|\^/| Maple 2016 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. #BEGIN OUTFILE1 # before write maple top matter # before write_ats library and user def block #BEGIN ATS LIBRARY BLOCK # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc # End Function number 2 # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc # End Function number 3 # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc # End Function number 4 # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 5 # Begin Function number 6 > omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 4 then > printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel); > else > printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel, Re(value), Im(value), postlabel) else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value), Im(value), postlabel) end if end if end proc # End Function number 6 # Begin Function number 7 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number -1 > if vallen = 5 then # if number 0 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 0; > fi;# end if -1; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc # End Function number 7 # Begin Function number 8 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number -1 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := sec_temp mod int_trunc(glob_sec_in_minute); > if (years_int > 0) then # if number 0 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 1 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 2 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 3 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 3 > else > fprintf(fd," 0.0 Seconds"); > fi;# end if 2 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " 0.0 Seconds") end if; fprintf(fd, "\n") end proc # End Function number 8 # Begin Function number 9 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 2 > years_int := int_trunc(secs_in / glob_sec_in_year); > sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year)); > days_int := int_trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ; > hours_int := int_trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour)); > minutes_int := int_trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod int_trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 3 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 4 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 5 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 6 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 6 > else > printf(" 0.0 Seconds\n"); > fi;# end if 5 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := int_trunc(secs_in/glob_sec_in_year); sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year); days_int := int_trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod int_trunc(glob_sec_in_day); hours_int := int_trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod int_trunc(glob_sec_in_hour); minutes_int := int_trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod int_trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" 0.0 Seconds\n") end if end proc # End Function number 9 # Begin Function number 10 > zero_ats_ar := proc(arr_a) > global ATS_MAX_TERMS; > local iii; > iii := 1; > while (iii <= ATS_MAX_TERMS) do # do number 1 > arr_a [iii] := glob__0; > iii := iii + 1; > od;# end do number 1 > end; zero_ats_ar := proc(arr_a) local iii; global ATS_MAX_TERMS; iii := 1; while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1 end do end proc # End Function number 10 # Begin Function number 11 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > global ATS_MAX_TERMS; > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := glob__0; > if (jjj_ats <= mmm_ats) then # if number 5 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6 > ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]); > fi;# end if 6; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 5; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; global ATS_MAX_TERMS; ret_ats := glob__0; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]) end if; iii_ats := iii_ats + 1 end do end if; ret_ats end proc # End Function number 11 # Begin Function number 12 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global ATS_MAX_TERMS; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := glob__0; > if (jjj_att < mmm_att) then # if number 5 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6 > ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att); > fi;# end if 6; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / c(mmm_att) ; > fi;# end if 5; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global ATS_MAX_TERMS; ret_att := glob__0; if jjj_att < mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/c(mmm_att) end if; ret_att end proc # End Function number 12 # Begin Function number 13 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc # End Function number 13 # Begin Function number 14 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc # End Function number 14 # Begin Function number 15 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc # End Function number 15 # Begin Function number 16 > logitem_good_digits := proc(file,rel_error) > global glob_small_float,glob_prec; > local good_digits; > fprintf(file,""); > fprintf(file,"%d",glob_min_good_digits); > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float, glob_prec; fprintf(file, ""); fprintf(file, "%d", glob_min_good_digits); fprintf(file, "") end proc # End Function number 16 # Begin Function number 17 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc # End Function number 17 # Begin Function number 18 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc # End Function number 18 # Begin Function number 19 > logitem_complex := proc(file,x) > fprintf(file,""); > fprintf(file,"%g + %g I",Re(x),Im(x)); > fprintf(file,""); > end; logitem_complex := proc(file, x) fprintf(file, ""); fprintf(file, "%g + %g I", Re(x), Im(x)); fprintf(file, "") end proc # End Function number 19 # Begin Function number 20 > logitem_h_reason := proc(file) > global glob_h_reason; > fprintf(file,""); > if (glob_h_reason = 1) then # if number 5 > fprintf(file,"Max H"); > elif > (glob_h_reason = 2) then # if number 6 > fprintf(file,"Display Interval"); > elif > (glob_h_reason = 3) then # if number 7 > fprintf(file,"Optimal"); > elif > (glob_h_reason = 4) then # if number 8 > fprintf(file,"Pole Accuracy"); > elif > (glob_h_reason = 5) then # if number 9 > fprintf(file,"Min H (Pole)"); > elif > (glob_h_reason = 6) then # if number 10 > fprintf(file,"Pole"); > elif > (glob_h_reason = 7) then # if number 11 > fprintf(file,"Opt Iter"); > else > fprintf(file,"Impossible"); > fi;# end if 11 > fprintf(file,""); > end; logitem_h_reason := proc(file) global glob_h_reason; fprintf(file, ""); if glob_h_reason = 1 then fprintf(file, "Max H") elif glob_h_reason = 2 then fprintf(file, "Display Interval") elif glob_h_reason = 3 then fprintf(file, "Optimal") elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy") elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)") elif glob_h_reason = 6 then fprintf(file, "Pole") elif glob_h_reason = 7 then fprintf(file, "Opt Iter") else fprintf(file, "Impossible") end if; fprintf(file, "") end proc # End Function number 20 # Begin Function number 21 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc # End Function number 21 # Begin Function number 22 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc # End Function number 22 # Begin Function number 23 > chk_data := proc() > global glob_max_iter,ALWAYS, ATS_MAX_TERMS; > local errflag; > errflag := false; > if (glob_max_iter < 2) then # if number 11 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 11; > if (errflag) then # if number 11 > quit; > fi;# end if 11 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, ATS_MAX_TERMS; errflag := false; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc # End Function number 23 # Begin Function number 24 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := c(clock_sec2); > sub1 := c(t_end2-t_start2); > sub2 := c(t2-t_start2); > if (sub1 = glob__0) then # if number 11 > sec_left := glob__0; > else > if (sub2 > glob__0) then # if number 12 > rrr := (sub1/sub2); > sec_left := rrr * c(ms2) - c(ms2); > else > sec_left := glob__0; > fi;# end if 12 > fi;# end if 11; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := c(clock_sec2); sub1 := c(t_end2 - t_start2); sub2 := c(t2 - t_start2); if sub1 = glob__0 then sec_left := glob__0 else if glob__0 < sub2 then rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2) else sec_left := glob__0 end if end if; sec_left end proc # End Function number 24 # Begin Function number 25 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 11 > rrr := (glob__100*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 11; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := glob__100*sub2/sub1 else rrr := 0. end if; rrr end proc # End Function number 25 # Begin Function number 26 > comp_rad_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := float_abs(term1 * glob_h / term2); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM RADIUS ANALYSIS > end; comp_rad_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2) else ret := glob_larger_float end if; ret end proc # End Function number 26 # Begin Function number 27 > comp_ord_from_ratio := proc(term1,term2,last_no) > #TOP TWO TERM ORDER ANALYSIS > global glob_h,glob_larger_float; > local ret; > if (float_abs(term2) > glob__0) then # if number 11 > ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM TWO TERM ORDER ANALYSIS > end; comp_ord_from_ratio := proc(term1, term2, last_no) local ret; global glob_h, glob_larger_float; if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)* c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no)) else ret := glob_larger_float end if; ret end proc # End Function number 27 # Begin Function number 28 > c := proc(in_val) > #To Force Conversion when needed > local ret; > ret := evalc(in_val); > ret; > #End Conversion > end; c := proc(in_val) local ret; ret := evalc(in_val); ret end proc # End Function number 28 # Begin Function number 29 > comp_rad_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM RADIUS ANALYSIS > global glob_h,glob_larger_float; > local ret,temp; > temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3); > if (float_abs(temp) > glob__0) then # if number 11 > ret := float_abs((term2*glob_h*term1)/(temp)); > else > ret := glob_larger_float; > fi;# end if 11; > ret; > #BOTTOM THREE TERM RADIUS ANALYSIS > end; comp_rad_from_three_terms := proc(term1, term2, term3, last_no) local ret, temp; global glob_h, glob_larger_float; temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2 - term1*term3*c(last_no) + term1*term3); if glob__0 < float_abs(temp) then ret := float_abs(term2*glob_h*term1/temp) else ret := glob_larger_float end if; ret end proc # End Function number 29 # Begin Function number 30 > comp_ord_from_three_terms := proc(term1,term2,term3,last_no) > #TOP THREE TERM ORDER ANALYSIS > local ret; > ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3)); > ret; > #TOP THREE TERM ORDER ANALYSIS > end; comp_ord_from_three_terms := proc(term1, term2, term3, last_no) local ret; ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3 - glob__4*term2*term2*c(last_no) + glob__4*term2*term2 + term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no)) /(term2*term2*c(last_no) - glob__2*term2*term2 - term1*term3*c(last_no) + term1*term3)); ret end proc # End Function number 30 # Begin Function number 31 > comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > #TOP SIX TERM RADIUS ANALYSIS > global glob_h,glob_larger_float,glob_six_term_ord_save; > local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs; > if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11 > rm0 := term6/term5; > rm1 := term5/term4; > rm2 := term4/term3; > rm3 := term3/term2; > rm4 := term2/term1; > nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2; > nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3; > dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; > dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; > ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; > ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; > if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12 > rad_c := glob_larger_float; > ord_no := glob_larger_float; > else > if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2; > if (float_abs(rcs) <> glob__0) then # if number 14 > if (rcs > glob__0) then # if number 15 > rad_c := float_abs( sqrt(rcs) * float_abs(glob_h)); > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 15 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 14 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 13 > fi;# end if 12 > else > rad_c := glob_larger_float; > ord_no := glob_larger_float; > fi;# end if 11; > glob_six_term_ord_save := ord_no; > rad_c; > #BOTTOM SIX TERM RADIUS ANALYSIS > end; comp_rad_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no, ds1, rcs; global glob_h, glob_larger_float, glob_six_term_ord_save; if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and term2 <> glob__0 and term1 <> glob__0 then rm0 := term6/term5; rm1 := term5/term4; rm2 := term4/term3; rm3 := term3/term2; rm4 := term2/term1; nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1 + c(last_no - 3)*rm2; nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2 + c(last_no - 4)*rm3; dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3; dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4; ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3; ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4; if float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0 then rad_c := glob_larger_float; ord_no := glob_larger_float else if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2; if float_abs(rcs) <> glob__0 then if glob__0 < rcs then rad_c := float_abs(sqrt(rcs)*float_abs(glob_h)) else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if end if else rad_c := glob_larger_float; ord_no := glob_larger_float end if; glob_six_term_ord_save := ord_no; rad_c end proc # End Function number 31 # Begin Function number 32 > comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no) > global glob_six_term_ord_save; > #TOP SIX TERM ORDER ANALYSIS > #TOP SAVED FROM SIX TERM RADIUS ANALYSIS > glob_six_term_ord_save; > #BOTTOM SIX TERM ORDER ANALYSIS > end; comp_ord_from_six_terms := proc( term1, term2, term3, term4, term5, term6, last_no) global glob_six_term_ord_save; glob_six_term_ord_save end proc # End Function number 32 # Begin Function number 33 > factorial_2 := proc(nnn) > ret := nnn!; > ret;; > end; Warning, `ret` is implicitly declared local to procedure `factorial_2` factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc # End Function number 33 # Begin Function number 34 > factorial_1 := proc(nnn) > global ATS_MAX_TERMS,array_fact_1; > local ret; > if (nnn <= ATS_MAX_TERMS) then # if number 11 > if (array_fact_1[nnn] = 0) then # if number 12 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 12; > else > ret := factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_1 := proc(nnn) local ret; global ATS_MAX_TERMS, array_fact_1; if nnn <= ATS_MAX_TERMS then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc # End Function number 34 # Begin Function number 35 > factorial_3 := proc(mmm,nnn) > global ATS_MAX_TERMS,array_fact_2; > local ret; > if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11 > if (array_fact_2[mmm,nnn] = 0) then # if number 12 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 12; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 11; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global ATS_MAX_TERMS, array_fact_2; if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc # End Function number 35 # Begin Function number 36 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc # End Function number 36 # Begin Function number 37 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc # End Function number 37 # Begin Function number 38 > float_abs := proc(x) > abs(x); > end; float_abs := proc(x) abs(x) end proc # End Function number 38 # Begin Function number 39 > expt := proc(x,y) > x^y; > end; expt := proc(x, y) x^y end proc # End Function number 39 # Begin Function number 40 > neg := proc(x) > -x; > end; neg := proc(x) -x end proc # End Function number 40 # Begin Function number 41 > int_trunc := proc(x) > trunc(x); > end; int_trunc := proc(x) trunc(x) end proc # End Function number 41 # Begin Function number 42 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer))); > omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,""); > omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,""); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS))); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(glob__10, c(-glob_desired_digits_correct))* c(float_abs(c(estimated_answer))); omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, ""); omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "") ; omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := c(float_abs(desired_abs_gbl_error)/( sqrt(c(estimated_steps))*c(ATS_MAX_TERMS))); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc # End Function number 42 #END ATS LIBRARY BLOCK #BEGIN USER FUNCTION BLOCK #BEGIN BLOCK 3 #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(cos(c(x))); > end; exact_soln_y1 := proc(x) return cos(c(x)) end proc > exact_soln_y2 := proc(x) > return(sin(c(x))); > end; exact_soln_y2 := proc(x) return sin(c(x)) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 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 + 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> local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[2,1] + array_given_rad_poles[2,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 4 > glob_least_given_sing := rad_given; > fi;# end if 4; > elif > (glob_type_given_pole = 3) then # if number 4 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > elif > (glob_type_given_pole = 5) then # if number 5 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 5; > if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," "); > if ((float_abs(array_rad_test_poles[2,1]) < glob_least_ratio_sing)) then # if number 6 > glob_least_ratio_sing := array_rad_test_poles[2,1]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," "); > if ((float_abs(array_rad_test_poles[2,2]) < glob_least_3_sing)) then # if number 6 > glob_least_3_sing := array_rad_test_poles[2,2]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 5; > if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," "); > if ((float_abs(array_rad_test_poles[2,3]) < glob_least_6_sing)) then # if number 6 > glob_least_6_sing := array_rad_test_poles[2,3]; > fi;# end if 6; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 5 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, glob_least_3_sing, glob_least_6_sing, glob_least_given_sing, glob_least_ratio_sing, array_x; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1] - array_given_rad_poles[1, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_rad_test_poles[1, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_rad_test_poles[1, 1], 4, " "); if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[1, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[1, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 2] and array_rad_test_poles[1, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_rad_test_poles[1, 2], 4, " "); if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[1, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if glob__small < array_rad_test_poles[1, 3] and array_rad_test_poles[1, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_rad_test_poles[1, 3], 4, " "); if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[1, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[1, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if; if glob_type_given_pole = 1 or glob_type_given_pole = 2 then rad_given := float_abs(array_x[1] - array_given_rad_poles[2, 1] - array_given_rad_poles[2, 2]*I); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_complex(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 1], 4, " "); if float_abs(rad_given) < float_abs(glob_least_given_sing) and 0. < float_abs(rad_given) then glob_least_given_sing := rad_given end if elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") elif glob_type_given_pole = 5 then omniout_str(ALWAYS, "SOME POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_rad_test_poles[2, 1] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_rad_test_poles[2, 1], 4, " "); if float_abs(array_rad_test_poles[2, 1]) < glob_least_ratio_sing then glob_least_ratio_sing := array_rad_test_poles[2, 1] end if; omniout_complex(ALWAYS, "Order of pole (ratio test) ", 4, array_ord_test_poles[2, 1], 4, " ") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 2] and array_rad_test_poles[2, 2] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_rad_test_poles[2, 2], 4, " "); if float_abs(array_rad_test_poles[2, 2]) < glob_least_3_sing then glob_least_3_sing := array_rad_test_poles[2, 2] end if; omniout_complex(ALWAYS, "Order of pole (three term test) ", 4, array_ord_test_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if glob__small < array_rad_test_poles[2, 3] and array_rad_test_poles[2, 3] < glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_rad_test_poles[2, 3], 4, " "); if float_abs(array_rad_test_poles[2, 3]) < glob_least_6_sing then glob_least_6_sing := array_rad_test_poles[2, 3] end if; omniout_complex(ALWAYS, "Order of pole (six term test) ", 4, array_ord_test_poles[2, 3], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") end if end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 5 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 5; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_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 (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 (min_size < glob__1) then # if number 5 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 5; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_y1[1]) < min_size then min_size := float_abs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; 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 min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_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; > 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; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_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; 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; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_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[1])) then # if number 5 > array_max_est_error[1] := c(est_tmp); > fi;# end if 5 > ; > 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[2])) then # if number 5 > array_max_est_error[2] := c(est_tmp); > fi;# end if 5 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_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[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if; 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[2]) <= c(est_tmp) then array_max_est_error[2] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5 > ret := true; > else > ret := false; > fi;# end if 5; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_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_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," ") > ; > ; > 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," ") > ; > #BOTTOM DISPLAY ALOT > end; display_alot := proc(iter) local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_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_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, " "); 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, " ") end proc # End Function number 8 # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 5 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 5; > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); if c(percent_done) < glob__100 then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(expect_sec); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(glob_optimal_expect_sec); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(glob_total_exp_sec) end if end proc # End Function number 9 # Begin Function number 10 > check_for_pole := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_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 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_y1_higher[1,last_no-1],array_y1_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_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 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_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no); > array_rad_test_poles[2,1] := rad_c; > array_ord_test_poles[2,1] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test2 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_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 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_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[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_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 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_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[2,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 15 > glob_min_pole_est := rad_c; > fi;# end if 15; > array_ord_test_poles[2,2] := tmp_ord; > fi;# end if 14; > fi;# end if 13; > #BOTTOM general radius test2 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_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 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_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[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_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 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_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[2,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 