2.871 h = 0.001 0.001 y2[1] (numeric) = 7.90836892382 6.98132636635 y2[1] (closed_form) = 6.09378488842 6.38450410333 absolute error = 1.91 relative error = 21.64 % Correct digits = 1 h = 0.001 0.001 y1[1] (numeric) = 7.01521872677 -6.85311169669 y1[1] (closed_form) = 6.42560334963 -6.05480800915 absolute error = 0.9924 relative error = 11.24 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 36.71 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 = 36.71 Order of pole (three term test) = 82.82 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59766.2MB, alloc=44.3MB, time=736.86 memory used=59812.6MB, alloc=44.3MB, time=737.43 x[1] = 0.7599 2.872 h = 0.001 0.003 y2[1] (numeric) = 7.94798318069 6.99993265714 y2[1] (closed_form) = 6.1062716844 6.38486880073 absolute error = 1.942 relative error = 21.98 % Correct digits = 1 h = 0.001 0.003 y1[1] (numeric) = 7.01428119194 -6.86803048532 y1[1] (closed_form) = 6.42588800987 -6.06729272384 absolute error = 0.9937 relative error = 11.24 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 174.6 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 = 174.6 Order of pole (three term test) = 83.03 0 NO COMPLEX POLE (six term test) for Equation 2 memory used=59859.2MB, alloc=44.3MB, time=738.01 memory used=59907.0MB, alloc=44.3MB, time=738.68 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; diff ( y1 , x , 1 ) = neg ( y2 ) ; Iterations = 754 Total Elapsed Time = 12 Minutes 18 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 12 Minutes 18 Seconds > quit memory used=59909.2MB, alloc=44.3MB, time=738.71