19 > glob_min_pole_est := rad_c; > fi;# end if 19; > array_ord_test_poles[2,3] := tmp_ord; > fi;# end if 18; > fi;# end if 17; > #BOTTOM general radius test2 > ; > if (true) then # if number 17 > display_poles(); > fi;# end if 17 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_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[1, 1] then array_rad_test_poles[1, 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[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_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[2, 1] then array_rad_test_poles[2, 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[2, 1] := rad_c; array_ord_test_poles[2, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_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[1, 2] then array_rad_test_poles[1, 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[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_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[2, 2] then array_rad_test_poles[2, 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[2, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_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[1, 3] then array_rad_test_poles[1, 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[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_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[2, 3] then array_rad_test_poles[2, 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[2, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[2, 3] := tmp_ord end if end if; display_poles() end proc # End Function number 10 # Begin Function number 11 > atomall := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, #Bottom Generate Globals Decl #BEGIN CONST > array_const_1, > array_const_0D0, #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre neg FULL $eq_no = 1 > array_tmp1[1] := neg(array_y2[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[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; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y2_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre neg FULL $eq_no = 1 > array_tmp1[2] := neg(array_y2[2]); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[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; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y2_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre neg FULL $eq_no = 1 > array_tmp1[3] := neg(array_y2[3]); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[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; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y2_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre neg FULL $eq_no = 1 > array_tmp1[4] := neg(array_y2[4]); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[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; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y2_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre neg FULL $eq_no = 1 > array_tmp1[5] := neg(array_y2[5]); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp2[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; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y2_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit neg FULL $eq_no = 1 > array_tmp1[kkk] := neg(array_y2[kkk]); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp2[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; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y2_set_initial[2,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; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1[1] := neg(array_y2[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y1_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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; if not array_y2_set_initial[2, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y2[2] := temporary; array_y2_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y2_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := neg(array_y2[2]); array_tmp2[2] := array_tmp1[2]; if not array_y1_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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; if not array_y2_set_initial[2, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y2[3] := temporary; array_y2_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y2_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1[3] := neg(array_y2[3]); array_tmp2[3] := array_tmp1[3]; if not array_y1_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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; if not array_y2_set_initial[2, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y2[4] := temporary; array_y2_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y2_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1[4] := neg(array_y2[4]); array_tmp2[4] := array_tmp1[4]; if not array_y1_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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; if not array_y2_set_initial[2, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y2[5] := temporary; array_y2_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y2_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1[5] := neg(array_y2[5]); array_tmp2[5] := array_tmp1[5]; if not array_y1_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp2[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; if not array_y2_set_initial[2, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y2[6] := temporary; array_y2_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y2_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1[kkk] := neg(array_y2[kkk]); array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y1_set_initial[1, kkk + order_d] then temporary := c(array_tmp2[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; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y2_set_initial[2, 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; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > #END CONST > array_y1_init, > array_y2_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_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y1_init:= Array(0..(40),[]); > array_y2_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_y1:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_y2:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > 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_y2_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y2_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y2_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]); > array_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_y1_init[term] := c(0.0); > term := term + 1; > od;# end do number 1; > 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_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_y1[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_y2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_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 <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y2_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=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_y1); > zero_ats_ar(array_x); > zero_ats_ar(array_y2); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_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_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y1_set_initial[1,31] := false; > array_y1_set_initial[1,32] := false; > array_y1_set_initial[1,33] := false; > array_y1_set_initial[1,34] := false; > array_y1_set_initial[1,35] := false; > array_y1_set_initial[1,36] := false; > array_y1_set_initial[1,37] := false; > array_y1_set_initial[1,38] := false; > array_y1_set_initial[1,39] := false; > array_y1_set_initial[1,40] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := false; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > array_y2_set_initial[2,31] := false; > array_y2_set_initial[2,32] := false; > array_y2_set_initial[2,33] := false; > array_y2_set_initial[2,34] := false; > array_y2_set_initial[2,35] := false; > array_y2_set_initial[2,36] := false; > array_y2_set_initial[2,37] := false; > array_y2_set_initial[2,38] := false; > array_y2_set_initial[2,39] := false; > array_y2_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/mtest2postcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; "); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.2 + 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,"glob_max_h := 0.00001;"); > 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,""); > omniout_str(ALWAYS,"glob_type_given_pole := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(cos(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(sin(c(x)));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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 := 0.2 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_max_h := 0.00001; > 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_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > 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; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 17; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 17 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 17; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 17 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_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 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 18 > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 18; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > 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_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > 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; > 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_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > 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; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 18; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > if (glob_subiter_method = 1 ) then # if number 18 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 19 > subiter := 1; > while (subiter <= 2) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 2 + ATS_MAX_TERMS) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 19; > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 19 > display_alot(current_iter); > fi;# end if 19; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 19 > check_for_pole(); > fi;# end if 19; > if (true) then # if number 19 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 19; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > 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 =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_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 > #Jump Series array_y2; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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 =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_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 > ; > 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 ( y1 , x , 1 ) = neg ( y2 ) ; "); > omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 ; "); > 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,"2017-11-26T15:12:47-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest2") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ") > ; > 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,"mtest2 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest2 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 ( y2 , x , 1 ) = y1 ; ") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > glob_desired_digits_correct := 0.0; > logditto(html_log_file) > ; > if (array_est_digits[2] <> -16) then # if number 25 > logitem_integer(html_log_file,array_est_digits[2]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 25; > if (glob_min_good_digits <> -16) then # if number 25 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 25; > if (glob_good_digits <> -16) then # if number 25 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 25; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logditto(html_log_file) > ; > if (glob_type_given_pole = 0) then # if number 25 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 4) then # if number 26 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 5) then # if number 27 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 3) then # if number 28 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 1) then # if number 29 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > elif > (glob_type_given_pole = 2) then # if number 30 > logditto(html_log_file) > ; > logditto(html_log_file) > ; > fi;# end if 30; > if (glob_least_ratio_sing < glob_large_float) then # if number 30 > glob_least_ratio_sing := 0; > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 30; > if (glob_least_3_sing < glob_large_float) then # if number 30 > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 30; > if (glob_least_6_sing < glob_large_float) then # if number 30 > glob_least_6_sing := 0.0; > logditto(html_log_file) > ; > else > logditto(html_log_file) > ; > fi;# end if 30; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > if (c(glob_percent_done) < glob__100) then # if number 30 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 30; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 29; > if (glob_html_log) then # if number 29 > fclose(html_log_file); > fi;# end if 29 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init, array_y2_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_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 64; max_terms := 40; glob_html_log := true; array_y1_init := Array(0 .. 40, []); array_y2_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_y1 := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_y2 := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); 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_y2_higher := Array(0 .. 2, 0 .. 41, []); array_y2_higher_work := Array(0 .. 2, 0 .. 41, []); array_y2_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y2_set_initial := Array(0 .. 3, 0 .. 41, []); array_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_y1_init[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_y2_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_y1[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_y2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 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 <= 2 do term := 1; while term <= 40 do array_y2_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y2_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y2_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 40 do array_y2_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_y1); zero_ats_ar(array_x); zero_ats_ar(array_y2); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_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_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y1_set_initial[1, 31] := false; array_y1_set_initial[1, 32] := false; array_y1_set_initial[1, 33] := false; array_y1_set_initial[1, 34] := false; array_y1_set_initial[1, 35] := false; array_y1_set_initial[1, 36] := false; array_y1_set_initial[1, 37] := false; array_y1_set_initial[1, 38] := false; array_y1_set_initial[1, 39] := false; array_y1_set_initial[1, 40] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := false; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; array_y2_set_initial[2, 31] := false; array_y2_set_initial[2, 32] := false; array_y2_set_initial[2, 33] := false; array_y2_set_initial[2, 34] := false; array_y2_set_initial[2, 35] := false; array_y2_set_initial[2, 36] := false; array_y2_set_initial[2, 37] := false; array_y2_set_initial[2, 38] := false; array_y2_set_initial[2, 39] := false; array_y2_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/mtest2postcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; "); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 ; "); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.2 + 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, "glob_max_h := 0.00001;"); 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, ""); omniout_str(ALWAYS, "glob_type_given_pole := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(cos(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(sin(c(x)));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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 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* I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 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(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.2 + 0.1*I; x_end := 99.0 + 99.0*I; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_max_h := 0.00001; 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; 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; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; found_h := true; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := c(x_start); array_x[2] := c(glob_h); glob_next_display := c(x_start); glob_min_pole_est := glob_larger_float; glob_least_given_sing := glob_larger_float; glob_least_ratio_sing := glob_larger_float; glob_least_3_sing := glob_larger_float; glob_least_6_sing := glob_larger_float; order_diff := 1; term_no := 1; while term_no <= order_diff do array_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; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; 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; 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; 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; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + ATS_MAX_TERMS do atomall(); subiter := subiter + 1 end do end if; if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then display_alot(current_iter) end if; if glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.) then check_for_pole() end if; glob_next_display := glob_next_display + glob_display_interval; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_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; order_diff := 2; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do 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 ( y1 , x , 1 ) = neg ( y2 ) ; ") ; omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 ; "); 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, "2017-11-26T15:12:47-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest2"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = neg ( y2 ) ; "); 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, "mtest2 diffeq.mxt"); logitem_str(html_log_file, "mtest2 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 ( y2 , x , 1 ) = y1 ; "); 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=4.0MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/mtest2postcpx.cpx################# diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 1 ) = y1 ; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.2 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_max_h := 0.00001; 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_y1 := proc(x) return(cos(c(x))); end; exact_soln_y2 := proc(x) return(sin(c(x))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.2 0.1 h = 0.0001 0.005 y1[1] (numeric) = 0.984970995703 -0.0199000611944 y1[1] (closed_form) = 0.984970995703 -0.0199000611944 absolute error = 0 relative error = 0 % Correct digits = 62 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.199663505514 0.0981700839054 absolute error = 0 relative error = 0 % Correct digits = 62 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=56.3MB, alloc=40.3MB, time=0.76 x[1] = 0.2001 0.105 h = 0.0001 0.003 y1[1] (numeric) = 0.985441879772 -0.0209081957303 y1[1] (closed_form) = 0.985454178853 -0.020908941147 absolute error = 1.232e-05 relative error = 0.00125 % Correct digits = 5 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.199864048451 0.103094096154 absolute error = 0.004928 relative error = 2.191 % Correct digits = 2 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2002 0.108 h = 0.001 0.001 y1[1] (numeric) = 0.985716423673 -0.0215170032553 y1[1] (closed_form) = 0.985747898456 -0.0215192332672 absolute error = 3.155e-05 relative error = 0.0032 % Correct digits = 4 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.200026250547 0.106048775656 absolute error = 0.007887 relative error = 3.484 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=105.7MB, alloc=44.3MB, time=1.43 x[1] = 0.2012 0.109 h = 0.001 0.003 y1[1] (numeric) = 0.985614930251 -0.0218148368447 y1[1] (closed_form) = 0.98565389936 -0.02182629401 absolute error = 4.062e-05 relative error = 0.00412 % Correct digits = 4 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.201033624049 0.107012803959 absolute error = 0.008948 relative error = 3.929 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=155.1MB, alloc=44.3MB, time=2.08 x[1] = 0.2022 0.112 h = 0.0001 0.004 y1[1] (numeric) = 0.985709776997 -0.0225119974451 y1[1] (closed_form) = 0.985777780735 -0.0225394530237 absolute error = 7.334e-05 relative error = 0.007438 % Correct digits = 4 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.20208588634 0.109947767175 absolute error = 0.01202 relative error = 5.227 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2023 0.116 h = 0.003 0.006 y1[1] (numeric) = 0.986082490982 -0.0233204684756 y1[1] (closed_form) = 0.986205236512 -0.0233593681006 absolute error = 0.0001288 relative error = 0.01305 % Correct digits = 4 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.202276282617 0.113889433029 absolute error = 0.01594 relative error = 6.865 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=204.4MB, alloc=44.3MB, time=2.74 x[1] = 0.2053 0.122 h = 0.0001 0.005 y1[1] (numeric) = 0.986072520969 -0.0248129597604 y1[1] (closed_form) = 0.986294628552 -0.0249327686785 absolute error = 0.0002524 relative error = 0.02558 % Correct digits = 4 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.205379884307 0.119734490579 absolute error = 0.02231 relative error = 9.384 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=253.8MB, alloc=44.3MB, time=3.40 x[1] = 0.2054 0.127 h = 0.0001 0.003 y1[1] (numeric) = 0.986543405038 -0.0258210942963 y1[1] (closed_form) = 0.986885076562 -0.0259724506573 absolute error = 0.0003737 relative error = 0.03785 % Correct digits = 3 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.205605805459 0.124664884332 absolute error = 0.02715 relative error = 11.29 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2055 0.13 h = 0.001 0.001 y1[1] (numeric) = 0.986817948939 -0.0264299018213 y1[1] (closed_form) = 0.987242939361 -0.0266021483526 absolute error = 0.0004586 relative error = 0.04643 % Correct digits = 3 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.205783373477 0.127623445418 absolute error = 0.03008 relative error = 12.42 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=303.4MB, alloc=44.3MB, time=4.06 x[1] = 0.2065 0.131 h = 0.001 0.003 y1[1] (numeric) = 0.986716455518 -0.0267277354107 y1[1] (closed_form) = 0.987164752719 -0.0269365423883 absolute error = 0.0004945 relative error = 0.05008 % Correct digits = 3 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.206797346508 0.128583880088 absolute error = 0.03124 relative error = 12.83 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=352.9MB, alloc=44.3MB, time=4.72 x[1] = 0.2075 0.134 h = 0.0001 0.004 y1[1] (numeric) = 0.986811302264 -0.0274248960111 y1[1] (closed_form) = 0.987347574353 -0.0276885887299 absolute error = 0.0005976 relative error = 0.0605 % Correct digits = 3 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.207866538189 0.131518334591 absolute error = 0.03434 relative error = 13.96 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2076 0.138 h = 0.003 0.006 y1[1] (numeric) = 0.987184016249 -0.0282333670416 y1[1] (closed_form) = 0.98786074505 -0.0285338253451 absolute error = 0.0007404 relative error = 0.07492 % Correct digits = 3 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.208077742888 0.135465934863 absolute error = 0.03823 relative error = 15.4 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=402.3MB, alloc=44.3MB, time=5.38 x[1] = 0.2106 0.144 h = 0.0001 0.005 y1[1] (numeric) = 0.987174046236 -0.0297258583264 y1[1] (closed_form) = 0.988062120836 -0.0302068649647 absolute error = 0.00101 relative error = 0.1022 % Correct digits = 3 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.211217824674 0.141305588706 absolute error = 0.04466 relative error = 17.57 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=451.8MB, alloc=44.3MB, time=6.04 x[1] = 0.2107 0.149 h = 0.0001 0.003 y1[1] (numeric) = 0.987644930305 -0.0307339928623 y1[1] (closed_form) = 0.988759860432 -0.0312779606873 absolute error = 0.001241 relative error = 0.1254 % Correct digits = 3 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.211470376899 0.146244559154 absolute error = 0.0495 relative error = 19.25 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2108 0.152 h = 0.001 0.001 y1[1] (numeric) = 0.987919474206 -0.0313428003873 y1[1] (closed_form) = 0.989181882728 -0.0319274345111 absolute error = 0.001391 relative error = 0.1406 % Correct digits = 3 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.211664081786 0.149208309288 absolute error = 0.05243 relative error = 20.25 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=501.3MB, alloc=44.3MB, time=6.70 x[1] = 0.2118 0.153 h = 0.001 0.003 y1[1] (numeric) = 0.987817980785 -0.0316406339767 y1[1] (closed_form) = 0.989119394907 -0.0322892960632 absolute error = 0.001454 relative error = 0.1469 % Correct digits = 3 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.212685340631 0.150165351732 absolute error = 0.0536 relative error = 20.59 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2128 0.156 h = 0.0001 0.004 y1[1] (numeric) = 0.987912827531 -0.0323377945771 y1[1] (closed_form) = 0.989361064761 -0.033080615245 absolute error = 0.001628 relative error = 0.1644 % Correct digits = 3 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.213772633535 0.153100386053 absolute error = 0.05671 relative error = 21.57 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=550.7MB, alloc=44.3MB, time=7.36 x[1] = 0.2129 0.16 h = 0.003 0.006 y1[1] (numeric) = 0.988285541516 -0.0331462656076 y1[1] (closed_form) = 0.989959987221 -0.0339516784415 absolute error = 0.001858 relative error = 0.1876 % Correct digits = 3 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.214005663601 0.157055671287 absolute error = 0.06061 relative error = 22.83 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=600.2MB, alloc=44.3MB, time=8.02 x[1] = 0.2159 0.166 h = 0.0001 0.005 y1[1] (numeric) = 0.988275571503 -0.0346387568924 y1[1] (closed_form) = 0.990273048382 -0.0357251668441 absolute error = 0.002274 relative error = 0.2295 % Correct digits = 3 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.217185019028 0.162891851533 absolute error = 0.06705 relative error = 24.7 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.216 0.171 h = 0.0001 0.003 y1[1] (numeric) = 0.988746455572 -0.0356468914283 y1[1] (closed_form) = 0.99107814788 -0.0368283273727 absolute error = 0.002614 relative error = 0.2636 % Correct digits = 3 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.217465469327 0.167841591564 absolute error = 0.07191 relative error = 26.18 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=649.6MB, alloc=44.3MB, time=8.68 x[1] = 0.2161 0.174 h = 0.001 0.001 y1[1] (numeric) = 0.989020999473 -0.0362556989533 y1[1] (closed_form) = 0.991564370614 -0.037497971858 absolute error = 0.002831 relative error = 0.2853 % Correct digits = 3 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.217676090595 0.170811836812 absolute error = 0.07484 relative error = 27.05 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=699.2MB, alloc=44.3MB, time=9.34 x[1] = 0.2171 0.175 h = 0.001 0.003 y1[1] (numeric) = 0.988919506051 -0.0365535325427 y1[1] (closed_form) = 0.991517468733 -0.0378874513342 absolute error = 0.00292 relative error = 0.2943 % Correct digits = 3 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.218705324068 0.171765685192 absolute error = 0.07602 relative error = 27.34 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2181 0.178 h = 0.0001 0.004 y1[1] (numeric) = 0.989014352797 -0.0372506931431 y1[1] (closed_form) = 0.99181791244 -0.0387184604982 absolute error = 0.003165 relative error = 0.3188 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.21981189842 0.174702383903 absolute error = 0.07914 relative error = 28.19 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=748.7MB, alloc=44.3MB, time=10.00 x[1] = 0.2182 0.182 h = 0.003 0.006 y1[1] (numeric) = 0.989387066783 -0.0380591641736 y1[1] (closed_form) = 0.992502656578 -0.039615887093 absolute error = 0.003483 relative error = 0.3506 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.220067782538 0.178667103058 absolute error = 0.08304 relative error = 29.3 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=798.1MB, alloc=44.3MB, time=10.65 x[1] = 0.2212 0.188 h = 0.0001 0.005 y1[1] (numeric) = 0.989377096769 -0.0395516554584 y1[1] (closed_form) = 0.992927132236 -0.0414907058638 absolute error = 0.004045 relative error = 0.407 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.223289222248 0.184501729071 absolute error = 0.08951 relative error = 30.9 % Correct digits = 1 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2213 0.193 h = 0.0001 0.003 y1[1] (numeric) = 0.989847980838 -0.0405597899943 y1[1] (closed_form) = 0.993839701424 -0.0426266219179 absolute error = 0.004495 relative error = 0.4519 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.223598852851 0.18946442998 absolute error = 0.09438 relative error = 32.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=847.5MB, alloc=44.3MB, time=11.31 x[1] = 0.2214 0.196 h = 0.001 0.001 y1[1] (numeric) = 0.99012252474 -0.0411685975193 y1[1] (closed_form) = 0.994390190103 -0.0433168557667 absolute error = 0.004778 relative error = 0.48 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.223827179242 0.192442475424 absolute error = 0.09732 relative error = 32.97 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2224 0.197 h = 0.0001 0.004 y1[1] (numeric) = 0.990021031318 -0.0414664311087 y1[1] (closed_form) = 0.994358761943 -0.0437341198011 absolute error = 0.004895 relative error = 0.4918 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.224865079048 0.193393324585 absolute error = 0.0985 relative error = 33.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=897.0MB, alloc=44.3MB, time=11.98 x[1] = 0.2225 0.201 h = 0.003 0.006 y1[1] (numeric) = 0.990393745303 -0.0422749021391 y1[1] (closed_form) = 0.995117783028 -0.0446536693978 absolute error = 0.005289 relative error = 0.531 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.22514132782 0.197367853008 absolute error = 0.1024 relative error = 34.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=946.4MB, alloc=44.3MB, time=12.63 x[1] = 0.2255 0.207 h = 0.0001 0.005 y1[1] (numeric) = 0.99038377529 -0.0437673934239 y1[1] (closed_form) = 0.995639187091 -0.0466151477439 absolute error = 0.005977 relative error = 0.5997 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.228401244886 0.203203217343 absolute error = 0.1089 relative error = 35.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2256 0.212 h = 0.0001 0.003 y1[1] (numeric) = 0.990854659359 -0.0447755279599 y1[1] (closed_form) = 0.996644784226 -0.0477785595758 absolute error = 0.006523 relative error = 0.6537 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.228736842239 0.208179197251 absolute error = 0.1138 relative error = 36.79 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=995.8MB, alloc=44.3MB, time=13.30 x[1] = 0.2257 0.215 h = 0.001 0.001 y1[1] (numeric) = 0.99112920326 -0.0453843354848 y1[1] (closed_form) = 0.997250914553 -0.0484861029005 absolute error = 0.006863 relative error = 0.6873 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.228980933686 0.211165225341 absolute error = 0.1167 relative error = 37.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1045.4MB, alloc=44.3MB, time=13.96 x[1] = 0.2267 0.216 h = 0.001 0.003 y1[1] (numeric) = 0.991027709838 -0.0456821690742 y1[1] (closed_form) = 0.997233050211 -0.0489272463045 absolute error = 0.007003 relative error = 0.7014 % Correct digits = 2 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.230026882185 0.212113760823 absolute error = 0.1179 relative error = 37.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2277 0.219 h = 0.0001 0.004 y1[1] (numeric) = 0.991122556585 -0.0463793296747 y1[1] (closed_form) = 0.997643206403 -0.0498326297333 absolute error = 0.007379 relative error = 0.7387 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.231172457892 0.215056693881 absolute error = 0.1211 relative error = 38.34 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1094.8MB, alloc=44.3MB, time=14.61 x[1] = 0.2278 0.223 h = 0.003 0.006 y1[1] (numeric) = 0.99149527057 -0.0471878007051 y1[1] (closed_form) = 0.998488274272 -0.0507796253382 absolute error = 0.007862 relative error = 0.7863 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.231473488309 0.219043920937 absolute error = 0.125 relative error = 39.22 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1144.2MB, alloc=44.3MB, time=15.27 x[1] = 0.2308 0.229 h = 0.0001 0.005 y1[1] (numeric) = 0.991485300557 -0.0486802919899 y1[1] (closed_form) = 0.999120673377 -0.0528442693503 absolute error = 0.008697 relative error = 0.8692 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.234780748461 0.224881308725 absolute error = 0.1315 relative error = 40.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2309 0.234 h = 0.0001 0.003 y1[1] (numeric) = 0.991956184626 -0.0496884265259 y1[1] (closed_form) = 1.00023406385 -0.0540418262429 absolute error = 0.009353 relative error = 0.9337 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.235147930256 0.229874340896 absolute error = 0.1364 relative error = 41.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1193.7MB, alloc=44.3MB, time=15.93 x[1] = 0.231 0.237 h = 0.001 0.001 y1[1] (numeric) = 0.992230728527 -0.0502972340508 y1[1] (closed_form) = 1.00090465285 -0.0547708016147 absolute error = 0.00976 relative error = 0.9736 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.235411205787 0.232870606108 absolute error = 0.1394 relative error = 42.09 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.232 0.238 h = 0.001 0.003 y1[1] (numeric) = 0.992129235105 -0.0505950676402 y1[1] (closed_form) = 1.00090205732 -0.0552400843304 absolute error = 0.009927 relative error = 0.9903 % Correct digits = 2 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.236467114427 0.233816504196 absolute error = 0.1406 relative error = 42.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1243.3MB, alloc=44.3MB, time=16.59 x[1] = 0.233 0.241 h = 0.0001 0.004 y1[1] (numeric) = 0.992224081851 -0.0512922282407 y1[1] (closed_form) = 1.00137087728 -0.056186527571 absolute error = 0.01037 relative error = 1.034 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.23763538856 0.236764198911 absolute error = 0.1437 relative error = 42.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1292.7MB, alloc=44.3MB, time=17.24 x[1] = 0.2331 0.245 h = 0.003 0.006 y1[1] (numeric) = 0.992596795836 -0.0521006992711 y1[1] (closed_form) = 1.00230215637 -0.0571615980259 absolute error = 0.01095 relative error = 1.09 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.23796226776 0.240765872262 absolute error = 0.1476 relative error = 43.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2361 0.251 h = 0.0001 0.005 y1[1] (numeric) = 0.992586825823 -0.0535931905559 y1[1] (closed_form) = 1.00304535733 -0.059330496509 absolute error = 0.01193 relative error = 1.187 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.241319740236 0.246607173591 absolute error = 0.1542 relative error = 44.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1342.0MB, alloc=44.3MB, time=17.90 x[1] = 0.2362 0.256 h = 0.0001 0.003 y1[1] (numeric) = 0.993057709892 -0.0546013250919 y1[1] (closed_form) = 1.00426676946 -0.0605630041181 absolute error = 0.0127 relative error = 1.262 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.241719838343 0.251619448828 absolute error = 0.1591 relative error = 45.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1391.4MB, alloc=44.3MB, time=18.56 x[1] = 0.2363 0.259 h = 0.001 0.001 y1[1] (numeric) = 0.993332253793 -0.0552101326168 y1[1] (closed_form) = 1.00500195286 -0.0613139002867 absolute error = 0.01317 relative error = 1.308 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.242003116773 0.254627255827 absolute error = 0.1621 relative error = 46.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2373 0.26 h = 0.001 0.003 y1[1] (numeric) = 0.993230760372 -0.0555079662063 y1[1] (closed_form) = 1.00501451552 -0.0618115356655 absolute error = 0.01336 relative error = 1.327 % Correct digits = 2 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.243069687568 0.255570701521 absolute error = 0.1633 relative error = 46.29 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1440.7MB, alloc=44.3MB, time=19.22 x[1] = 0.2383 0.263 h = 0.0001 0.004 y1[1] (numeric) = 0.993325607118 -0.0562051268067 y1[1] (closed_form) = 1.00554199227 -0.0627995795601 absolute error = 0.01388 relative error = 1.378 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.244261880223 0.258524229352 absolute error = 0.1664 relative error = 46.8 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1490.1MB, alloc=44.3MB, time=19.87 x[1] = 0.2384 0.267 h = 0.003 0.006 y1[1] (numeric) = 0.993698321103 -0.0570135978371 y1[1] (closed_form) = 1.00655967976 -0.0638033866125 absolute error = 0.01454 relative error = 1.442 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.2446156905 0.262542097218 absolute error = 0.1704 relative error = 47.49 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2414 0.273 h = 0.0001 0.005 y1[1] (numeric) = 0.99368835109 -0.0585060891219 y1[1] (closed_form) = 1.00741351559 -0.0660777017445 absolute error = 0.01568 relative error = 1.553 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.248026268343 0.268389192247 absolute error = 0.177 relative error = 48.42 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1539.4MB, alloc=44.3MB, time=20.53 x[1] = 0.2415 0.278 h = 0.0001 0.003 y1[1] (numeric) = 0.994159235159 -0.0595142236579 y1[1] (closed_form) = 1.00874321882 -0.0673460068534 absolute error = 0.01655 relative error = 1.637 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.248460634127 0.273422902451 absolute error = 0.1819 relative error = 49.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2416 0.281 h = 0.001 0.001 y1[1] (numeric) = 0.99443377906 -0.0601230311828 y1[1] (closed_form) = 1.00954315668 -0.0681193376273 absolute error = 0.01709 relative error = 1.689 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.248764746084 0.276443556499 absolute error = 0.1849 relative error = 49.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1588.9MB, alloc=44.3MB, time=21.19 x[1] = 0.2426 0.282 h = 0.001 0.003 y1[1] (numeric) = 0.994332285639 -0.0604208647723 y1[1] (closed_form) = 1.00957076719 -0.0686455554822 absolute error = 0.01732 relative error = 1.711 % Correct digits = 2 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.249842685335 0.277384731194 absolute error = 0.1861 relative error = 49.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1638.4MB, alloc=44.3MB, time=21.84 x[1] = 0.2436 0.285 h = 0.0001 0.004 y1[1] (numeric) = 0.994427132385 -0.0611180253727 y1[1] (closed_form) = 1.0101569108 -0.0696757735196 absolute error = 0.01791 relative error = 1.768 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.251060028876 0.280345160682 absolute error = 0.1893 relative error = 50.3 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2437 0.289 h = 0.003 0.006 y1[1] (numeric) = 0.99479984637 -0.0619264964032 y1[1] (closed_form) = 1.01126123657 -0.0707090121708 absolute error = 0.01866 relative error = 1.84 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.251441868577 0.284380972385 absolute error = 0.1933 relative error = 50.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1687.9MB, alloc=44.3MB, time=22.50 x[1] = 0.2467 0.295 h = 0.0001 0.005 y1[1] (numeric) = 0.994789876357 -0.063418987688 y1[1] (closed_form) = 1.01222556614 -0.0730899799934 absolute error = 0.01994 relative error = 1.965 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.254908470393 0.290235731532 absolute error = 0.1999 relative error = 51.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1737.4MB, alloc=44.3MB, time=23.16 x[1] = 0.2468 0.3 h = 0.0001 0.003 y1[1] (numeric) = 0.995260760426 -0.0644271222239 y1[1] (closed_form) = 1.01366387091 -0.0743949709616 absolute error = 0.02093 relative error = 2.059 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.255378475842 0.295293070384 absolute error = 0.2048 relative error = 52.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2469 0.303 h = 0.001 0.001 y1[1] (numeric) = 0.995535304327 -0.0650359297488 y1[1] (closed_form) = 1.01452874759 -0.0751912754796 absolute error = 0.02154 relative error = 2.117 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.255704264447 0.298327877742 absolute error = 0.2079 relative error = 52.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1786.9MB, alloc=44.3MB, time=23.82 x[1] = 0.2479 0.304 h = 0.0001 0.004 y1[1] (numeric) = 0.995433810905 -0.0653337633383 y1[1] (closed_form) = 1.01457129583 -0.0757463221647 absolute error = 0.02179 relative error = 2.141 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.256794283111 0.299266959147 absolute error = 0.2091 relative error = 53.01 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1836.2MB, alloc=44.3MB, time=24.47 x[1] = 0.248 0.308 h = 0.003 0.006 y1[1] (numeric) = 0.99580652489 -0.0661422343687 y1[1] (closed_form) = 1.01575076843 -0.0768044403887 absolute error = 0.02262 relative error = 2.22 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.257200899928 0.303319970363 absolute error = 0.2131 relative error = 53.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.251 0.314 h = 0.0001 0.005 y1[1] (numeric) = 0.995796554877 -0.0676347256535 y1[1] (closed_form) = 1.01681140567 -0.0792769434828 absolute error = 0.02402 relative error = 2.356 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.260717961836 0.309183532168 absolute error = 0.2197 relative error = 54.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1885.5MB, alloc=44.3MB, time=25.13 x[1] = 0.2511 0.319 h = 0.0001 0.003 y1[1] (numeric) = 0.996267438946 -0.0686428601895 y1[1] (closed_form) = 1.01834392309 -0.080612956432 absolute error = 0.02511 relative error = 2.458 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.261219442885 0.314263415458 absolute error = 0.2247 relative error = 54.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2512 0.322 h = 0.001 0.001 y1[1] (numeric) = 0.996541982847 -0.0692516677144 y1[1] (closed_form) = 1.01926514596 -0.0814287102743 absolute error = 0.02578 relative error = 2.521 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.261564385427 0.317311724712 absolute error = 0.2277 relative error = 55.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1935.0MB, alloc=44.3MB, time=25.79 x[1] = 0.2522 0.323 h = 0.001 0.003 y1[1] (numeric) = 0.996440489426 -0.0695495013038 y1[1] (closed_form) = 1.01932081168 -0.0820086056681 absolute error = 0.02605 relative error = 2.548 % Correct digits = 2 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.262665396908 0.318249299216 absolute error = 0.2289 relative error = 55.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=1984.5MB, alloc=44.3MB, time=26.44 x[1] = 0.2532 0.326 h = 0.0001 0.004 y1[1] (numeric) = 0.996535336172 -0.0702466619043 y1[1] (closed_form) = 1.02001672525 -0.0831182393262 absolute error = 0.02678 relative error = 2.617 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.263932753611 0.321225740748 absolute error = 0.2321 relative error = 55.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2533 0.33 h = 0.003 0.006 y1[1] (numeric) = 0.996908050157 -0.0710551329347 y1[1] (closed_form) = 1.02128335995 -0.0842071685206 absolute error = 0.0277 relative error = 2.703 % Correct digits = 2 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.264369468577 0.325299969249 absolute error = 0.2362 relative error = 56.34 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2033.8MB, alloc=44.3MB, time=27.10 x[1] = 0.2563 0.336 h = 0.0001 0.005 y1[1] (numeric) = 0.996898080144 -0.0725476242195 y1[1] (closed_form) = 1.02245431276 -0.0867888236995 absolute error = 0.02926 relative error = 2.851 % Correct digits = 2 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.267948037387 0.331174685796 absolute error = 0.2428 relative error = 57 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2083.3MB, alloc=44.3MB, time=27.76 x[1] = 0.2564 0.341 h = 0.0001 0.003 y1[1] (numeric) = 0.997368964213 -0.0735557587555 y1[1] (closed_form) = 1.02409613015 -0.0881632830024 absolute error = 0.03046 relative error = 2.963 % Correct digits = 2 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.268487743626 0.336282303706 absolute error = 0.2479 relative error = 57.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2565 0.344 h = 0.001 0.001 y1[1] (numeric) = 0.997643508114 -0.0741645662804 y1[1] (closed_form) = 1.02508270654 -0.0890030793426 absolute error = 0.03119 relative error = 3.032 % Correct digits = 2 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.268855951683 0.339347211366 absolute error = 0.2509 relative error = 57.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2132.7MB, alloc=44.3MB, time=28.42 x[1] = 0.2575 0.345 h = 0.001 0.003 y1[1] (numeric) = 0.997542014692 -0.0744623998698 y1[1] (closed_form) = 1.02515310859 -0.0896123076118 absolute error = 0.03149 relative error = 3.06 % Correct digits = 2 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.269970377128 0.340283021765 absolute error = 0.2521 relative error = 58.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2182.1MB, alloc=44.3MB, time=29.07 x[1] = 0.2585 0.348 h = 0.0001 0.004 y1[1] (numeric) = 0.997636861439 -0.0751595604703 y1[1] (closed_form) = 1.02590781891 -0.0907659379622 absolute error = 0.03229 relative error = 3.135 % Correct digits = 2 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.271266472603 0.343269422691 absolute error = 0.2553 relative error = 58.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2586 0.352 h = 0.003 0.006 y1[1] (numeric) = 0.998009575424 -0.0759680315007 y1[1] (closed_form) = 1.02726193922 -0.0918864699964 absolute error = 0.0333 relative error = 3.229 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.27173443501 0.347366624158 absolute error = 0.2594 relative error = 58.82 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2231.4MB, alloc=44.3MB, time=29.73 x[1] = 0.2616 0.358 h = 0.0001 0.005 y1[1] (numeric) = 0.997999605411 -0.0774605227855 y1[1] (closed_form) = 1.02854313939 -0.0945787273825 absolute error = 0.03501 relative error = 3.39 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.27537751236 0.35325433928 absolute error = 0.2661 relative error = 59.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2617 0.363 h = 0.0001 0.003 y1[1] (numeric) = 0.99847048948 -0.0784686573215 y1[1] (closed_form) = 1.03029468472 -0.0959926425872 absolute error = 0.03633 relative error = 3.511 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.275956881041 0.358391894621 absolute error = 0.2712 relative error = 59.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2280.9MB, alloc=44.3MB, time=30.38 x[1] = 0.2618 0.366 h = 0.001 0.001 y1[1] (numeric) = 0.998745033381 -0.0790774648464 y1[1] (closed_form) = 1.03134686858 -0.0968570943948 absolute error = 0.03713 relative error = 3.585 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.276349237276 0.361474712174 absolute error = 0.2742 relative error = 60.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2330.4MB, alloc=44.3MB, time=31.04 x[1] = 0.2628 0.367 h = 0.001 0.003 y1[1] (numeric) = 0.998643539959 -0.0793752984358 y1[1] (closed_form) = 1.03143189699 -0.0974959497195 absolute error = 0.03746 relative error = 3.616 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.277477803025 0.362408925223 absolute error = 0.2755 relative error = 60.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2638 0.37 h = 0.0001 0.004 y1[1] (numeric) = 0.998738386705 -0.0800724590363 y1[1] (closed_form) = 1.03224547908 -0.0986942787404 absolute error = 0.03833 relative error = 3.697 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.278803924673 0.365406344838 absolute error = 0.2787 relative error = 60.64 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2379.6MB, alloc=44.3MB, time=31.70 x[1] = 0.2639 0.374 h = 0.003 0.006 y1[1] (numeric) = 0.99911110069 -0.0808809300667 y1[1] (closed_form) = 1.03368744107 -0.0998472402953 absolute error = 0.03944 relative error = 3.797 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.279304303416 0.369528278143 absolute error = 0.2828 relative error = 61.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2429.1MB, alloc=44.3MB, time=32.36 x[1] = 0.2669 0.38 h = 0.0001 0.005 y1[1] (numeric) = 0.999101130677 -0.0823734213515 y1[1] (closed_form) = 1.03507884483 -0.102651626149 absolute error = 0.0413 relative error = 3.97 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.283014923387 0.375430826552 absolute error = 0.2895 relative error = 61.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.267 0.385 h = 0.0001 0.003 y1[1] (numeric) = 0.999572014746 -0.0833815558875 y1[1] (closed_form) = 1.03694058694 -0.104106050383 absolute error = 0.04273 relative error = 4.1 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.283635416827 0.380600526534 absolute error = 0.2946 relative error = 62.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2478.6MB, alloc=44.3MB, time=33.02 x[1] = 0.2671 0.388 h = 0.001 0.001 y1[1] (numeric) = 0.999846558647 -0.0839903634124 y1[1] (closed_form) = 1.03805865638 -0.104995797169 absolute error = 0.0436 relative error = 4.179 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.284052819093 0.383702568003 absolute error = 0.2977 relative error = 62.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2528.1MB, alloc=44.3MB, time=33.67 x[1] = 0.2681 0.389 h = 0.001 0.003 y1[1] (numeric) = 0.999745065226 -0.0842881970018 y1[1] (closed_form) = 1.03815820091 -0.105664590648 absolute error = 0.04396 relative error = 4.213 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.28519625756 0.384635346429 absolute error = 0.299 relative error = 62.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2691 0.392 h = 0.0001 0.004 y1[1] (numeric) = 0.999839911972 -0.0849853576023 y1[1] (closed_form) = 1.03903074625 -0.106908354427 absolute error = 0.04491 relative error = 4.299 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.286553709042 0.387644842049 absolute error = 0.3022 relative error = 62.7 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2577.6MB, alloc=44.3MB, time=34.34 x[1] = 0.2692 0.396 h = 0.003 0.006 y1[1] (numeric) = 1.00021262596 -0.0857938286327 y1[1] (closed_form) = 1.04056093844 -0.108094607455 absolute error = 0.0461 relative error = 4.407 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.287087693562 0.391793269778 absolute error = 0.3064 relative error = 63.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2627.0MB, alloc=44.3MB, time=35.02 x[1] = 0.2722 0.402 h = 0.0001 0.005 y1[1] (numeric) = 1.00020265594 -0.0872863199175 y1[1] (closed_form) = 1.04206252613 -0.111012724859 absolute error = 0.04812 relative error = 4.591 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.29086892449 0.397712477199 absolute error = 0.3131 relative error = 63.55 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2723 0.407 h = 0.0001 0.003 y1[1] (numeric) = 1.00067354001 -0.0882944544535 y1[1] (closed_form) = 1.04403497463 -0.112508755419 absolute error = 0.04966 relative error = 4.73 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.291532031251 0.402916534095 absolute error = 0.3183 relative error = 64 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2676.4MB, alloc=44.3MB, time=35.71 x[1] = 0.2724 0.41 h = 0.001 0.001 y1[1] (numeric) = 1.00094808391 -0.0889032619784 y1[1] (closed_form) = 1.04521923189 -0.113424463593 absolute error = 0.05061 relative error = 4.814 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.291975393302 0.406039116426 absolute error = 0.3214 relative error = 64.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2734 0.411 h = 0.0001 0.004 y1[1] (numeric) = 1.00084659049 -0.0892010955678 y1[1] (closed_form) = 1.04533318196 -0.11412352336 absolute error = 0.05099 relative error = 4.849 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.293134443347 0.406970618833 absolute error = 0.3226 relative error = 64.33 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2725.9MB, alloc=44.3MB, time=36.39 x[1] = 0.2735 0.415 h = 0.003 0.006 y1[1] (numeric) = 1.00121930448 -0.0900095665983 y1[1] (closed_form) = 1.04694006689 -0.115338092195 absolute error = 0.05227 relative error = 4.962 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.293697979211 0.411143686727 absolute error = 0.3268 relative error = 64.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2775.3MB, alloc=44.3MB, time=37.06 x[1] = 0.2765 0.421 h = 0.0001 0.005 y1[1] (numeric) = 1.00120933446 -0.0915020578831 y1[1] (closed_form) = 1.0485378818 -0.118354136193 absolute error = 0.05442 relative error = 5.157 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.297542246362 0.417079580407 absolute error = 0.3336 relative error = 65.11 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2766 0.426 h = 0.0001 0.003 y1[1] (numeric) = 1.00168021853 -0.092510192419 y1[1] (closed_form) = 1.05060657612 -0.119885565204 absolute error = 0.05606 relative error = 5.302 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.298242800943 0.422315518722 absolute error = 0.3388 relative error = 65.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2824.8MB, alloc=44.3MB, time=37.74 x[1] = 0.2767 0.429 h = 0.001 0.001 y1[1] (numeric) = 1.00195476243 -0.093118999944 y1[1] (closed_form) = 1.05184838667 -0.120823380755 absolute error = 0.05707 relative error = 5.39 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.298708986604 0.425457163388 absolute error = 0.3419 relative error = 65.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2874.3MB, alloc=44.3MB, time=38.43 x[1] = 0.2777 0.43 h = 0.001 0.003 y1[1] (numeric) = 1.00185326901 -0.0934168335334 y1[1] (closed_form) = 1.05197501378 -0.121548598796 absolute error = 0.05748 relative error = 5.428 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.299882084139 0.426387889294 absolute error = 0.3432 relative error = 65.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2787 0.433 h = 0.0001 0.004 y1[1] (numeric) = 1.00194811576 -0.0941139941338 y1[1] (closed_form) = 1.0529581386 -0.122878277809 absolute error = 0.05856 relative error = 5.524 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.301301188566 0.42942307427 absolute error = 0.3465 relative error = 66.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2923.7MB, alloc=44.3MB, time=39.12 x[1] = 0.2788 0.437 h = 0.003 0.006 y1[1] (numeric) = 1.00232082974 -0.0949224651643 y1[1] (closed_form) = 1.05465407437 -0.124127832019 absolute error = 0.05993 relative error = 5.644 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.301900580318 0.433625942831 absolute error = 0.3507 relative error = 66.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=2973.0MB, alloc=44.3MB, time=39.80 x[1] = 0.2818 0.443 h = 0.0001 0.005 y1[1] (numeric) = 1.00231085973 -0.0964149564491 y1[1] (closed_form) = 1.05636212074 -0.127260797093 absolute error = 0.06223 relative error = 5.849 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.305821243808 0.439581906833 absolute error = 0.3575 relative error = 66.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2819 0.448 h = 0.0001 0.003 y1[1] (numeric) = 1.0027817438 -0.097423090985 y1[1] (closed_form) = 1.05854259255 -0.128835986726 absolute error = 0.064 relative error = 6.002 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.306567229011 0.444856352855 absolute error = 0.3628 relative error = 67.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3022.5MB, alloc=44.3MB, time=40.49 x[1] = 0.282 0.451 h = 0.001 0.001 y1[1] (numeric) = 1.0030562877 -0.09803189851 y1[1] (closed_form) = 1.05985122625 -0.129801072304 absolute error = 0.06508 relative error = 6.095 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.307061103762 0.448021009385 absolute error = 0.366 relative error = 67.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.283 0.452 h = 0.001 0.003 y1[1] (numeric) = 1.00295479428 -0.0983297320994 y1[1] (closed_form) = 1.0599920561 -0.130557214316 absolute error = 0.06551 relative error = 6.134 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.308251204391 0.448950752081 absolute error = 0.3672 relative error = 67.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3072.1MB, alloc=44.3MB, time=41.18 x[1] = 0.284 0.455 h = 0.0001 0.004 y1[1] (numeric) = 1.00304964103 -0.0990268926998 y1[1] (closed_form) = 1.06103450546 -0.131934623761 absolute error = 0.06667 relative error = 6.236 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.309705452935 0.452001044698 absolute error = 0.3705 relative error = 67.63 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3121.4MB, alloc=44.3MB, time=41.86 x[1] = 0.2841 0.459 h = 0.003 0.006 y1[1] (numeric) = 1.00342235501 -0.0998353637303 y1[1] (closed_form) = 1.06281997387 -0.133220128569 absolute error = 0.06814 relative error = 6.361 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.310341954033 0.456235490319 absolute error = 0.3748 relative error = 67.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2871 0.465 h = 0.0001 0.005 y1[1] (numeric) = 1.003412385 -0.101327855015 y1[1] (closed_form) = 1.06463829976 -0.136471841456 absolute error = 0.0706 relative error = 6.577 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.314342190419 0.462213325735 absolute error = 0.3817 relative error = 68.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3170.8MB, alloc=44.3MB, time=42.55 x[1] = 0.2872 0.47 h = 0.0001 0.003 y1[1] (numeric) = 1.00388326907 -0.102335989551 y1[1] (closed_form) = 1.06693117584 -0.138092018399 absolute error = 0.07248 relative error = 6.737 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.315135176448 0.467528510228 absolute error = 0.387 relative error = 68.64 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3220.3MB, alloc=44.3MB, time=43.24 x[1] = 0.2873 0.473 h = 0.001 0.001 y1[1] (numeric) = 1.00415781297 -0.102944797076 y1[1] (closed_form) = 1.06830700424 -0.139085119207 absolute error = 0.07363 relative error = 6.834 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.315657703513 0.470717506279 absolute error = 0.3902 relative error = 68.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2883 0.474 h = 0.001 0.003 y1[1] (numeric) = 1.00405631955 -0.103242630665 y1[1] (closed_form) = 1.0684619247 -0.139872562776 absolute error = 0.07409 relative error = 6.876 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.316865566664 0.471646412103 absolute error = 0.3914 relative error = 68.89 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3269.8MB, alloc=44.3MB, time=43.94 x[1] = 0.2893 0.477 h = 0.0001 0.004 y1[1] (numeric) = 1.00415116629 -0.103939791266 y1[1] (closed_form) = 1.06956385264 -0.141298573763 absolute error = 0.07533 relative error = 6.982 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.31835633373 0.474712863902 absolute error = 0.3948 relative error = 69.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3319.2MB, alloc=44.3MB, time=44.62 x[1] = 0.2894 0.481 h = 0.003 0.006 y1[1] (numeric) = 1.00452388028 -0.104748262296 y1[1] (closed_form) = 1.07143936792 -0.142621031664 absolute error = 0.07689 relative error = 7.114 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.319031221918 0.478980668721 absolute error = 0.3991 relative error = 69.34 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2924 0.487 h = 0.0001 0.005 y1[1] (numeric) = 1.00451391026 -0.106240753581 y1[1] (closed_form) = 1.073368044 -0.145993398958 absolute error = 0.07951 relative error = 7.34 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.323114249137 0.484982168057 absolute error = 0.406 relative error = 69.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3368.6MB, alloc=44.3MB, time=45.30 x[1] = 0.2925 0.492 h = 0.0001 0.003 y1[1] (numeric) = 1.00498479433 -0.107248888117 y1[1] (closed_form) = 1.07577399187 -0.147659836628 absolute error = 0.08151 relative error = 7.507 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.323955837128 0.490340329396 absolute error = 0.4114 relative error = 70 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2926 0.495 h = 0.001 0.001 y1[1] (numeric) = 1.00525933823 -0.107857695642 y1[1] (closed_form) = 1.07721741063 -0.14868172631 absolute error = 0.08273 relative error = 7.608 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.324507998468 0.493554997041 absolute error = 0.4146 relative error = 70.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3418.2MB, alloc=44.3MB, time=45.99 x[1] = 0.2936 0.496 h = 0.001 0.003 y1[1] (numeric) = 1.00515784481 -0.108155529231 y1[1] (closed_form) = 1.07738630868 -0.149500866579 absolute error = 0.08322 relative error = 7.651 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.32573439147 0.494483207809 absolute error = 0.4159 relative error = 70.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3467.8MB, alloc=44.3MB, time=46.67 x[1] = 0.2946 0.499 h = 0.0001 0.004 y1[1] (numeric) = 1.00525269156 -0.108852689832 y1[1] (closed_form) = 1.07854788503 -0.150976386248 absolute error = 0.08454 relative error = 7.762 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.327263071885 0.497566869182 absolute error = 0.4193 relative error = 70.4 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2947 0.503 h = 0.003 0.006 y1[1] (numeric) = 1.00562540554 -0.109661160862 y1[1] (closed_form) = 1.08051399384 -0.152336837583 absolute error = 0.08619 relative error = 7.899 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.327977650187 0.501869821592 absolute error = 0.4236 relative error = 70.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3517.1MB, alloc=44.3MB, time=47.35 x[1] = 0.2977 0.509 h = 0.0001 0.005 y1[1] (numeric) = 1.00561543553 -0.111153652147 y1[1] (closed_form) = 1.08255311294 -0.155831846626 absolute error = 0.08897 relative error = 8.135 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.332146729439 0.507896768833 absolute error = 0.4306 relative error = 70.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3566.5MB, alloc=44.3MB, time=48.03 x[1] = 0.2978 0.514 h = 0.0001 0.003 y1[1] (numeric) = 1.0060863196 -0.112161786683 y1[1] (closed_form) = 1.08507284088 -0.157545865898 absolute error = 0.0911 relative error = 8.308 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.33303855271 0.513300153653 absolute error = 0.436 relative error = 71.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.2979 0.517 h = 0.001 0.001 y1[1] (numeric) = 1.0063608635 -0.112770594208 y1[1] (closed_form) = 1.08658426978 -0.158597346988 absolute error = 0.09239 relative error = 8.414 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.333621349787 0.516541829759 absolute error = 0.4393 relative error = 71.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3616.1MB, alloc=44.3MB, time=48.72 x[1] = 0.2989 0.518 h = 0.0001 0.004 y1[1] (numeric) = 1.00625937008 -0.113068427797 y1[1] (closed_form) = 1.08676703138 -0.159448596813 absolute error = 0.09291 relative error = 8.459 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.334867048254 0.517469482646 absolute error = 0.4406 relative error = 71.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3665.6MB, alloc=44.3MB, time=49.41 x[1] = 0.299 0.522 h = 0.003 0.006 y1[1] (numeric) = 1.00663208406 -0.113876898828 y1[1] (closed_form) = 1.08881205278 -0.160841525434 absolute error = 0.09465 relative error = 8.6 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.335616406166 0.521804620581 absolute error = 0.4449 relative error = 71.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.302 0.528 h = 0.0001 0.005 y1[1] (numeric) = 1.00662211405 -0.115369390113 y1[1] (closed_form) = 1.09094782314 -0.164442436645 absolute error = 0.09757 relative error = 8.843 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.339861870159 0.527855973387 absolute error = 0.452 relative error = 71.99 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3715.0MB, alloc=44.3MB, time=50.10 x[1] = 0.3021 0.533 h = 0.0001 0.003 y1[1] (numeric) = 1.00709299812 -0.116377524649 y1[1] (closed_form) = 1.09356667658 -0.166197139513 absolute error = 0.0998 relative error = 9.022 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.340797692422 0.533300716397 absolute error = 0.4574 relative error = 72.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3022 0.536 h = 0.001 0.001 y1[1] (numeric) = 1.00736754202 -0.116986332174 y1[1] (closed_form) = 1.09513736693 -0.167273939558 absolute error = 0.1012 relative error = 9.131 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.341407333623 0.536567096491 absolute error = 0.4607 relative error = 72.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3764.5MB, alloc=44.3MB, time=50.79 x[1] = 0.3032 0.537 h = 0.001 0.003 y1[1] (numeric) = 1.0072660486 -0.117284165763 y1[1] (closed_form) = 1.09533235912 -0.16815300919 absolute error = 0.1017 relative error = 9.178 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.342670281806 0.53749461809 absolute error = 0.462 relative error = 72.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3814.0MB, alloc=44.3MB, time=51.49 x[1] = 0.3042 0.54 h = 0.0001 0.004 y1[1] (numeric) = 1.00736089535 -0.117981326363 y1[1] (closed_form) = 1.09660604969 -0.169722476625 absolute error = 0.1032 relative error = 9.296 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.344273061611 0.540613586683 absolute error = 0.4655 relative error = 72.63 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3043 0.544 h = 0.003 0.006 y1[1] (numeric) = 1.00773360933 -0.118789797394 y1[1] (closed_form) = 1.0987427817 -0.171155429904 absolute error = 0.105 relative error = 9.442 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.345064583519 0.544987234675 absolute error = 0.4699 relative error = 72.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3863.5MB, alloc=44.3MB, time=52.18 x[1] = 0.3073 0.55 h = 0.0001 0.005 y1[1] (numeric) = 1.00772363932 -0.120282288679 y1[1] (closed_form) = 1.10098925137 -0.174882897245 absolute error = 0.1081 relative error = 9.694 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.34940226855 0.551067372616 absolute error = 0.477 relative error = 73.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3912.8MB, alloc=44.3MB, time=52.87 x[1] = 0.3074 0.555 h = 0.0001 0.003 y1[1] (numeric) = 1.00819452339 -0.121290423215 y1[1] (closed_form) = 1.10372332849 -0.176687758948 absolute error = 0.1104 relative error = 9.879 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.350391428302 0.556561564174 absolute error = 0.4825 relative error = 73.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3075 0.558 h = 0.001 0.001 y1[1] (numeric) = 1.00846906729 -0.12189923074 y1[1] (closed_form) = 1.10536288461 -0.17779571654 absolute error = 0.1119 relative error = 9.991 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.35103360718 0.559857466883 absolute error = 0.4859 relative error = 73.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=3962.4MB, alloc=44.3MB, time=53.57 x[1] = 0.3085 0.559 h = 0.001 0.003 y1[1] (numeric) = 1.00836757387 -0.122197064329 y1[1] (closed_form) = 1.10557153037 -0.178707713047 absolute error = 0.1124 relative error = 10.04 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.352317325948 0.560784682589 absolute error = 0.4872 relative error = 73.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4012.0MB, alloc=44.3MB, time=54.26 x[1] = 0.3095 0.562 h = 0.0001 0.004 y1[1] (numeric) = 1.00846242061 -0.122894224929 y1[1] (closed_form) = 1.10690545341 -0.180329484744 absolute error = 0.114 relative error = 10.16 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.35396211757 0.563923878196 absolute error = 0.4906 relative error = 73.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3096 0.566 h = 0.003 0.006 y1[1] (numeric) = 1.0088351346 -0.12370269596 y1[1] (closed_form) = 1.10913453602 -0.181803614322 absolute error = 0.1159 relative error = 10.31 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.354797184361 0.568337845694 absolute error = 0.4951 relative error = 73.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4061.4MB, alloc=44.3MB, time=54.95 x[1] = 0.3126 0.572 h = 0.0001 0.005 y1[1] (numeric) = 1.00882516459 -0.125195187245 y1[1] (closed_form) = 1.11149185991 -0.185659861147 absolute error = 0.1191 relative error = 10.57 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.359230486074 0.574448529219 absolute error = 0.5023 relative error = 74.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3127 0.577 h = 0.0001 0.003 y1[1] (numeric) = 1.00929604865 -0.126203321781 y1[1] (closed_form) = 1.1143419863 -0.187516342196 absolute error = 0.1216 relative error = 10.76 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.360274715638 0.579994443562 absolute error = 0.5079 relative error = 74.39 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4110.8MB, alloc=44.3MB, time=55.63 x[1] = 0.3128 0.58 h = 0.001 0.001 y1[1] (numeric) = 1.00957059256 -0.126812129306 y1[1] (closed_form) = 1.11605089731 -0.188656344854 absolute error = 0.1231 relative error = 10.88 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.36095049364 0.583321221795 absolute error = 0.5113 relative error = 74.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4160.3MB, alloc=44.3MB, time=56.86 x[1] = 0.3138 0.581 h = 0.001 0.003 y1[1] (numeric) = 1.00946909913 -0.127109962895 y1[1] (closed_form) = 1.11627307907 -0.189601732694 absolute error = 0.1237 relative error = 10.93 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.362255784512 0.584248254962 absolute error = 0.5126 relative error = 74.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3148 0.584 h = 0.0001 0.004 y1[1] (numeric) = 1.00956394588 -0.127807123495 y1[1] (closed_form) = 1.11766746452 -0.191276859152 absolute error = 0.1254 relative error = 11.06 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.363944069966 0.587408725218 absolute error = 0.5161 relative error = 74.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4209.9MB, alloc=44.3MB, time=57.76 x[1] = 0.3149 0.588 h = 0.003 0.006 y1[1] (numeric) = 1.00993665986 -0.128615594526 y1[1] (closed_form) = 1.11998957023 -0.192793356978 absolute error = 0.1274 relative error = 11.21 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.364824091781 0.591864829898 absolute error = 0.5206 relative error = 74.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4259.3MB, alloc=44.3MB, time=58.49 x[1] = 0.3179 0.594 h = 0.0001 0.005 y1[1] (numeric) = 1.00992668985 -0.130108085811 y1[1] (closed_form) = 1.12245792374 -0.196780691208 absolute error = 0.1308 relative error = 11.48 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.369356456539 0.598007811083 absolute error = 0.5279 relative error = 75.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.318 0.599 h = 0.0001 0.003 y1[1] (numeric) = 1.01039757392 -0.131116220347 y1[1] (closed_form) = 1.12542496588 -0.198690302716 absolute error = 0.1334 relative error = 11.67 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.370457525409 0.603607733187 absolute error = 0.5335 relative error = 75.33 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4308.8MB, alloc=44.3MB, time=59.17 x[1] = 0.3181 0.602 h = 0.001 0.001 y1[1] (numeric) = 1.01067211782 -0.131725027872 y1[1] (closed_form) = 1.12720374505 -0.19986326874 absolute error = 0.135 relative error = 11.79 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.371167986501 0.606966746094 absolute error = 0.5369 relative error = 75.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4358.3MB, alloc=44.3MB, time=59.86 x[1] = 0.3191 0.603 h = 0.001 0.003 y1[1] (numeric) = 1.0105706244 -0.132022861461 y1[1] (closed_form) = 1.12743934362 -0.200842530755 absolute error = 0.1356 relative error = 11.84 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.372495660791 0.60789371496 absolute error = 0.5382 relative error = 75.49 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3201 0.606 h = 0.0001 0.004 y1[1] (numeric) = 1.01066547115 -0.132720022061 y1[1] (closed_form) = 1.12889443654 -0.202572100897 absolute error = 0.1373 relative error = 11.97 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.374228946882 0.611076507059 absolute error = 0.5418 relative error = 75.61 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4407.8MB, alloc=44.3MB, time=60.65 x[1] = 0.3202 0.61 h = 0.003 0.006 y1[1] (numeric) = 1.01103818513 -0.133528493092 y1[1] (closed_form) = 1.13131027038 -0.204132199933 absolute error = 0.1395 relative error = 12.13 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.375155364184 0.615576575323 absolute error = 0.5464 relative error = 75.79 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3232 0.616 h = 0.0001 0.005 y1[1] (numeric) = 1.01102821512 -0.135020984377 y1[1] (closed_form) = 1.13388984897 -0.208253015148 absolute error = 0.143 relative error = 12.41 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.379790291049 0.621753597865 absolute error = 0.5537 relative error = 76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4457.3MB, alloc=44.3MB, time=61.33 x[1] = 0.3233 0.621 h = 0.0001 0.003 y1[1] (numeric) = 1.01149909919 -0.136029118913 y1[1] (closed_form) = 1.13697471425 -0.210217319717 absolute error = 0.1458 relative error = 12.61 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.380950007228 0.627409824074 absolute error = 0.5594 relative error = 76.22 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4506.7MB, alloc=44.3MB, time=62.00 x[1] = 0.3234 0.624 h = 0.001 0.001 y1[1] (numeric) = 1.01177364309 -0.136637926438 y1[1] (closed_form) = 1.13882389901 -0.211424198732 absolute error = 0.1474 relative error = 12.73 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.381696258707 0.630802437414 absolute error = 0.5629 relative error = 76.34 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3244 0.625 h = 0.0001 0.004 y1[1] (numeric) = 1.01167214967 -0.136935760027 y1[1] (closed_form) = 1.13907279342 -0.212437836335 absolute error = 0.1481 relative error = 12.78 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.383047137917 0.631729454968 absolute error = 0.5642 relative error = 76.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4556.3MB, alloc=44.3MB, time=62.68 x[1] = 0.3245 0.629 h = 0.003 0.006 y1[1] (numeric) = 1.01204486365 -0.137744231057 y1[1] (closed_form) = 1.14157043487 -0.214035356489 absolute error = 0.1503 relative error = 12.94 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.384014114873 0.63626941178 absolute error = 0.5688 relative error = 76.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4605.6MB, alloc=44.3MB, time=63.35 x[1] = 0.3275 0.635 h = 0.0001 0.005 y1[1] (numeric) = 1.01203489364 -0.139236722342 y1[1] (closed_form) = 1.14424755424 -0.218271722198 absolute error = 0.154 relative error = 13.22 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.388739733833 0.642478405335 absolute error = 0.5762 relative error = 76.73 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3276 0.64 h = 0.0001 0.003 y1[1] (numeric) = 1.01250577771 -0.140244856878 y1[1] (closed_form) = 1.14743527344 -0.220282977036 absolute error = 0.1569 relative error = 13.43 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.389950701725 0.648185672885 absolute error = 0.582 relative error = 76.94 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4655.1MB, alloc=44.3MB, time=64.02 x[1] = 0.3277 0.643 h = 0.001 0.001 y1[1] (numeric) = 1.01278032161 -0.140853664403 y1[1] (closed_form) = 1.14934592976 -0.221518984153 absolute error = 0.1586 relative error = 13.55 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.390728242973 0.651608752066 absolute error = 0.5855 relative error = 77.06 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4704.5MB, alloc=44.3MB, time=64.70 x[1] = 0.3287 0.644 h = 0.001 0.003 y1[1] (numeric) = 1.01267882819 -0.141151497993 y1[1] (closed_form) = 1.1496065884 -0.222562470581 absolute error = 0.1593 relative error = 13.6 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.392099759805 0.652536187827 absolute error = 0.5868 relative error = 77.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3297 0.647 h = 0.0001 0.004 y1[1] (numeric) = 1.01277367493 -0.141848658593 y1[1] (closed_form) = 1.1511760282 -0.224395649127 absolute error = 0.1611 relative error = 13.74 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.393920585465 0.65576388145 absolute error = 0.5905 relative error = 77.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4753.9MB, alloc=44.3MB, time=65.37 x[1] = 0.3298 0.651 h = 0.003 0.006 y1[1] (numeric) = 1.01314638892 -0.142657129623 y1[1] (closed_form) = 1.15376881224 -0.226039167092 absolute error = 0.1635 relative error = 13.91 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.39493670068 0.660351243345 absolute error = 0.5951 relative error = 77.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3328 0.657 h = 0.0001 0.005 y1[1] (numeric) = 1.01313641891 -0.144149620908 y1[1] (closed_form) = 1.15655760312 -0.230413696724 absolute error = 0.1674 relative error = 14.19 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.399771519277 0.666597543746 absolute error = 0.6026 relative error = 77.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4803.3MB, alloc=44.3MB, time=66.04 x[1] = 0.3329 0.662 h = 0.0001 0.003 y1[1] (numeric) = 1.01360730297 -0.145157755444 y1[1] (closed_form) = 1.15986496307 -0.232482680533 absolute error = 0.1703 relative error = 14.4 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.401044578217 0.672365443437 absolute error = 0.6085 relative error = 77.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4852.8MB, alloc=44.3MB, time=66.72 x[1] = 0.333 0.665 h = 0.001 0.001 y1[1] (numeric) = 1.01388184688 -0.145766562969 y1[1] (closed_form) = 1.16184710163 -0.233754445883 absolute error = 0.1721 relative error = 14.53 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.401860018726 0.675824697127 absolute error = 0.612 relative error = 77.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.334 0.666 h = 0.001 0.003 y1[1] (numeric) = 1.01378035345 -0.146064396559 y1[1] (closed_form) = 1.16212083219 -0.234833292537 absolute error = 0.1729 relative error = 14.58 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.403256296407 0.676752387458 absolute error = 0.6134 relative error = 77.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4902.4MB, alloc=44.3MB, time=67.39 x[1] = 0.335 0.669 h = 0.0001 0.004 y1[1] (numeric) = 1.0138752002 -0.146761557159 y1[1] (closed_form) = 1.16375177733 -0.236724243657 absolute error = 0.1748 relative error = 14.72 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.405126566143 0.68000541637 absolute error = 0.617 relative error = 77.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=4951.8MB, alloc=44.3MB, time=68.06 x[1] = 0.3351 0.673 h = 0.003 0.006 y1[1] (numeric) = 1.01424791419 -0.147570028189 y1[1] (closed_form) = 1.16644050277 -0.238415113435 absolute error = 0.1772 relative error = 14.89 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.40619335274 0.684642037855 absolute error = 0.6218 relative error = 78.11 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3381 0.679 h = 0.0001 0.005 y1[1] (numeric) = 1.01423794417 -0.149062519474 y1[1] (closed_form) = 1.16934121642 -0.242930451833 absolute error = 0.1813 relative error = 15.18 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.411141032027 0.690927365366 absolute error = 0.6294 relative error = 78.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5001.3MB, alloc=44.3MB, time=68.73 x[1] = 0.3382 0.684 h = 0.0001 0.003 y1[1] (numeric) = 1.01470882824 -0.15007065401 y1[1] (closed_form) = 1.17276924249 -0.245058879243 absolute error = 0.1844 relative error = 15.39 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.412478107607 0.696758230015 absolute error = 0.6353 relative error = 78.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5050.8MB, alloc=44.3MB, time=69.41 x[1] = 0.3383 0.687 h = 0.001 0.001 y1[1] (numeric) = 1.01498337214 -0.150679461535 y1[1] (closed_form) = 1.17482347039 -0.246367444924 absolute error = 0.1863 relative error = 15.52 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.413332625914 0.700255045192 absolute error = 0.6389 relative error = 78.57 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3393 0.688 h = 0.001 0.003 y1[1] (numeric) = 1.01488187872 -0.150977295125 y1[1] (closed_form) = 1.17511014608 -0.247482207515 absolute error = 0.187 relative error = 15.58 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.414754517394 0.701183087411 absolute error = 0.6402 relative error = 78.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5100.2MB, alloc=44.3MB, time=70.09 x[1] = 0.3403 0.691 h = 0.0001 0.004 y1[1] (numeric) = 1.01497672547 -0.151674455725 y1[1] (closed_form) = 1.17680289912 -0.249432173701 absolute error = 0.1891 relative error = 15.72 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.416675842567 0.704462498562 absolute error = 0.644 relative error = 78.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3404 0.695 h = 0.003 0.006 y1[1] (numeric) = 1.01534943945 -0.152482926755 y1[1] (closed_form) = 1.17958839748 -0.251171793256 absolute error = 0.1916 relative error = 15.89 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.417794868263 0.709150244785 absolute error = 0.6488 relative error = 78.82 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5149.6MB, alloc=44.3MB, time=70.76 x[1] = 0.3434 0.701 h = 0.0001 0.005 y1[1] (numeric) = 1.01533946944 -0.15397541804 y1[1] (closed_form) = 1.18260130334 -0.255830675563 absolute error = 0.1958 relative error = 16.19 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.422859129847 0.715476311144 absolute error = 0.6564 relative error = 78.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5199.0MB, alloc=44.3MB, time=71.44 x[1] = 0.3435 0.706 h = 0.0001 0.003 y1[1] (numeric) = 1.01581035351 -0.154983552576 y1[1] (closed_form) = 1.18615106206 -0.258020316451 absolute error = 0.1991 relative error = 16.4 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.424262191533 0.721372487346 absolute error = 0.6624 relative error = 79.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3436 0.709 h = 0.001 0.001 y1[1] (numeric) = 1.01608489741 -0.155592360101 y1[1] (closed_form) = 1.1882780107 -0.25936675815 absolute error = 0.201 relative error = 16.53 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.425156992751 0.724908258997 absolute error = 0.6661 relative error = 79.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5248.6MB, alloc=44.3MB, time=72.12 x[1] = 0.3446 0.71 h = 0.001 0.003 y1[1] (numeric) = 1.01598340399 -0.155890193691 y1[1] (closed_form) = 1.18857750221 -0.260518011779 absolute error = 0.2018 relative error = 16.59 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.426605362738 0.72583674461 absolute error = 0.6674 relative error = 79.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5298.0MB, alloc=44.3MB, time=73.16 x[1] = 0.3456 0.713 h = 0.0001 0.004 y1[1] (numeric) = 1.01607825073 -0.156587354291 y1[1] (closed_form) = 1.19033238017 -0.262528276847 absolute error = 0.2039 relative error = 16.73 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.428579384142 0.729143585071 absolute error = 0.6712 relative error = 79.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3457 0.717 h = 0.003 0.006 y1[1] (numeric) = 1.01645096472 -0.157395825321 y1[1] (closed_form) = 1.1932155157 -0.264318088939 absolute error = 0.2066 relative error = 16.9 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.42975225239 0.733884332306 absolute error = 0.6761 relative error = 79.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5347.3MB, alloc=44.3MB, time=74.21 x[1] = 0.3487 0.723 h = 0.0001 0.005 y1[1] (numeric) = 1.01644099471 -0.158888316606 y1[1] (closed_form) = 1.1963409009 -0.269123341909 absolute error = 0.211 relative error = 17.21 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.434936880536 0.740252840634 absolute error = 0.6838 relative error = 79.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5396.9MB, alloc=44.3MB, time=75.50 x[1] = 0.3488 0.728 h = 0.0001 0.003 y1[1] (numeric) = 1.01691187877 -0.159896451142 y1[1] (closed_form) = 1.20001350003 -0.271376022447 absolute error = 0.2144 relative error = 17.42 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.436407943107 0.746216689371 absolute error = 0.6899 relative error = 79.81 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3489 0.731 h = 0.001 0.001 y1[1] (numeric) = 1.01718642268 -0.160505258667 y1[1] (closed_form) = 1.2022138251 -0.272761450079 absolute error = 0.2164 relative error = 17.56 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.437344259802 0.749792820853 absolute error = 0.6936 relative error = 79.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5446.4MB, alloc=44.3MB, time=76.82 x[1] = 0.3499 0.732 h = 0.0001 0.004 y1[1] (numeric) = 1.01708492925 -0.160803092257 y1[1] (closed_form) = 1.20252600051 -0.273949789478 absolute error = 0.2172 relative error = 17.61 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.438819985179 0.750721835392 absolute error = 0.695 relative error = 79.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5495.8MB, alloc=44.3MB, time=77.61 x[1] = 0.35 0.736 h = 0.003 0.006 y1[1] (numeric) = 1.01745764324 -0.161611563287 y1[1] (closed_form) = 1.20549451812 -0.275782818118 absolute error = 0.22 relative error = 17.79 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.440039849476 0.7555103835 absolute error = 0.6999 relative error = 80.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.353 0.742 h = 0.0001 0.005 y1[1] (numeric) = 1.01744767323 -0.163104054572 y1[1] (closed_form) = 1.20871875592 -0.280715051784 absolute error = 0.2245 relative error = 18.09 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.445330631869 0.761918277971 absolute error = 0.7078 relative error = 80.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5545.2MB, alloc=44.3MB, time=78.30 x[1] = 0.3531 0.747 h = 0.0001 0.003 y1[1] (numeric) = 1.0179185573 -0.164112189108 y1[1] (closed_form) = 1.21249879216 -0.283022018893 absolute error = 0.228 relative error = 18.31 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.446861031734 0.767943122569 absolute error = 0.7139 relative error = 80.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3532 0.75 h = 0.001 0.001 y1[1] (numeric) = 1.0181931012 -0.164720996633 y1[1] (closed_form) = 1.21476330395 -0.284441034586 absolute error = 0.2302 relative error = 18.45 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.447833588509 0.771555639903 absolute error = 0.7177 relative error = 80.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5594.8MB, alloc=44.3MB, time=78.99 x[1] = 0.3542 0.751 h = 0.001 0.003 y1[1] (numeric) = 1.01809160777 -0.165018830222 y1[1] (closed_form) = 1.21508674115 -0.285661638685 absolute error = 0.231 relative error = 18.51 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.449333564714 0.772485513839 absolute error = 0.7191 relative error = 80.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5644.4MB, alloc=44.3MB, time=79.68 x[1] = 0.3552 0.754 h = 0.0001 0.004 y1[1] (numeric) = 1.01818645452 -0.165715990823 y1[1] (closed_form) = 1.21695886786 -0.287786917501 absolute error = 0.2333 relative error = 18.65 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.451409757288 0.775846856771 absolute error = 0.7229 relative error = 80.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3553 0.758 h = 0.0001 0.004 y1[1] (numeric) = 1.01855916851 -0.166524461853 y1[1] (closed_form) = 1.2200267367 -0.289672934286 absolute error = 0.2361 relative error = 18.83 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.452686524247 0.780691948617 absolute error = 0.7279 relative error = 80.66 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5693.8MB, alloc=44.3MB, time=80.36 x[1] = 0.3554 0.762 h = 0.003 0.006 y1[1] (numeric) = 1.01893188249 -0.167332932883 y1[1] (closed_form) = 1.22311388205 -0.291564558972 absolute error = 0.239 relative error = 19.01 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.453971154229 0.785549161593 absolute error = 0.7329 relative error = 80.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5743.3MB, alloc=44.3MB, time=81.03 x[1] = 0.3584 0.768 h = 0.0001 0.005 y1[1] (numeric) = 1.01892191248 -0.168825424168 y1[1] (closed_form) = 1.22647651198 -0.296671028616 absolute error = 0.2438 relative error = 19.32 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.459410214946 0.792015581161 absolute error = 0.7409 relative error = 80.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3585 0.773 h = 0.0001 0.003 y1[1] (numeric) = 1.01939279655 -0.169833558704 y1[1] (closed_form) = 1.23040584129 -0.299051611952 absolute error = 0.2474 relative error = 19.54 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.461022361798 0.798127988318 absolute error = 0.7472 relative error = 81.06 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5793.0MB, alloc=44.3MB, time=81.70 x[1] = 0.3586 0.776 h = 0.001 0.001 y1[1] (numeric) = 1.01966734045 -0.170442366229 y1[1] (closed_form) = 1.23275956735 -0.300516207623 absolute error = 0.2497 relative error = 19.68 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.462044870849 0.801792755345 absolute error = 0.751 relative error = 81.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3596 0.777 h = 0.001 0.003 y1[1] (numeric) = 1.01956584703 -0.170740199819 y1[1] (closed_form) = 1.2330990143 -0.301781278122 absolute error = 0.2505 relative error = 19.74 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.463578948727 0.802724536149 memory used=5842.6MB, alloc=44.3MB, time=82.36 absolute error = 0.7524 relative error = 81.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3606 0.78 h = 0.0001 0.004 y1[1] (numeric) = 1.01966069377 -0.171437360419 y1[1] (closed_form) = 1.23504763641 -0.303979650801 absolute error = 0.2529 relative error = 19.88 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.465721660318 0.806123874466 absolute error = 0.7563 relative error = 81.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5891.9MB, alloc=44.3MB, time=83.04 x[1] = 0.3607 0.784 h = 0.003 0.006 y1[1] (numeric) = 1.02003340776 -0.172245831449 y1[1] (closed_form) = 1.23823532058 -0.305926079774 absolute error = 0.2559 relative error = 20.06 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.467065133809 0.811039938632 absolute error = 0.7614 relative error = 81.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3637 0.79 h = 0.0001 0.005 y1[1] (numeric) = 1.02002343774 -0.173738322734 y1[1] (closed_form) = 1.24171155844 -0.311188053074 absolute error = 0.2608 relative error = 20.38 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.472636364448 0.817554110127 absolute error = 0.7694 relative error = 81.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5941.4MB, alloc=44.3MB, time=83.71 x[1] = 0.3638 0.795 h = 0.0001 0.003 y1[1] (numeric) = 1.02049432181 -0.17474645727 y1[1] (closed_form) = 1.2457674414 -0.313637510325 absolute error = 0.2646 relative error = 20.6 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.474322798279 0.823741553603 absolute error = 0.7758 relative error = 81.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=5991.0MB, alloc=44.3MB, time=84.88 x[1] = 0.3639 0.798 h = 0.001 0.001 y1[1] (numeric) = 1.02076886571 -0.175355264795 y1[1] (closed_form) = 1.2481967429 -0.315144638905 absolute error = 0.267 relative error = 20.74 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.475390668726 0.827451058047 absolute error = 0.7797 relative error = 81.7 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3649 0.799 h = 0.001 0.003 y1[1] (numeric) = 1.02066737229 -0.175653098385 y1[1] (closed_form) = 1.24854848771 -0.316448728946 absolute error = 0.2679 relative error = 20.8 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.47695483787 0.828383634239 absolute error = 0.7811 relative error = 81.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6040.6MB, alloc=44.3MB, time=86.10 x[1] = 0.3659 0.802 h = 0.0001 0.004 y1[1] (numeric) = 1.02076221904 -0.176350258985 y1[1] (closed_form) = 1.25056072904 -0.31871299356 absolute error = 0.2703 relative error = 20.95 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.479157131879 0.831814716016 absolute error = 0.7851 relative error = 81.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6089.9MB, alloc=44.3MB, time=86.77 x[1] = 0.366 0.806 h = 0.003 0.006 y1[1] (numeric) = 1.02113493302 -0.177158730015 y1[1] (closed_form) = 1.25384995142 -0.320715857665 absolute error = 0.2734 relative error = 21.13 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.480561207912 0.836791559397 absolute error = 0.7902 relative error = 81.89 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.369 0.812 h = 0.0001 0.005 y1[1] (numeric) = 1.02112496301 -0.1786512213 y1[1] (closed_form) = 1.25744015493 -0.326136544394 absolute error = 0.2786 relative error = 21.44 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.486268667745 0.843355153467 absolute error = 0.7984 relative error = 82.01 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6139.4MB, alloc=44.3MB, time=87.44 x[1] = 0.3691 0.817 h = 0.0001 0.003 y1[1] (numeric) = 1.02159584708 -0.179659355836 y1[1] (closed_form) = 1.26162386945 -0.328656938228 absolute error = 0.2825 relative error = 21.67 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.48803160046 0.849620060954 absolute error = 0.8049 relative error = 82.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6189.0MB, alloc=44.3MB, time=88.12 x[1] = 0.3692 0.82 h = 0.001 0.001 y1[1] (numeric) = 1.02187039098 -0.180268163361 y1[1] (closed_form) = 1.26412950247 -0.330207853409 absolute error = 0.2849 relative error = 21.81 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.489146184293 0.853375745014 absolute error = 0.8088 relative error = 82.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3702 0.821 h = 0.001 0.003 y1[1] (numeric) = 1.02176889756 -0.180565996951 y1[1] (closed_form) = 1.26449340138 -0.331551639589 absolute error = 0.2859 relative error = 21.87 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.490741375336 0.854309176986 absolute error = 0.8102 relative error = 82.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6238.6MB, alloc=44.3MB, time=88.80 x[1] = 0.3712 0.824 h = 0.0001 0.004 y1[1] (numeric) = 1.02186374431 -0.181263157551 y1[1] (closed_form) = 1.26656965129 -0.333883297758 absolute error = 0.2884 relative error = 22.02 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.493005056027 0.857773052919 absolute error = 0.8143 relative error = 82.3 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3713 0.828 h = 0.003 0.006 y1[1] (numeric) = 1.02223645829 -0.182071628581 y1[1] (closed_form) = 1.26996144442 -0.335944277252 absolute error = 0.2916 relative error = 22.2 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.494471535442 0.862812617114 absolute error = 0.8195 relative error = 82.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6288.0MB, alloc=44.3MB, time=89.49 x[1] = 0.3743 0.834 h = 0.0001 0.005 y1[1] (numeric) = 1.02222648828 -0.183564119866 y1[1] (closed_form) = 1.27366598623 -0.341526986124 absolute error = 0.2969 relative error = 22.52 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.500319357376 0.869427295171 absolute error = 0.8278 relative error = 82.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6337.5MB, alloc=44.3MB, time=90.19 x[1] = 0.3744 0.839 h = 0.0001 0.003 y1[1] (numeric) = 1.02269737235 -0.184572254402 y1[1] (closed_form) = 1.27797885196 -0.344120441362 absolute error = 0.301 relative error = 22.75 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.502161053823 0.875772111836 absolute error = 0.8344 relative error = 82.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3745 0.842 h = 0.001 0.001 y1[1] (numeric) = 1.02297191625 -0.185181061927 y1[1] (closed_form) = 1.28056159717 -0.345716434598 absolute error = 0.3035 relative error = 22.88 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.503323735098 0.879575427874 absolute error = 0.8383 relative error = 82.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6387.1MB, alloc=44.3MB, time=90.88 x[1] = 0.3755 0.843 h = 0.001 0.003 y1[1] (numeric) = 1.02287042283 -0.185478895517 y1[1] (closed_form) = 1.28093750269 -0.347100614448 absolute error = 0.3045 relative error = 22.94 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.504950893017 0.880509769171 absolute error = 0.8398 relative error = 82.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6436.7MB, alloc=44.3MB, time=91.58 x[1] = 0.3765 0.846 h = 0.0001 0.004 y1[1] (numeric) = 1.02296526957 -0.186176056117 y1[1] (closed_form) = 1.28307816401 -0.349501213447 absolute error = 0.3071 relative error = 23.1 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.507277800292 0.884007490589 absolute error = 0.8439 relative error = 82.8 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3766 0.85 h = 0.003 0.006 y1[1] (numeric) = 1.02333798356 -0.186984527147 y1[1] (closed_form) = 1.28657359362 -0.351622039004 absolute error = 0.3105 relative error = 23.28 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.508808527005 0.889111731242 absolute error = 0.8492 relative error = 82.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6486.2MB, alloc=44.3MB, time=92.29 x[1] = 0.3796 0.856 h = 0.0001 0.005 y1[1] (numeric) = 1.02332801354 -0.188477018432 y1[1] (closed_form) = 1.29039286073 -0.357370179268 absolute error = 0.316 relative error = 23.6 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.514800919856 0.895779145253 absolute error = 0.8576 relative error = 83.01 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6535.8MB, alloc=44.3MB, time=92.99 x[1] = 0.3797 0.861 h = 0.0001 0.003 y1[1] (numeric) = 1.02379889761 -0.189485152968 y1[1] (closed_form) = 1.29483623916 -0.360038884162 absolute error = 0.3202 relative error = 23.83 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.51672369943 0.902206334325 absolute error = 0.8643 relative error = 83.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3798 0.864 h = 0.001 0.001 y1[1] (numeric) = 1.02407344151 -0.190093960493 y1[1] (closed_form) = 1.29749690189 -0.361681285445 absolute error = 0.3228 relative error = 23.97 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.517935895241 0.906058745203 absolute error = 0.8683 relative error = 83.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6585.5MB, alloc=44.3MB, time=93.70 x[1] = 0.3808 0.865 h = 0.0001 0.004 y1[1] (numeric) = 1.02397194809 -0.190391794083 y1[1] (closed_form) = 1.29788466259 -0.363106577711 absolute error = 0.3238 relative error = 24.03 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.519595979798 0.90699404233 absolute error = 0.8698 relative error = 83.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3809 0.869 h = 0.003 0.006 y1[1] (numeric) = 1.02434466208 -0.191200265113 y1[1] (closed_form) = 1.30147091976 -0.365279089488 absolute error = 0.3273 relative error = 24.21 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.521182716454 0.912156327438 absolute error = 0.8752 relative error = 83.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6635.0MB, alloc=44.3MB, time=94.40 x[1] = 0.3839 0.875 h = 0.0001 0.005 y1[1] (numeric) = 1.02433469207 -0.192692756398 y1[1] (closed_form) = 1.30539128676 -0.371171062453 absolute error = 0.3329 relative error = 24.53 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.527302326302 0.918872242078 absolute error = 0.8837 relative error = 83.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6684.4MB, alloc=44.3MB, time=95.10 x[1] = 0.384 0.88 h = 0.0001 0.003 y1[1] (numeric) = 1.02480557613 -0.193700890934 y1[1] (closed_form) = 1.30994906151 -0.37390476392 absolute error = 0.3373 relative error = 24.76 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.529295778192 0.925373325785 absolute error = 0.8905 relative error = 83.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3841 0.883 h = 0.001 0.001 y1[1] (numeric) = 1.02508012004 -0.194309698459 y1[1] (closed_form) = 1.31267803187 -0.375587265066 absolute error = 0.34 relative error = 24.9 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.530551146455 0.929269788967 absolute error = 0.8945 relative error = 83.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6734.0MB, alloc=44.3MB, time=95.79 x[1] = 0.3851 0.884 h = 0.001 0.003 y1[1] (numeric) = 1.02497862661 -0.194607532048 y1[1] (closed_form) = 1.31307637444 -0.377048398812 absolute error = 0.341 relative error = 24.96 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.532240341334 0.93020634862 absolute error = 0.896 relative error = 83.61 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6783.6MB, alloc=44.3MB, time=96.49 x[1] = 0.3861 0.887 h = 0.0001 0.004 y1[1] (numeric) = 1.02507347336 -0.195304692649 y1[1] (closed_form) = 1.31533887479 -0.379580779241 absolute error = 0.3438 relative error = 25.11 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.534689489311 0.933770655753 absolute error = 0.9003 relative error = 83.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3862 0.891 h = 0.003 0.006 y1[1] (numeric) = 1.02544618735 -0.196113163679 y1[1] (closed_form) = 1.31903086229 -0.381816481592 absolute error = 0.3474 relative error = 25.3 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.536343999766 0.939001318505 absolute error = 0.9057 relative error = 83.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6833.0MB, alloc=44.3MB, time=97.18 x[1] = 0.3892 0.897 h = 0.0001 0.005 y1[1] (numeric) = 1.02543621733 -0.197605654964 y1[1] (closed_form) = 1.32306675427 -0.38788049803 absolute error = 0.3533 relative error = 25.62 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.542616202702 0.945773069465 absolute error = 0.9144 relative error = 83.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6882.5MB, alloc=44.3MB, time=97.88 x[1] = 0.3893 0.902 h = 0.0001 0.003 y1[1] (numeric) = 1.0259071014 -0.1986137895 y1[1] (closed_form) = 1.32775771481 -0.390693676936 absolute error = 0.3578 relative error = 25.85 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.544695174485 0.952361188383 absolute error = 0.9212 relative error = 83.97 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3894 0.905 h = 0.001 0.001 y1[1] (numeric) = 1.0261816453 -0.199222597025 y1[1] (closed_form) = 1.33056618395 -0.392425155947 absolute error = 0.3605 relative error = 25.99 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.546002767752 0.956309515397 absolute error = 0.9254 relative error = 84.03 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6932.0MB, alloc=44.3MB, time=98.57 x[1] = 0.3904 0.906 h = 0.001 0.003 y1[1] (numeric) = 1.02608015188 -0.199520430614 y1[1] (closed_form) = 1.33097609777 -0.393928798933 absolute error = 0.3616 relative error = 26.05 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.547726715714 0.957247109847 absolute error = 0.9269 relative error = 84.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3914 0.909 h = 0.0001 0.004 y1[1] (numeric) = 1.02617499863 -0.200217591215 y1[1] (closed_form) = 1.333304255 -0.396534800631 absolute error = 0.3645 relative error = 26.2 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.550244547811 0.960848297435 absolute error = 0.9312 relative error = 84.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=6981.3MB, alloc=44.3MB, time=99.25 x[1] = 0.3915 0.913 h = 0.003 0.006 y1[1] (numeric) = 1.02654771261 -0.201026062245 y1[1] (closed_form) = 1.33710313469 -0.398835573902 absolute error = 0.3682 relative error = 26.39 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.551968806278 0.966149336747 absolute error = 0.9368 relative error = 84.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7030.8MB, alloc=44.3MB, time=99.92 x[1] = 0.3945 0.919 h = 0.0001 0.005 y1[1] (numeric) = 1.0265377426 -0.20251855353 y1[1] (closed_form) = 1.34125497745 -0.405075339777 absolute error = 0.3743 relative error = 26.71 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.558398041234 0.972978548635 absolute error = 0.9455 relative error = 84.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3946 0.924 h = 0.0001 0.003 y1[1] (numeric) = 1.02700862667 -0.203526688066 y1[1] (closed_form) = 1.34608060642 -0.407970372731 absolute error = 0.379 relative error = 26.94 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.560565017225 0.979656221583 absolute error = 0.9525 relative error = 84.39 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7080.3MB, alloc=44.3MB, time=100.60 x[1] = 0.3947 0.927 h = 0.001 0.001 y1[1] (numeric) = 1.02728317057 -0.204135495591 y1[1] (closed_form) = 1.34896945097 -0.409752274013 absolute error = 0.3818 relative error = 27.08 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.561926352478 0.983657907607 absolute error = 0.9567 relative error = 84.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7129.8MB, alloc=44.3MB, time=101.27 x[1] = 0.3957 0.928 h = 0.001 0.003 y1[1] (numeric) = 1.02718167715 -0.20443332918 y1[1] (closed_form) = 1.34939077226 -0.411299207383 absolute error = 0.3829 relative error = 27.14 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.563686058174 0.984596562271 absolute error = 0.9583 relative error = 84.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3967 0.931 h = 0.0001 0.004 y1[1] (numeric) = 1.02727652389 -0.205130489781 y1[1] (closed_form) = 1.35178504006 -0.413980561452 absolute error = 0.3859 relative error = 27.3 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.566274562188 0.988235684973 absolute error = 0.9626 relative error = 84.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7179.2MB, alloc=44.3MB, time=101.94 x[1] = 0.3968 0.935 h = 0.003 0.006 y1[1] (numeric) = 1.02764923788 -0.205938960811 y1[1] (closed_form) = 1.35569200736 -0.416348340583 absolute error = 0.3897 relative error = 27.48 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.568070591093 0.993609115583 absolute error = 0.9683 relative error = 84.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7228.7MB, alloc=44.3MB, time=102.62 x[1] = 0.3998 0.941 h = 0.0001 0.005 y1[1] (numeric) = 1.02763926787 -0.207431452096 y1[1] (closed_form) = 1.35996023861 -0.422767669032 absolute error = 0.396 relative error = 27.81 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.574661381997 1.00049740258 absolute error = 0.9771 relative error = 84.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.3999 0.946 h = 0.0001 0.003 y1[1] (numeric) = 1.02811015193 -0.208439586632 y1[1] (closed_form) = 1.36492206093 -0.425747001366 absolute error = 0.4008 relative error = 28.03 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.576918907523 1.00726716869 absolute error = 0.9843 relative error = 84.79 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7278.2MB, alloc=44.3MB, time=103.30 x[1] = 0.4 0.949 h = 0.001 0.001 y1[1] (numeric) = 1.02838469584 -0.209048394157 y1[1] (closed_form) = 1.36789218241 -0.427580811057 absolute error = 0.4038 relative error = 28.17 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.578335538689 1.01132372069 absolute error = 0.9886 relative error = 84.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.401 0.95 h = 0.001 0.003 y1[1] (numeric) = 1.02828320241 -0.209346227746 y1[1] (closed_form) = 1.36832474248 -0.429171838353 absolute error = 0.4049 relative error = 28.24 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.58013202332 1.01226345313 absolute error = 0.9901 relative error = 84.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7327.6MB, alloc=44.3MB, time=103.98 x[1] = 0.402 0.953 h = 0.0001 0.004 y1[1] (numeric) = 1.02837804916 -0.210043388347 y1[1] (closed_form) = 1.37078558713 -0.431930325671 absolute error = 0.408 relative error = 28.39 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.582793228117 1.01594156642 absolute error = 0.9945 relative error = 84.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7377.1MB, alloc=44.3MB, time=104.65 x[1] = 0.4021 0.957 h = 0.003 0.006 y1[1] (numeric) = 1.02875076315 -0.210851859377 y1[1] (closed_form) = 1.37480187109 -0.434367101361 absolute error = 0.412 relative error = 28.57 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.58466309949 1.02138941933 absolute error = 1 relative error = 84.99 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4051 0.963 h = 0.0001 0.005 y1[1] (numeric) = 1.02874079313 -0.212344350662 y1[1] (closed_form) = 1.37918693971 -0.440969914527 absolute error = 0.4184 relative error = 28.9 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.591420057703 1.02833838487 absolute error = 1.009 relative error = 85.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7426.7MB, alloc=44.3MB, time=105.31 x[1] = 0.4052 0.968 h = 0.0001 0.003 y1[1] (numeric) = 1.0292116772 -0.213352485198 y1[1] (closed_form) = 1.38428652278 -0.444036061772 absolute error = 0.4234 relative error = 29.13 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.59377074085 1.03520280413 absolute error = 1.017 relative error = 85.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7476.2MB, alloc=44.3MB, time=105.98 x[1] = 0.4053 0.971 h = 0.001 0.001 y1[1] (numeric) = 1.0294862211 -0.213961292723 y1[1] (closed_form) = 1.38733884766 -0.445923308634 absolute error = 0.4265 relative error = 29.26 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.595244259865 1.03931574121 absolute error = 1.021 relative error = 85.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4063 0.972 h = 0.0001 0.004 y1[1] (numeric) = 1.02938472768 -0.214259126312 y1[1] (closed_form) = 1.38778247267 -0.447559256122 absolute error = 0.4276 relative error = 29.33 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.59707856165 1.0402565609 absolute error = 1.022 relative error = 85.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7525.5MB, alloc=44.3MB, time=106.65 x[1] = 0.4064 0.976 h = 0.003 0.006 y1[1] (numeric) = 1.02975744167 -0.215067597343 y1[1] (closed_form) = 1.39189471796 -0.450055736569 absolute error = 0.4317 relative error = 29.51 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.59901277255 1.04577102731 absolute error = 1.028 relative error = 85.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7574.8MB, alloc=44.3MB, time=107.31 x[1] = 0.4094 0.982 h = 0.0001 0.005 y1[1] (numeric) = 1.02974747165 -0.216560088627 y1[1] (closed_form) = 1.39638297508 -0.456818313403 absolute error = 0.4383 relative error = 29.84 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.605915774694 1.05277555426 absolute error = 1.037 relative error = 85.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4095 0.987 h = 0.0001 0.003 y1[1] (numeric) = 1.03021835572 -0.217568223163 y1[1] (closed_form) = 1.40160350185 -0.459959589907 absolute error = 0.4435 relative error = 30.06 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.608347613133 1.05972466729 absolute error = 1.045 relative error = 85.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7624.3MB, alloc=44.3MB, time=107.98 x[1] = 0.4096 0.99 h = 0.001 0.001 y1[1] (numeric) = 1.03049289962 -0.218177030688 y1[1] (closed_form) = 1.4047280078 -0.46189309642 absolute error = 0.4466 relative error = 30.2 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.609870707389 1.06388806888 absolute error = 1.049 relative error = 85.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4106 0.991 h = 0.001 0.003 y1[1] (numeric) = 1.0303914062 -0.218474864278 y1[1] (closed_form) = 1.40518156271 -0.463568260075 absolute error = 0.4478 relative error = 30.26 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.611738392695 1.06483029329 absolute error = 1.051 relative error = 85.57 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7673.9MB, alloc=44.3MB, time=108.65 x[1] = 0.4116 0.994 h = 0.0001 0.004 y1[1] (numeric) = 1.03048625295 -0.219172024878 y1[1] (closed_form) = 1.40776854576 -0.46647438182 absolute error = 0.4511 relative error = 30.42 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.614539927967 1.06858469603 absolute error = 1.055 relative error = 85.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7723.4MB, alloc=44.3MB, time=109.32 x[1] = 0.4117 0.998 h = 0.003 0.006 y1[1] (numeric) = 1.03085896693 -0.219980495909 y1[1] (closed_form) = 1.41199250997 -0.469043699975 absolute error = 0.4553 relative error = 30.6 % Correct digits = 1 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.61655194913 1.07417743492 absolute error = 1.061 relative error = 85.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4147 1.004 h = 0.0001 0.005 y1[1] (numeric) = 1.03084899692 -0.221472987193 y1[1] (closed_form) = 1.41659851692 -0.475997350754 absolute error = 0.4622 relative error = 30.93 % Correct digits = 1 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.623629921692 1.08124565176 absolute error = 1.071 relative error = 85.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7772.8MB, alloc=44.3MB, time=109.99 x[1] = 0.4148 1.009 h = 0.0001 0.003 y1[1] (numeric) = 1.03131988099 -0.222481121729 y1[1] (closed_form) = 1.42195986634 -0.479230295157 absolute error = 0.4675 relative error = 31.15 % Correct digits = 1 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.62615991287 1.08829427187 absolute error = 1.078 relative error = 85.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7822.3MB, alloc=44.3MB, time=110.66 x[1] = 0.4149 1.012 h = 0.001 0.001 y1[1] (numeric) = 1.03159442489 -0.223089929254 y1[1] (closed_form) = 1.42516838571 -0.481220188351 absolute error = 0.4707 relative error = 31.29 % Correct digits = 1 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.627742943611 1.09251693864 absolute error = 1.083 relative error = 85.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4159 1.013 h = 0.001 0.003 y1[1] (numeric) = 1.03149293147 -0.223387762844 y1[1] (closed_form) = 1.42563267791 -0.482941873557 absolute error = 0.4719 relative error = 31.35 % Correct digits = 1 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.629650425017 1.09346025845 absolute error = 1.084 relative error = 85.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7871.8MB, alloc=44.3MB, time=111.34 x[1] = 0.4169 1.016 h = 0.0001 0.004 y1[1] (numeric) = 1.03158777821 -0.224084923444 y1[1] (closed_form) = 1.42828766252 -0.485930500389 absolute error = 0.4753 relative error = 31.51 % Correct digits = 1 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.632530689929 1.09725670169 absolute error = 1.089 relative error = 85.97 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7921.2MB, alloc=44.3MB, time=112.00 x[1] = 0.417 1.02 h = 0.003 0.006 y1[1] (numeric) = 1.0319604922 -0.224893394475 y1[1] (closed_form) = 1.43262467224 -0.488574812767 absolute error = 0.4796 relative error = 31.69 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.634622743007 1.10292979367 absolute error = 1.095 relative error = 86.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.42 1.026 h = 0.0001 0.005 y1[1] (numeric) = 1.03195052219 -0.226385885759 y1[1] (closed_form) = 1.43734890729 -0.495723782022 absolute error = 0.4867 relative error = 32.01 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.64188056143 1.11006327224 absolute error = 1.104 relative error = 86.12 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=7970.6MB, alloc=44.3MB, time=112.66 x[1] = 0.4201 1.031 h = 0.0001 0.003 y1[1] (numeric) = 1.03242140625 -0.227394020295 y1[1] (closed_form) = 1.44285276974 -0.499051118659 absolute error = 0.4922 relative error = 32.24 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.64451150269 1.11721402302 absolute error = 1.112 relative error = 86.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4202 1.034 h = 0.001 0.001 y1[1] (numeric) = 1.03269595016 -0.22800282782 y1[1] (closed_form) = 1.4461463013 -0.501099054055 absolute error = 0.4955 relative error = 32.38 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.646156176457 1.12149751099 absolute error = 1.116 relative error = 86.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8020.3MB, alloc=44.3MB, time=113.34 x[1] = 0.4212 1.035 h = 0.001 0.003 y1[1] (numeric) = 1.03259445673 -0.22830066141 y1[1] (closed_form) = 1.44662114094 -0.502868154048 absolute error = 0.4968 relative error = 32.44 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.648104543624 1.12244191143 absolute error = 1.118 relative error = 86.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8069.7MB, alloc=44.3MB, time=114.00 x[1] = 0.4222 1.038 h = 0.0001 0.004 y1[1] (numeric) = 1.03268930348 -0.22899782201 y1[1] (closed_form) = 1.44934464057 -0.505941267741 absolute error = 0.5003 relative error = 32.59 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.651065736754 1.12628145431 absolute error = 1.123 relative error = 86.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4223 1.042 h = 0.003 0.006 y1[1] (numeric) = 1.03306201747 -0.229806293041 y1[1] (closed_form) = 1.45379605643 -0.508662791411 absolute error = 0.5048 relative error = 32.77 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.653240098626 1.13203699798 absolute error = 1.129 relative error = 86.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8119.1MB, alloc=44.3MB, time=114.67 x[1] = 0.4253 1.048 h = 0.0001 0.005 y1[1] (numeric) = 1.03305204745 -0.231298784325 y1[1] (closed_form) = 1.45863900622 -0.516011440294 absolute error = 0.512 relative error = 33.09 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.660682735568 1.13923729795 absolute error = 1.139 relative error = 86.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8168.6MB, alloc=44.3MB, time=115.34 x[1] = 0.4254 1.053 h = 0.0001 0.003 y1[1] (numeric) = 1.03352293152 -0.232306918861 y1[1] (closed_form) = 1.46428711504 -0.519435969772 absolute error = 0.5177 relative error = 33.32 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.6634174941 1.146492826 absolute error = 1.146 relative error = 86.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4255 1.056 h = 0.001 0.001 y1[1] (numeric) = 1.03379747542 -0.232915726386 y1[1] (closed_form) = 1.46766668276 -0.521543649181 absolute error = 0.5211 relative error = 33.46 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.665125559721 1.15083870454 absolute error = 1.151 relative error = 86.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8218.2MB, alloc=44.3MB, time=116.01 x[1] = 0.4265 1.057 h = 0.001 0.003 y1[1] (numeric) = 1.033695982 -0.233213559976 y1[1] (closed_form) = 1.46815187375 -0.523361081274 absolute error = 0.5224 relative error = 33.52 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.667115921207 1.15178416179 absolute error = 1.153 relative error = 86.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8267.6MB, alloc=44.3MB, time=116.68 x[1] = 0.4275 1.06 h = 0.0001 0.004 y1[1] (numeric) = 1.03379082875 -0.233910720576 y1[1] (closed_form) = 1.47094441341 -0.526520718098 absolute error = 0.526 relative error = 33.67 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.670160288078 1.15566786425 absolute error = 1.157 relative error = 86.64 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4276 1.064 h = 0.003 0.006 y1[1] (numeric) = 1.03416354273 -0.234719191607 y1[1] (closed_form) = 1.47551163021 -0.529321732014 absolute error = 0.5306 relative error = 33.85 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.672419292381 1.16150797658 absolute error = 1.164 relative error = 86.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8317.1MB, alloc=44.3MB, time=117.34 x[1] = 0.4306 1.07 h = 0.0001 0.005 y1[1] (numeric) = 1.03415357272 -0.236211682891 y1[1] (closed_form) = 1.4804737889 -0.536874540405 absolute error = 0.5381 relative error = 34.17 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.680051820348 1.16877664498 absolute error = 1.173 relative error = 86.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4307 1.075 h = 0.0001 0.003 y1[1] (numeric) = 1.03462445679 -0.237219817427 y1[1] (closed_form) = 1.48626792053 -0.540399141284 absolute error = 0.544 relative error = 34.4 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.682893335107 1.17613962047 absolute error = 1.181 relative error = 86.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8366.7MB, alloc=44.3MB, time=118.01 x[1] = 0.4308 1.078 h = 0.001 0.001 y1[1] (numeric) = 1.03489900069 -0.237828624952 y1[1] (closed_form) = 1.48973457369 -0.54256831382 absolute error = 0.5475 relative error = 34.53 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.684666584865 1.18054947262 absolute error = 1.186 relative error = 86.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8416.2MB, alloc=44.3MB, time=118.68 x[1] = 0.4318 1.079 h = 0.0001 0.004 y1[1] (numeric) = 1.03479750727 -0.238126458542 y1[1] (closed_form) = 1.49022991339 -0.544435019777 absolute error = 0.5489 relative error = 34.59 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.686700068618 1.18149595354 absolute error = 1.188 relative error = 86.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4319 1.083 h = 0.003 0.006 y1[1] (numeric) = 1.03517022125 -0.238934929572 y1[1] (closed_form) = 1.49489893585 -0.54730492676 absolute error = 0.5536 relative error = 34.77 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.689032801451 1.18741161651 absolute error = 1.194 relative error = 86.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8465.6MB, alloc=44.3MB, time=119.34 x[1] = 0.4349 1.089 h = 0.0001 0.005 y1[1] (numeric) = 1.03516025124 -0.240427420857 y1[1] (closed_form) = 1.49996661329 -0.555035720302 absolute error = 0.5613 relative error = 35.09 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.696832082174 1.19474270909 absolute error = 1.204 relative error = 87.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8515.1MB, alloc=44.3MB, time=120.01 x[1] = 0.435 1.094 h = 0.0001 0.003 y1[1] (numeric) = 1.03563113531 -0.241435555393 y1[1] (closed_form) = 1.50588913222 -0.55864705615 absolute error = 0.5672 relative error = 35.32 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.69976657517 1.20220164903 absolute error = 1.212 relative error = 87.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4351 1.097 h = 0.001 0.001 y1[1] (numeric) = 1.03590567921 -0.242044362918 y1[1] (closed_form) = 1.50943236697 -0.560869542607 absolute error = 0.5709 relative error = 35.45 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.701596614548 1.20666865219 absolute error = 1.217 relative error = 87.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8564.6MB, alloc=44.3MB, time=120.68 x[1] = 0.4361 1.098 h = 0.001 0.003 y1[1] (numeric) = 1.03580418579 -0.242342196507 y1[1] (closed_form) = 1.5099368775 -0.562779317474 absolute error = 0.5723 relative error = 35.51 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.703668123443 1.20761651273 absolute error = 1.219 relative error = 87.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8614.1MB, alloc=44.3MB, time=121.34 x[1] = 0.4371 1.101 h = 0.0001 0.004 y1[1] (numeric) = 1.03589903253 -0.243039357108 y1[1] (closed_form) = 1.5128604109 -0.566104726636 absolute error = 0.5761 relative error = 35.66 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.706872844032 1.2115862656 absolute error = 1.224 relative error = 87.22 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4372 1.105 h = 0.003 0.006 y1[1] (numeric) = 1.03627174652 -0.243847828138 y1[1] (closed_form) = 1.51764794991 -0.569058516293 absolute error = 0.5809 relative error = 35.84 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.709294692308 1.21759051632 absolute error = 1.23 relative error = 87.29 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8663.6MB, alloc=44.3MB, time=122.00 x[1] = 0.4402 1.111 h = 0.0001 0.005 y1[1] (numeric) = 1.03626177651 -0.245340319423 y1[1] (closed_form) = 1.52283582989 -0.577002122713 absolute error = 0.5889 relative error = 36.16 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.71729355969 1.22499288404 absolute error = 1.24 relative error = 87.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4403 1.116 h = 0.0001 0.003 y1[1] (numeric) = 1.03673266058 -0.246348453959 y1[1] (closed_form) = 1.52890782892 -0.580719077334 absolute error = 0.595 relative error = 36.38 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.720340442897 1.23256434161 absolute error = 1.248 relative error = 87.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8713.1MB, alloc=44.3MB, time=122.67 x[1] = 0.4404 1.119 h = 0.001 0.001 y1[1] (numeric) = 1.03700720448 -0.246957261484 y1[1] (closed_form) = 1.53254019133 -0.583006427889 absolute error = 0.5987 relative error = 36.52 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.722239101907 1.23709832407 absolute error = 1.253 relative error = 87.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8762.7MB, alloc=44.3MB, time=123.34 x[1] = 0.4414 1.12 h = 0.001 0.003 y1[1] (numeric) = 1.03690571106 -0.247255095073 y1[1] (closed_form) = 1.53305446689 -0.584967298027 absolute error = 0.6002 relative error = 36.58 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.724355885941 1.23804713488 absolute error = 1.255 relative error = 87.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4424 1.123 h = 0.0001 0.004 y1[1] (numeric) = 1.0370005578 -0.247952255674 y1[1] (closed_form) = 1.5360486303 -0.588385359397 absolute error = 0.6041 relative error = 36.73 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.727650462271 1.24206411217 absolute error = 1.26 relative error = 87.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8812.3MB, alloc=44.3MB, time=124.00 x[1] = 0.4425 1.127 h = 0.003 0.006 y1[1] (numeric) = 1.03737327179 -0.248760726704 y1[1] (closed_form) = 1.54095617972 -0.591425494966 absolute error = 0.6091 relative error = 36.9 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.730163930464 1.24815912329 absolute error = 1.266 relative error = 87.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8861.9MB, alloc=44.3MB, time=124.67 x[1] = 0.4455 1.133 h = 0.0001 0.005 y1[1] (numeric) = 1.03736330177 -0.250253217989 y1[1] (closed_form) = 1.54626477492 -0.59958674584 absolute error = 0.6173 relative error = 37.22 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.738367757735 1.25563427559 absolute error = 1.277 relative error = 87.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4456 1.138 h = 0.0001 0.003 y1[1] (numeric) = 1.03783418584 -0.251261352525 y1[1] (closed_form) = 1.55248815555 -0.603412429978 absolute error = 0.6236 relative error = 37.44 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.741530186095 1.26332099221 absolute error = 1.285 relative error = 87.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8911.3MB, alloc=44.3MB, time=125.34 x[1] = 0.4457 1.141 h = 0.001 0.001 y1[1] (numeric) = 1.03810872974 -0.25187016005 y1[1] (closed_form) = 1.55621076826 -0.605766534617 absolute error = 0.6274 relative error = 37.57 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.743499387782 1.2679235783 absolute error = 1.29 relative error = 87.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=8961.0MB, alloc=44.3MB, time=126.01 x[1] = 0.4467 1.142 h = 0.001 0.003 y1[1] (numeric) = 1.03800723632 -0.252167993639 y1[1] (closed_form) = 1.55673458601 -0.607779513969 absolute error = 0.6289 relative error = 37.63 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.745662633325 1.26887327831 absolute error = 1.292 relative error = 87.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4477 1.145 h = 0.0001 0.004 y1[1] (numeric) = 1.03810208307 -0.25286515424 y1[1] (closed_form) = 1.55979994739 -0.611292484211 absolute error = 0.633 relative error = 37.78 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.749049504299 1.2729385431 absolute error = 1.297 relative error = 87.81 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9010.5MB, alloc=44.3MB, time=126.67 x[1] = 0.4478 1.149 h = 0.003 0.006 y1[1] (numeric) = 1.03847479705 -0.25367362527 y1[1] (closed_form) = 1.56482903566 -0.614421496287 absolute error = 0.6381 relative error = 37.96 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.751657159822 1.27912650729 absolute error = 1.304 relative error = 87.87 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4508 1.155 h = 0.0001 0.005 y1[1] (numeric) = 1.03846482704 -0.255166116555 y1[1] (closed_form) = 1.57025886305 -0.622805350575 absolute error = 0.6465 relative error = 38.27 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.76007143063 1.28667593898 absolute error = 1.314 relative error = 87.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9059.9MB, alloc=44.3MB, time=127.34 x[1] = 0.4509 1.16 h = 0.0001 0.003 y1[1] (numeric) = 1.03893571111 -0.256174251091 y1[1] (closed_form) = 1.57663557045 -0.626742959848 absolute error = 0.653 relative error = 38.49 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.763352638644 1.29448068166 absolute error = 1.322 relative error = 88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9109.5MB, alloc=44.3MB, time=128.00 x[1] = 0.451 1.163 h = 0.001 0.001 y1[1] (numeric) = 1.03921025501 -0.256783058616 y1[1] (closed_form) = 1.58044958165 -0.629165760041 absolute error = 0.657 relative error = 38.62 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.765394354218 1.29915351056 absolute error = 1.328 relative error = 88.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.452 1.164 h = 0.001 0.003 y1[1] (numeric) = 1.03910876159 -0.257080892205 y1[1] (closed_form) = 1.58098271095 -0.631231888533 absolute error = 0.6585 relative error = 38.68 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.767605269031 1.30010402825 absolute error = 1.329 relative error = 88.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9159.0MB, alloc=44.3MB, time=128.68 x[1] = 0.453 1.167 h = 0.0001 0.004 y1[1] (numeric) = 1.03920360833 -0.257778052806 y1[1] (closed_form) = 1.58411984857 -0.634842084188 absolute error = 0.6627 relative error = 38.83 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.771086926891 1.3042186441 absolute error = 1.335 relative error = 88.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9208.6MB, alloc=44.3MB, time=129.35 x[1] = 0.4531 1.171 h = 0.003 0.006 y1[1] (numeric) = 1.03957632232 -0.258586523836 y1[1] (closed_form) = 1.58927203884 -0.638062572231 absolute error = 0.668 relative error = 39 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.773791401776 1.31050177445 absolute error = 1.341 relative error = 88.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4561 1.177 h = 0.0001 0.005 y1[1] (numeric) = 1.03956635231 -0.260079015121 y1[1] (closed_form) = 1.59482361873 -0.646674118654 absolute error = 0.6766 relative error = 39.31 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.782421713041 1.31812696512 absolute error = 1.352 relative error = 88.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9258.0MB, alloc=44.3MB, time=130.03 x[1] = 0.4562 1.182 h = 0.0001 0.003 y1[1] (numeric) = 1.04003723638 -0.261087149657 y1[1] (closed_form) = 1.60135564186 -0.650726935469 absolute error = 0.6833 relative error = 39.53 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.785825016891 1.326052527 absolute error = 1.361 relative error = 88.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9307.6MB, alloc=44.3MB, time=130.70 x[1] = 0.4563 1.185 h = 0.001 0.001 y1[1] (numeric) = 1.04031178028 -0.261695957182 y1[1] (closed_form) = 1.60526222542 -0.653220425321 absolute error = 0.6874 relative error = 39.66 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.787941267003 1.33079725298 absolute error = 1.366 relative error = 88.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4573 1.186 h = 0.0001 0.004 y1[1] (numeric) = 1.04021028686 -0.261993790771 y1[1] (closed_form) = 1.60580442748 -0.655340769284 absolute error = 0.6889 relative error = 39.72 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.790201080769 1.33174850609 absolute error = 1.368 relative error = 88.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9357.1MB, alloc=44.3MB, time=131.36 x[1] = 0.4574 1.19 h = 0.003 0.006 y1[1] (numeric) = 1.04058300084 -0.262802261802 y1[1] (closed_form) = 1.61106499123 -0.658640639716 absolute error = 0.6944 relative error = 39.89 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.792989882917 1.33811653755 absolute error = 1.375 relative error = 88.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4604 1.196 h = 0.0001 0.005 y1[1] (numeric) = 1.04057303083 -0.264294753087 y1[1] (closed_form) = 1.61672458735 -0.667450892933 absolute error = 0.7032 relative error = 40.2 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.801809798955 1.34581077814 absolute error = 1.385 relative error = 88.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9406.6MB, alloc=44.3MB, time=132.02 x[1] = 0.4605 1.201 h = 0.0001 0.003 y1[1] (numeric) = 1.0410439149 -0.265302887623 y1[1] (closed_form) = 1.62339335455 -0.671603689554 absolute error = 0.7101 relative error = 40.42 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.80531943333 1.35384410383 absolute error = 1.394 relative error = 88.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9456.2MB, alloc=44.3MB, time=132.69 x[1] = 0.4606 1.204 h = 0.001 0.001 y1[1] (numeric) = 1.0413184588 -0.265911695147 y1[1] (closed_form) = 1.6273814563 -0.674158542365 absolute error = 0.7142 relative error = 40.55 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.807500613544 1.35865297444 absolute error = 1.399 relative error = 88.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4616 1.205 h = 0.001 0.003 y1[1] (numeric) = 1.04121696538 -0.266209528737 y1[1] (closed_form) = 1.62793193378 -0.676326323518 absolute error = 0.7158 relative error = 40.61 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.809803512513 1.35960538908 absolute error = 1.401 relative error = 88.55 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9505.7MB, alloc=44.3MB, time=133.36 x[1] = 0.4626 1.208 h = 0.0001 0.004 y1[1] (numeric) = 1.04131181212 -0.266906689337 y1[1] (closed_form) = 1.63120542976 -0.680122936874 absolute error = 0.7202 relative error = 40.75 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.813467750538 1.36381586952 absolute error = 1.407 relative error = 88.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9555.3MB, alloc=44.3MB, time=134.02 x[1] = 0.4627 1.212 h = 0.003 0.006 y1[1] (numeric) = 1.04168452611 -0.267715160368 y1[1] (closed_form) = 1.63659212978 -0.683519289288 absolute error = 0.7258 relative error = 40.92 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.816358420585 1.37028327411 absolute error = 1.414 relative error = 88.63 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4657 1.218 h = 0.0001 0.005 y1[1] (numeric) = 1.04167455609 -0.269207651653 y1[1] (closed_form) = 1.64237451664 -0.692567051096 absolute error = 0.7349 relative error = 41.23 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.825405085902 1.37805605419 absolute error = 1.425 relative error = 88.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9604.9MB, alloc=44.3MB, time=134.68 x[1] = 0.4658 1.223 h = 0.0001 0.003 y1[1] (numeric) = 1.04214544016 -0.270215786189 y1[1] (closed_form) = 1.64920245927 -0.696841375862 absolute error = 0.742 relative error = 41.44 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.829043177562 1.38621550952 absolute error = 1.434 relative error = 88.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9654.4MB, alloc=44.3MB, time=135.34 x[1] = 0.4659 1.226 h = 0.001 0.001 y1[1] (numeric) = 1.04241998406 -0.270824593713 y1[1] (closed_form) = 1.65328541145 -0.699470758353 absolute error = 0.7463 relative error = 41.57 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.83130276822 1.39109942217 absolute error = 1.439 relative error = 88.79 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4669 1.227 h = 0.001 0.003 y1[1] (numeric) = 1.04231849064 -0.271122427303 y1[1] (closed_form) = 1.65384450789 -0.701694814016 absolute error = 0.7479 relative error = 41.63 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.833656915807 1.39205240474 absolute error = 1.441 relative error = 88.8 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9704.0MB, alloc=44.3MB, time=136.00 x[1] = 0.4679 1.23 h = 0.0001 0.004 y1[1] (numeric) = 1.04241333739 -0.271819587903 y1[1] (closed_form) = 1.65719151904 -0.705595614021 absolute error = 0.7524 relative error = 41.77 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.83742336482 1.3963153126 absolute error = 1.446 relative error = 88.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.468 1.234 h = 0.003 0.006 y1[1] (numeric) = 1.04278605137 -0.272628058934 y1[1] (closed_form) = 1.66270601918 -0.709091253167 absolute error = 0.7582 relative error = 41.94 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.840418729002 1.40288436478 absolute error = 1.454 relative error = 88.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9753.5MB, alloc=44.3MB, time=136.66 x[1] = 0.471 1.24 h = 0.0001 0.005 y1[1] (numeric) = 1.04277608136 -0.274120550219 y1[1] (closed_form) = 1.668611723 -0.7183819972 absolute error = 0.7675 relative error = 42.25 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.84969808093 1.4107371183 absolute error = 1.465 relative error = 88.94 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9803.1MB, alloc=44.3MB, time=137.32 x[1] = 0.4711 1.245 h = 0.0001 0.003 y1[1] (numeric) = 1.04324696543 -0.275128684755 y1[1] (closed_form) = 1.67560095723 -0.722781391272 absolute error = 0.7748 relative error = 42.46 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.853468191493 1.41902557489 absolute error = 1.474 relative error = 89 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4712 1.248 h = 0.001 0.001 y1[1] (numeric) = 1.04352150933 -0.275737492279 y1[1] (closed_form) = 1.67978000811 -0.725487454456 absolute error = 0.7792 relative error = 42.58 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.855808361809 1.42398622929 absolute error = 1.479 relative error = 89.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9852.7MB, alloc=44.3MB, time=137.98 x[1] = 0.4722 1.249 h = 0.001 0.003 y1[1] (numeric) = 1.04342001591 -0.276035325869 y1[1] (closed_form) = 1.68034745973 -0.727768929016 absolute error = 0.7809 relative error = 42.64 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.858215053576 1.42493966524 absolute error = 1.481 relative error = 89.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9902.3MB, alloc=44.3MB, time=138.64 x[1] = 0.4732 1.252 h = 0.0001 0.004 y1[1] (numeric) = 1.04351486266 -0.276732486469 y1[1] (closed_form) = 1.68376860231 -0.731776474717 absolute error = 0.7855 relative error = 42.78 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.862086424973 1.42925606569 absolute error = 1.487 relative error = 89.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4733 1.256 h = 0.003 0.006 y1[1] (numeric) = 1.04388757664 -0.2775409575 y1[1] (closed_form) = 1.6894126015 -0.735374280415 absolute error = 0.7914 relative error = 42.95 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.865189380964 1.43592906187 absolute error = 1.494 relative error = 89.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=9951.9MB, alloc=44.3MB, time=139.30 x[1] = 0.4763 1.262 h = 0.0001 0.005 y1[1] (numeric) = 1.04387760663 -0.279033448785 y1[1] (closed_form) = 1.69544214805 -0.744913619851 absolute error = 0.801 relative error = 43.25 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.874707481571 1.44386320497 absolute error = 1.506 relative error = 89.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10001.4MB, alloc=44.3MB, time=139.96 x[1] = 0.4764 1.267 h = 0.0001 0.003 y1[1] (numeric) = 1.0443484907 -0.280041583321 y1[1] (closed_form) = 1.70259483442 -0.749441719025 absolute error = 0.8085 relative error = 43.46 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.878613262932 1.45228356245 absolute error = 1.515 relative error = 89.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4765 1.27 h = 0.001 0.001 y1[1] (numeric) = 1.0446230346 -0.280650390845 y1[1] (closed_form) = 1.70687125823 -0.752226671286 absolute error = 0.813 relative error = 43.59 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.881036236755 1.45732267452 absolute error = 1.52 relative error = 89.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10051.1MB, alloc=44.3MB, time=140.62 x[1] = 0.4775 1.271 h = 0.001 0.003 y1[1] (numeric) = 1.04452154118 -0.280948224435 y1[1] (closed_form) = 1.70744679166 -0.75456673726 absolute error = 0.8147 relative error = 43.64 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.883496792325 1.45827643725 absolute error = 1.522 relative error = 89.29 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4785 1.274 h = 0.0001 0.004 y1[1] (numeric) = 1.04461638792 -0.281645385035 y1[1] (closed_form) = 1.71094269082 -0.758683653659 absolute error = 0.8195 relative error = 43.79 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.887475857814 1.46264739535 absolute error = 1.528 relative error = 89.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10100.6MB, alloc=44.3MB, time=141.28 x[1] = 0.4786 1.278 h = 0.003 0.006 y1[1] (numeric) = 1.04498910191 -0.282453856066 y1[1] (closed_form) = 1.7167179232 -0.762386582511 absolute error = 0.8256 relative error = 43.95 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.890689376583 1.46942665425 absolute error = 1.536 relative error = 89.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10150.0MB, alloc=44.3MB, time=141.93 x[1] = 0.4816 1.284 h = 0.0001 0.005 y1[1] (numeric) = 1.04497913189 -0.283946347351 y1[1] (closed_form) = 1.72287183677 -0.772180272749 absolute error = 0.8354 relative error = 44.25 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.900452415772 1.4774435845 absolute error = 1.547 relative error = 89.42 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4817 1.289 h = 0.0001 0.003 y1[1] (numeric) = 1.04545001596 -0.284954481887 y1[1] (closed_form) = 1.7301901803 -0.776840809622 absolute error = 0.8431 relative error = 44.45 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.904497612441 1.48599877101 absolute error = 1.557 relative error = 89.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10199.6MB, alloc=44.3MB, time=142.60 x[1] = 0.4818 1.292 h = 0.001 0.001 y1[1] (numeric) = 1.04572455986 -0.285563289411 y1[1] (closed_form) = 1.73456527727 -0.779706918021 absolute error = 0.8477 relative error = 44.58 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.907005669671 1.4911180731 absolute error = 1.562 relative error = 89.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10249.4MB, alloc=44.3MB, time=143.26 x[1] = 0.4828 1.293 h = 0.0001 0.004 y1[1] (numeric) = 1.04562306644 -0.285861123001 y1[1] (closed_form) = 1.73514860917 -0.782106776524 absolute error = 0.8495 relative error = 44.64 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.909521433302 1.49207202361 absolute error = 1.564 relative error = 89.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4829 1.297 h = 0.003 0.006 y1[1] (numeric) = 1.04599578043 -0.286669594031 y1[1] (closed_form) = 1.74103951996 -0.78590102735 absolute error = 0.8558 relative error = 44.8 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.912831253448 1.49894599054 absolute error = 1.572 relative error = 89.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10298.9MB, alloc=44.3MB, time=143.92 x[1] = 0.4859 1.303 h = 0.0001 0.005 y1[1] (numeric) = 1.04598581041 -0.288162085316 y1[1] (closed_form) = 1.74730402816 -0.795916883753 absolute error = 0.8658 relative error = 45.09 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.922809175776 1.50703830604 absolute error = 1.584 relative error = 89.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10348.5MB, alloc=44.3MB, time=144.58 x[1] = 0.486 1.308 h = 0.0001 0.003 y1[1] (numeric) = 1.04645669448 -0.289170219852 y1[1] (closed_form) = 1.75476840363 -0.800692473206 absolute error = 0.8737 relative error = 45.3 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.92697579339 1.51571363894 absolute error = 1.593 relative error = 89.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4861 1.311 h = 0.001 0.001 y1[1] (numeric) = 1.04673123838 -0.289779027377 y1[1] (closed_form) = 1.75923050083 -0.803629102336 absolute error = 0.8785 relative error = 45.42 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.929557973505 1.52090441746 absolute error = 1.599 relative error = 89.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10398.2MB, alloc=44.3MB, time=145.24 x[1] = 0.4871 1.312 h = 0.001 0.003 y1[1] (numeric) = 1.04662974496 -0.290076860966 y1[1] (closed_form) = 1.75982104283 -0.806081324154 absolute error = 0.8803 relative error = 45.48 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.932122354331 1.52185908844 absolute error = 1.601 relative error = 89.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4881 1.315 h = 0.0001 0.004 y1[1] (numeric) = 1.04672459171 -0.290774021567 y1[1] (closed_form) = 1.7634591193 -0.810408063493 absolute error = 0.8853 relative error = 45.62 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.936308723464 1.5263357631 absolute error = 1.607 relative error = 89.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10447.7MB, alloc=44.3MB, time=145.90 x[1] = 0.4882 1.319 h = 0.003 0.006 y1[1] (numeric) = 1.04709730569 -0.291582492597 y1[1] (closed_form) = 1.7694846217 -0.81431312776 absolute error = 0.8917 relative error = 45.78 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.939734808003 1.53332040544 absolute error = 1.615 relative error = 89.79 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10497.1MB, alloc=44.3MB, time=146.56 x[1] = 0.4912 1.325 h = 0.0001 0.005 y1[1] (numeric) = 1.04708733568 -0.293074983882 y1[1] (closed_form) = 1.77587453729 -0.824594426255 absolute error = 0.902 relative error = 46.07 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.949969521842 1.54149813389 absolute error = 1.627 relative error = 89.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4913 1.33 h = 0.0001 0.003 y1[1] (numeric) = 1.04755821975 -0.294083118418 y1[1] (closed_form) = 1.78350883919 -0.829509636642 absolute error = 0.9101 relative error = 46.27 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.954282741451 1.55031386913 absolute error = 1.637 relative error = 89.89 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10546.6MB, alloc=44.3MB, time=147.22 x[1] = 0.4914 1.333 h = 0.001 0.001 y1[1] (numeric) = 1.04783276365 -0.294691925943 y1[1] (closed_form) = 1.78807212707 -0.832531784932 absolute error = 0.915 relative error = 46.39 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.956954380366 1.55558813469 absolute error = 1.642 relative error = 89.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10596.2MB, alloc=44.3MB, time=147.88 x[1] = 0.4924 1.334 h = 0.001 0.003 y1[1] (numeric) = 1.04773127023 -0.294989759532 y1[1] (closed_form) = 1.78866992746 -0.835046115719 absolute error = 0.9169 relative error = 46.45 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.959576540185 1.55654271721 absolute error = 1.644 relative error = 89.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4934 1.337 h = 0.0001 0.004 y1[1] (numeric) = 1.04782611698 -0.295686920133 y1[1] (closed_form) = 1.79238462912 -0.839490103883 absolute error = 0.922 relative error = 46.58 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.963878866657 1.56107703006 absolute error = 1.65 relative error = 89.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10645.7MB, alloc=44.3MB, time=148.54 x[1] = 0.4935 1.341 h = 0.003 0.006 y1[1] (numeric) = 1.04819883096 -0.296495391163 y1[1] (closed_form) = 1.79854655954 -0.843509167251 absolute error = 0.9286 relative error = 46.74 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.967424406561 1.56817473325 absolute error = 1.658 relative error = 90.01 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10695.1MB, alloc=44.3MB, time=149.20 x[1] = 0.4965 1.347 h = 0.0001 0.005 y1[1] (numeric) = 1.04818886095 -0.297987882448 y1[1] (closed_form) = 1.80506239805 -0.854062085559 absolute error = 0.9392 relative error = 47.03 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.977922485342 1.57643921615 absolute error = 1.671 relative error = 90.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4966 1.352 h = 0.0001 0.003 y1[1] (numeric) = 1.04865974502 -0.298996016984 y1[1] (closed_form) = 1.81286896073 -0.85912093829 absolute error = 0.9475 relative error = 47.23 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.982386329427 1.58539836711 absolute error = 1.681 relative error = 90.11 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10744.5MB, alloc=44.3MB, time=149.85 x[1] = 0.4967 1.355 h = 0.001 0.001 y1[1] (numeric) = 1.04893428892 -0.299604824509 y1[1] (closed_form) = 1.81753481498 -0.862231047847 absolute error = 0.9525 relative error = 47.35 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.985149875257 1.59075790129 absolute error = 1.687 relative error = 90.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.4977 1.356 h = 0.001 0.003 y1[1] (numeric) = 1.0488327955 -0.299902658098 y1[1] (closed_form) = 1.81813955992 -0.86480877336 absolute error = 0.9544 relative error = 47.41 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.987831232196 1.59171221902 absolute error = 1.689 relative error = 90.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10794.1MB, alloc=44.3MB, time=150.52 x[1] = 0.4987 1.359 h = 0.0001 0.004 y1[1] (numeric) = 1.04892764224 -0.300599818699 y1[1] (closed_form) = 1.82193154397 -0.869372902799 absolute error = 0.9597 relative error = 47.54 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.992252535018 1.59630523398 absolute error = 1.695 relative error = 90.17 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10843.5MB, alloc=44.3MB, time=151.17 x[1] = 0.4988 1.363 h = 0.003 0.006 y1[1] (numeric) = 1.04930035623 -0.301408289729 y1[1] (closed_form) = 1.82823177447 -0.873509234723 absolute error = 0.9665 relative error = 47.7 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 0.99592080209 1.60351840715 absolute error = 1.703 relative error = 90.22 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5018 1.369 h = 0.0001 0.005 y1[1] (numeric) = 1.04929038621 -0.302900781014 y1[1] (closed_form) = 1.83487404548 -0.884340103769 absolute error = 0.9774 relative error = 47.98 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.00668895955 1.61187096411 absolute error = 1.715 relative error = 90.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10893.0MB, alloc=44.3MB, time=151.83 x[1] = 0.5019 1.374 h = 0.0001 0.003 y1[1] (numeric) = 1.04976127028 -0.30390891555 y1[1] (closed_form) = 1.84285524832 -0.889546725919 absolute error = 0.9859 relative error = 48.18 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.01130755271 1.62097657442 absolute error = 1.726 relative error = 90.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10942.6MB, alloc=44.3MB, time=152.49 x[1] = 0.502 1.377 h = 0.001 0.001 y1[1] (numeric) = 1.05003581418 -0.304517723075 y1[1] (closed_form) = 1.84762507088 -0.892747302872 absolute error = 0.991 relative error = 48.3 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.01416551536 1.62642317626 absolute error = 1.732 relative error = 90.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.503 1.378 h = 0.001 0.003 y1[1] (numeric) = 1.04993432076 -0.304815556664 y1[1] (closed_form) = 1.84823643491 -0.895389739393 absolute error = 0.993 relative error = 48.35 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.01690751447 1.62737703895 absolute error = 1.734 relative error = 90.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=10992.2MB, alloc=44.3MB, time=153.15 x[1] = 0.504 1.381 h = 0.0001 0.004 y1[1] (numeric) = 1.05002916751 -0.305512717265 y1[1] (closed_form) = 1.85210636576 -0.900076975354 absolute error = 0.9984 relative error = 48.48 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.02145088059 1.63202981897 absolute error = 1.74 relative error = 90.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11041.8MB, alloc=44.3MB, time=153.81 x[1] = 0.5041 1.385 h = 0.003 0.006 y1[1] (numeric) = 1.05040188149 -0.306321188295 y1[1] (closed_form) = 1.85854680409 -0.904333931009 absolute error = 1.005 relative error = 48.64 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.02524522952 1.63936089525 absolute error = 1.748 relative error = 90.42 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5071 1.391 h = 0.0001 0.005 y1[1] (numeric) = 1.05039191148 -0.30781367958 y1[1] (closed_form) = 1.86531601003 -0.915449237927 absolute error = 1.017 relative error = 48.92 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.03629032307 1.64780282308 absolute error = 1.761 relative error = 90.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11091.2MB, alloc=44.3MB, time=154.47 x[1] = 0.5072 1.396 h = 0.0001 0.003 y1[1] (numeric) = 1.05086279555 -0.308821814116 y1[1] (closed_form) = 1.87347427755 -0.920807864671 absolute error = 1.025 relative error = 49.11 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.04106789462 1.65705796706 absolute error = 1.771 relative error = 90.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5073 1.399 h = 0.001 0.001 y1[1] (numeric) = 1.05113733945 -0.309430621641 y1[1] (closed_form) = 1.87834949666 -0.924101480644 absolute error = 1.031 relative error = 49.23 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.04402284733 1.66259345326 absolute error = 1.778 relative error = 90.55 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11140.8MB, alloc=44.3MB, time=155.13 x[1] = 0.5083 1.4 h = 0.003 0.006 y1[1] (numeric) = 1.05103584603 -0.30972845523 y1[1] (closed_form) = 1.87896714226 -0.9268099755 absolute error = 1.033 relative error = 49.29 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.04682696122 1.66354665632 absolute error = 1.78 relative error = 90.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11190.3MB, alloc=44.3MB, time=155.78 x[1] = 0.5113 1.406 h = 0.0001 0.005 y1[1] (numeric) = 1.05102587602 -0.311220946515 y1[1] (closed_form) = 1.88581658782 -0.938128002477 absolute error = 1.044 relative error = 49.57 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.05806889997 1.67204361515 absolute error = 1.793 relative error = 90.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5114 1.411 h = 0.0001 0.003 y1[1] (numeric) = 1.05149676009 -0.312229081051 y1[1] (closed_form) = 1.89409412674 -0.943598240291 absolute error = 1.053 relative error = 49.76 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.06296220014 1.68139928655 absolute error = 1.803 relative error = 90.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11239.7MB, alloc=44.3MB, time=156.44 x[1] = 0.5115 1.414 h = 0.001 0.001 y1[1] (numeric) = 1.05177130399 -0.312837888576 y1[1] (closed_form) = 1.89904026632 -0.94696008205 absolute error = 1.058 relative error = 49.87 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.06598769179 1.68699445618 absolute error = 1.81 relative error = 90.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11289.4MB, alloc=44.3MB, time=157.10 x[1] = 0.5125 1.415 h = 0.001 0.003 y1[1] (numeric) = 1.05166981057 -0.313135722166 y1[1] (closed_form) = 1.89966032521 -0.949714963445 absolute error = 1.06 relative error = 49.93 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.06883537945 1.68794546943 absolute error = 1.812 relative error = 90.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5135 1.418 h = 0.0001 0.004 y1[1] (numeric) = 1.05176465731 -0.313832882766 y1[1] (closed_form) = 1.90366007617 -0.954618923423 absolute error = 1.066 relative error = 50.06 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.07359353494 1.6926982823 absolute error = 1.818 relative error = 90.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11338.9MB, alloc=44.3MB, time=157.76 x[1] = 0.5136 1.422 h = 0.003 0.006 y1[1] (numeric) = 1.0521373713 -0.314641353796 y1[1] (closed_form) = 1.91033836504 -0.95909097383 absolute error = 1.073 relative error = 50.21 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.0776116488 1.70023058392 absolute error = 1.827 relative error = 90.75 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11388.4MB, alloc=44.3MB, time=158.42 x[1] = 0.5166 1.428 h = 0.0001 0.005 y1[1] (numeric) = 1.05212740128 -0.316133845081 y1[1] (closed_form) = 1.91731540136 -0.970704763285 absolute error = 1.085 relative error = 50.48 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.08914246495 1.70881886688 absolute error = 1.84 relative error = 90.8 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5167 1.433 h = 0.0001 0.003 y1[1] (numeric) = 1.05259828535 -0.317141979617 y1[1] (closed_form) = 1.9257740872 -0.976334469939 absolute error = 1.094 relative error = 50.67 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.09420220618 1.71832921925 absolute error = 1.851 relative error = 90.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11438.0MB, alloc=44.3MB, time=159.08 x[1] = 0.5168 1.436 h = 0.001 0.001 y1[1] (numeric) = 1.05287282925 -0.317750787142 y1[1] (closed_form) = 1.93082802531 -0.979793881519 absolute error = 1.1 relative error = 50.78 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.09732922618 1.7240163119 absolute error = 1.857 relative error = 90.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5178 1.437 h = 0.001 0.003 y1[1] (numeric) = 1.05277133583 -0.318048620732 y1[1] (closed_form) = 1.93145373166 -0.982617158094 absolute error = 1.102 relative error = 50.84 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.10024157242 1.72496624774 absolute error = 1.859 relative error = 90.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11487.6MB, alloc=44.3MB, time=159.74 x[1] = 0.5188 1.44 h = 0.0001 0.004 y1[1] (numeric) = 1.05286618258 -0.318745781332 y1[1] (closed_form) = 1.9355331672 -0.987652584673 absolute error = 1.107 relative error = 50.97 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.10513046482 1.72978159246 absolute error = 1.866 relative error = 90.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11537.1MB, alloc=44.3MB, time=160.39 x[1] = 0.5189 1.444 h = 0.003 0.006 y1[1] (numeric) = 1.05323889656 -0.319554252362 y1[1] (closed_form) = 1.9423568776 -0.99225476835 absolute error = 1.115 relative error = 51.12 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.10928416798 1.73743836725 absolute error = 1.875 relative error = 90.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5219 1.45 h = 0.0001 0.005 y1[1] (numeric) = 1.05322892655 -0.321046743647 y1[1] (closed_form) = 1.94946197714 -1.00417124244 absolute error = 1.127 relative error = 51.39 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.12111112164 1.74611920075 absolute error = 1.888 relative error = 90.99 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11586.5MB, alloc=44.3MB, time=161.05 x[1] = 0.522 1.455 h = 0.0001 0.003 y1[1] (numeric) = 1.05369981062 -0.322054878183 y1[1] (closed_form) = 1.95810435345 -1.00996495736 absolute error = 1.136 relative error = 51.57 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.12634182876 1.75578739007 absolute error = 1.899 relative error = 91.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11636.2MB, alloc=44.3MB, time=161.71 x[1] = 0.5221 1.458 h = 0.001 0.001 y1[1] (numeric) = 1.05397435452 -0.322663685708 y1[1] (closed_form) = 1.9632675875 -1.01352469466 absolute error = 1.142 relative error = 51.69 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.12957312913 1.76156826933 absolute error = 1.906 relative error = 91.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5231 1.459 h = 0.001 0.003 y1[1] (numeric) = 1.0538728611 -0.322961519298 y1[1] (closed_form) = 1.96389856815 -1.01641779953 absolute error = 1.144 relative error = 51.74 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.13255168329 1.76251688165 absolute error = 1.908 relative error = 91.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11685.7MB, alloc=44.3MB, time=162.37 x[1] = 0.5241 1.462 h = 0.0001 0.004 y1[1] (numeric) = 1.05396770784 -0.323658679898 y1[1] (closed_form) = 1.96805837383 -1.02158793988 absolute error = 1.15 relative error = 51.87 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.13757466459 1.76739581346 absolute error = 1.915 relative error = 91.09 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11735.2MB, alloc=44.3MB, time=163.03 x[1] = 0.5242 1.466 h = 0.003 0.006 y1[1] (numeric) = 1.05434042183 -0.324467150928 y1[1] (closed_form) = 1.97502954354 -1.02632394647 absolute error = 1.158 relative error = 52.01 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.14186763652 1.77517958361 absolute error = 1.924 relative error = 91.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5272 1.472 h = 0.0001 0.005 y1[1] (numeric) = 1.05433045182 -0.325959642213 y1[1] (closed_form) = 1.98226316652 -1.03855019523 absolute error = 1.17 relative error = 52.28 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.15399814439 1.78395416718 absolute error = 1.937 relative error = 91.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11784.7MB, alloc=44.3MB, time=163.68 x[1] = 0.5273 1.477 h = 0.0001 0.003 y1[1] (numeric) = 1.05480133589 -0.326967776749 y1[1] (closed_form) = 1.99109182238 -1.04451257546 absolute error = 1.18 relative error = 52.46 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.15940445699 1.79378338149 absolute error = 1.948 relative error = 91.22 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5274 1.48 h = 0.001 0.001 y1[1] (numeric) = 1.05507587979 -0.327576584274 y1[1] (closed_form) = 1.99636587621 -1.04817546559 absolute error = 1.185 relative error = 52.57 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.16274285914 1.7996599294 absolute error = 1.955 relative error = 91.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11834.3MB, alloc=44.3MB, time=164.34 x[1] = 0.5284 1.481 h = 0.0001 0.004 y1[1] (numeric) = 1.05497438637 -0.327874417864 y1[1] (closed_form) = 1.99700174412 -1.05113986496 absolute error = 1.188 relative error = 52.63 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.16578920046 1.80060695606 absolute error = 1.957 relative error = 91.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11883.8MB, alloc=44.3MB, time=165.00 x[1] = 0.5285 1.485 h = 0.003 0.006 y1[1] (numeric) = 1.05534710035 -0.328682888894 y1[1] (closed_form) = 2.00410315685 -1.05599229899 absolute error = 1.195 relative error = 52.77 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.17020351362 1.80850379902 absolute error = 1.967 relative error = 91.29 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5315 1.491 h = 0.0001 0.005 y1[1] (numeric) = 1.05533713034 -0.330175380179 y1[1] (closed_form) = 2.01145157485 -1.06848946141 absolute error = 1.208 relative error = 53.04 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.18260023653 1.81736375783 absolute error = 1.98 relative error = 91.33 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11933.3MB, alloc=44.3MB, time=165.66 x[1] = 0.5316 1.496 h = 0.0001 0.003 y1[1] (numeric) = 1.05580801441 -0.331183514715 y1[1] (closed_form) = 2.02044476885 -1.07459858238 absolute error = 1.218 relative error = 53.22 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.18815953904 1.82733632398 absolute error = 1.992 relative error = 91.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=11982.9MB, alloc=44.3MB, time=166.32 x[1] = 0.5317 1.499 h = 0.001 0.001 y1[1] (numeric) = 1.05608255831 -0.33179232224 y1[1] (closed_form) = 2.02581672906 -1.07835123724 absolute error = 1.224 relative error = 53.33 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.19159127398 1.83329806444 absolute error = 1.999 relative error = 91.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5327 1.5 h = 0.001 0.003 y1[1] (numeric) = 1.05598106489 -0.332090155829 y1[1] (closed_form) = 2.02645735649 -1.08137815261 absolute error = 1.226 relative error = 53.38 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.19469727556 1.83424433731 absolute error = 2.001 relative error = 91.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12032.5MB, alloc=44.3MB, time=166.98 x[1] = 0.5337 1.503 h = 0.0001 0.004 y1[1] (numeric) = 1.05607591163 -0.33278731643 y1[1] (closed_form) = 2.03077025424 -1.0868069052 absolute error = 1.232 relative error = 53.5 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.19997816093 1.8392460855 absolute error = 2.008 relative error = 91.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12081.9MB, alloc=44.3MB, time=167.64 x[1] = 0.5338 1.507 h = 0.003 0.006 y1[1] (numeric) = 1.05644862562 -0.33359578746 y1[1] (closed_form) = 2.0380230607 -1.09180025804 absolute error = 1.24 relative error = 53.65 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.20453880831 1.84727473138 absolute error = 2.017 relative error = 91.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5368 1.513 h = 0.0001 0.005 y1[1] (numeric) = 1.0564386556 -0.335088278745 y1[1] (closed_form) = 2.04550091043 -1.10462084122 absolute error = 1.253 relative error = 53.91 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.21725330209 1.85623068964 absolute error = 2.031 relative error = 91.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12131.5MB, alloc=44.3MB, time=168.30 x[1] = 0.5369 1.518 h = 0.0001 0.003 y1[1] (numeric) = 1.05690953967 -0.336096413281 y1[1] (closed_form) = 2.05468538193 -1.11090758347 absolute error = 1.263 relative error = 54.08 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.22299711966 1.86637035831 absolute error = 2.043 relative error = 91.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.537 1.521 h = 0.001 0.001 y1[1] (numeric) = 1.05718408357 -0.336705220806 y1[1] (closed_form) = 2.06017110365 -1.11476882813 absolute error = 1.269 relative error = 54.19 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.22654137414 1.87243135485 absolute error = 2.05 relative error = 91.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12181.0MB, alloc=44.3MB, time=168.95 x[1] = 0.538 1.522 h = 0.001 0.003 y1[1] (numeric) = 1.05708259015 -0.337003054395 y1[1] (closed_form) = 2.06081587783 -1.11786986125 absolute error = 1.272 relative error = 54.24 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.22971818682 1.87337552953 absolute error = 2.052 relative error = 91.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12230.7MB, alloc=44.3MB, time=169.61 x[1] = 0.539 1.525 h = 0.0001 0.004 y1[1] (numeric) = 1.0571774369 -0.337700214996 y1[1] (closed_form) = 2.06521117618 -1.12344305708 absolute error = 1.278 relative error = 54.36 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.23514316357 1.87844391299 absolute error = 2.06 relative error = 91.61 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5391 1.529 h = 0.003 0.006 y1[1] (numeric) = 1.05755015088 -0.338508686026 y1[1] (closed_form) = 2.07261751853 -1.1285812968 absolute error = 1.286 relative error = 54.51 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.2398540969 1.88660695859 absolute error = 2.069 relative error = 91.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12280.2MB, alloc=44.3MB, time=170.27 x[1] = 0.5421 1.535 h = 0.0001 0.005 y1[1] (numeric) = 1.05754018087 -0.340001177311 y1[1] (closed_form) = 2.08022521933 -1.14173288991 absolute error = 1.299 relative error = 54.76 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.25289424706 1.89566003428 absolute error = 2.083 relative error = 91.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12329.6MB, alloc=44.3MB, time=170.93 x[1] = 0.5422 1.54 h = 0.0001 0.003 y1[1] (numeric) = 1.05801106494 -0.341009311847 y1[1] (closed_form) = 2.08960368956 -1.14820226169 absolute error = 1.31 relative error = 54.94 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.25882756317 1.90597008882 absolute error = 2.095 relative error = 91.73 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5423 1.543 h = 0.001 0.001 y1[1] (numeric) = 1.05828560884 -0.341618119372 y1[1] (closed_form) = 2.09520477336 -1.15217513595 absolute error = 1.316 relative error = 55.04 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.26248736664 1.91213227821 absolute error = 2.102 relative error = 91.75 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12379.3MB, alloc=44.3MB, time=171.59 x[1] = 0.5433 1.544 h = 0.001 0.003 y1[1] (numeric) = 1.05818411542 -0.341915952961 y1[1] (closed_form) = 2.09585326504 -1.15535185101 absolute error = 1.318 relative error = 55.09 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.265736659 1.91307404427 absolute error = 2.105 relative error = 91.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12428.9MB, alloc=44.3MB, time=172.25 x[1] = 0.5443 1.547 h = 0.0001 0.004 y1[1] (numeric) = 1.05827896217 -0.342613113562 y1[1] (closed_form) = 2.10033166812 -1.1610730561 absolute error = 1.325 relative error = 55.21 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.27130938254 1.91821010858 absolute error = 2.112 relative error = 91.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5444 1.551 h = 0.003 0.006 y1[1] (numeric) = 1.05865167615 -0.343421584592 y1[1] (closed_form) = 2.10789372477 -1.16636025263 absolute error = 1.333 relative error = 55.35 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.27617465339 1.92651017697 absolute error = 2.122 relative error = 91.82 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12478.4MB, alloc=44.3MB, time=172.90 x[1] = 0.5474 1.557 h = 0.0001 0.005 y1[1] (numeric) = 1.05864170614 -0.344914075877 y1[1] (closed_form) = 2.11563167798 -1.17985062603 absolute error = 1.347 relative error = 55.61 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.28954851659 1.93566145639 absolute error = 2.136 relative error = 91.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5475 1.562 h = 0.0001 0.003 y1[1] (numeric) = 1.05911259021 -0.345922210413 y1[1] (closed_form) = 2.12520691402 -1.18650776409 absolute error = 1.358 relative error = 55.78 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.29567644086 1.94614521363 absolute error = 2.149 relative error = 91.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12527.9MB, alloc=44.3MB, time=173.56 x[1] = 0.5476 1.565 h = 0.001 0.001 y1[1] (numeric) = 1.05938713411 -0.346531017938 y1[1] (closed_form) = 2.13092498702 -1.19059538554 absolute error = 1.364 relative error = 55.88 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.29945489903 1.95241055182 absolute error = 2.156 relative error = 91.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12577.5MB, alloc=44.3MB, time=174.22 x[1] = 0.5486 1.566 h = 0.001 0.003 y1[1] (numeric) = 1.05928564069 -0.346828851527 y1[1] (closed_form) = 2.13157675099 -1.19384938214 absolute error = 1.366 relative error = 55.93 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.30277837213 1.95334958086 absolute error = 2.158 relative error = 91.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5496 1.569 h = 0.0001 0.004 y1[1] (numeric) = 1.05938048743 -0.347526012128 y1[1] (closed_form) = 2.13613896633 -1.19972224934 absolute error = 1.373 relative error = 56.05 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.30850258102 1.95855436801 absolute error = 2.166 relative error = 91.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12627.1MB, alloc=44.3MB, time=174.88 x[1] = 0.5497 1.573 h = 0.003 0.006 y1[1] (numeric) = 1.05975320142 -0.348334483158 y1[1] (closed_form) = 2.14385895192 -1.20516257685 absolute error = 1.382 relative error = 56.19 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.31352634331 1.96699410869 absolute error = 2.176 relative error = 91.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12676.7MB, alloc=44.3MB, time=175.58 x[1] = 0.5527 1.579 h = 0.0001 0.005 y1[1] (numeric) = 1.0597432314 -0.349826974443 y1[1] (closed_form) = 2.15172753924 -1.21899968573 absolute error = 1.396 relative error = 56.44 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.32724215122 1.97624464511 absolute error = 2.191 relative error = 92.02 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5528 1.584 h = 0.0001 0.003 y1[1] (numeric) = 1.06021411547 -0.350835108979 y1[1] (closed_form) = 2.16150235411 -1.22584985834 absolute error = 1.407 relative error = 56.61 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.33356992251 1.98690545569 absolute error = 2.203 relative error = 92.06 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12726.4MB, alloc=44.3MB, time=176.24 x[1] = 0.5529 1.587 h = 0.001 0.001 y1[1] (numeric) = 1.06048865937 -0.351443916504 y1[1] (closed_form) = 2.16733907 -1.23005542418 absolute error = 1.413 relative error = 56.71 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.33747021926 1.99327591798 absolute error = 2.21 relative error = 92.09 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12776.0MB, alloc=44.3MB, time=176.90 x[1] = 0.5539 1.588 h = 0.0001 0.004 y1[1] (numeric) = 1.06038716595 -0.351741750093 y1[1] (closed_form) = 2.16799364453 -1.23338833787 absolute error = 1.416 relative error = 56.76 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.34086960735 1.99421186303 absolute error = 2.213 relative error = 92.09 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.554 1.592 h = 0.003 0.006 y1[1] (numeric) = 1.06075987994 -0.352550221124 y1[1] (closed_form) = 2.17585326496 -1.23896198151 absolute error = 1.424 relative error = 56.89 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.34603149288 2.00277592826 absolute error = 2.223 relative error = 92.12 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12825.5MB, alloc=44.3MB, time=177.55 x[1] = 0.557 1.598 h = 0.0001 0.005 y1[1] (numeric) = 1.06074990992 -0.354042712408 y1[1] (closed_form) = 2.18383885 -1.253102501 absolute error = 1.439 relative error = 57.14 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.36004716494 2.01211692891 absolute error = 2.238 relative error = 92.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5571 1.603 h = 0.0001 0.003 y1[1] (numeric) = 1.06122079399 -0.355050846944 y1[1] (closed_form) = 2.19379013066 -1.2601207288 absolute error = 1.45 relative error = 57.3 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.36654909002 2.02293531822 absolute error = 2.251 relative error = 92.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12875.2MB, alloc=44.3MB, time=178.22 x[1] = 0.5572 1.606 h = 0.001 0.001 y1[1] (numeric) = 1.06149533789 -0.355659654469 y1[1] (closed_form) = 2.19973177322 -1.26442899903 absolute error = 1.457 relative error = 57.41 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.37055558739 2.02939936894 absolute error = 2.258 relative error = 92.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12924.8MB, alloc=44.3MB, time=178.88 x[1] = 0.5582 1.607 h = 0.001 0.003 y1[1] (numeric) = 1.06139384447 -0.355957488059 y1[1] (closed_form) = 2.20038935144 -1.26783115393 absolute error = 1.459 relative error = 57.45 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.37402177787 2.03033330001 absolute error = 2.261 relative error = 92.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5592 1.61 h = 0.0001 0.004 y1[1] (numeric) = 1.06148869122 -0.356654648659 y1[1] (closed_form) = 2.20511132776 -1.27399523799 absolute error = 1.466 relative error = 57.57 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.38003726112 2.03567063728 absolute error = 2.269 relative error = 92.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=12974.2MB, alloc=44.3MB, time=179.53 x[1] = 0.5593 1.614 h = 0.003 0.006 y1[1] (numeric) = 1.0618614052 -0.35746311969 y1[1] (closed_form) = 2.21313314744 -1.27973003807 absolute error = 1.475 relative error = 57.7 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.38536561621 2.04437942872 absolute error = 2.279 relative error = 92.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13023.7MB, alloc=44.3MB, time=180.19 x[1] = 0.5623 1.62 h = 0.0001 0.005 y1[1] (numeric) = 1.06185143519 -0.358955610974 y1[1] (closed_form) = 2.22125011899 -1.29423259662 absolute error = 1.49 relative error = 57.94 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.39973901835 2.05382165644 absolute error = 2.295 relative error = 92.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5624 1.625 h = 0.0001 0.003 y1[1] (numeric) = 1.06232231926 -0.35996374551 y1[1] (closed_form) = 2.23140640182 -1.30145398767 absolute error = 1.501 relative error = 58.11 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.40645085274 2.06482349106 absolute error = 2.307 relative error = 92.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13073.5MB, alloc=44.3MB, time=180.85 x[1] = 0.5625 1.628 h = 0.001 0.001 y1[1] (numeric) = 1.06259686316 -0.360572553035 y1[1] (closed_form) = 2.23746987558 -1.30588634928 absolute error = 1.508 relative error = 58.21 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.41058530364 2.07139643374 absolute error = 2.315 relative error = 92.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13123.0MB, alloc=44.3MB, time=181.51 x[1] = 0.5635 1.629 h = 0.001 0.003 y1[1] (numeric) = 1.06249536974 -0.360870386625 y1[1] (closed_form) = 2.23812937966 -1.30937056871 absolute error = 1.511 relative error = 58.25 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.41413073157 2.0723266055 absolute error = 2.318 relative error = 92.39 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5645 1.632 h = 0.0001 0.004 y1[1] (numeric) = 1.06259021649 -0.361567547225 y1[1] (closed_form) = 2.24293725324 -1.31569725261 absolute error = 1.518 relative error = 58.37 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.42030885979 2.07773567102 absolute error = 2.326 relative error = 92.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13172.5MB, alloc=44.3MB, time=182.17 x[1] = 0.5646 1.636 h = 0.003 0.006 y1[1] (numeric) = 1.06296293047 -0.362376018256 y1[1] (closed_form) = 2.25112359205 -1.32159769459 absolute error = 1.527 relative error = 58.5 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.42580814481 2.08659191653 absolute error = 2.336 relative error = 92.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5676 1.642 h = 0.0001 0.005 y1[1] (numeric) = 1.06295296046 -0.36386850954 y1[1] (closed_form) = 2.25937226856 -1.33647079727 absolute error = 1.542 relative error = 58.74 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.44054803228 2.09613632412 absolute error = 2.352 relative error = 92.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13222.1MB, alloc=44.3MB, time=182.83 x[1] = 0.5677 1.647 h = 0.0001 0.003 y1[1] (numeric) = 1.06342384453 -0.364876644076 y1[1] (closed_form) = 2.26973649987 -1.34390101259 absolute error = 1.554 relative error = 58.9 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.44747540188 2.10732505473 absolute error = 2.365 relative error = 92.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13271.8MB, alloc=44.3MB, time=183.49 x[1] = 0.5678 1.65 h = 0.001 0.001 y1[1] (numeric) = 1.06369838843 -0.365485451601 y1[1] (closed_form) = 2.2759235356 -1.3484609005 absolute error = 1.561 relative error = 59 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.45174122423 2.11400892189 absolute error = 2.373 relative error = 92.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5688 1.651 h = 0.001 0.003 y1[1] (numeric) = 1.06359689501 -0.365783285191 y1[1] (closed_form) = 2.27658445365 -1.35202892679 absolute error = 1.563 relative error = 59.04 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.45536772298 2.11493493158 absolute error = 2.376 relative error = 92.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13321.4MB, alloc=44.3MB, time=184.15 x[1] = 0.5698 1.654 h = 0.0001 0.004 y1[1] (numeric) = 1.06369174175 -0.366480445791 y1[1] (closed_form) = 2.28147894101 -1.3585222163 absolute error = 1.571 relative error = 59.15 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.46171257442 2.12041675061 absolute error = 2.384 relative error = 92.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13370.9MB, alloc=44.3MB, time=184.80 x[1] = 0.5699 1.658 h = 0.003 0.006 y1[1] (numeric) = 1.06406445574 -0.367288916822 y1[1] (closed_form) = 2.2898321552 -1.36459289953 absolute error = 1.58 relative error = 59.28 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.46738736205 2.12942320543 absolute error = 2.394 relative error = 92.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5729 1.664 h = 0.0001 0.005 y1[1] (numeric) = 1.06405448572 -0.368781408106 y1[1] (closed_form) = 2.29821282877 -1.37984525107 absolute error = 1.595 relative error = 59.52 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.48250268102 2.13907070679 absolute error = 2.411 relative error = 92.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13420.6MB, alloc=44.3MB, time=185.47 x[1] = 0.573 1.669 h = 0.0001 0.003 y1[1] (numeric) = 1.06452536979 -0.369789542642 y1[1] (closed_form) = 2.30878800099 -1.38749009538 absolute error = 1.607 relative error = 59.68 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.48965135359 2.150449819 absolute error = 2.424 relative error = 92.66 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13470.3MB, alloc=44.3MB, time=186.13 x[1] = 0.5731 1.672 h = 0.001 0.001 y1[1] (numeric) = 1.06479991369 -0.370398350167 y1[1] (closed_form) = 2.31510035605 -1.39218103148 absolute error = 1.615 relative error = 59.77 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.49405205106 2.15724666311 absolute error = 2.432 relative error = 92.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5741 1.673 h = 0.001 0.003 y1[1] (numeric) = 1.06469842027 -0.370696183757 y1[1] (closed_form) = 2.31576215727 -1.39583464551 absolute error = 1.617 relative error = 59.82 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.49776149001 2.15816808714 absolute error = 2.435 relative error = 92.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13519.9MB, alloc=44.3MB, time=186.78 x[1] = 0.5751 1.676 h = 0.0001 0.004 y1[1] (numeric) = 1.06479326702 -0.371393344357 y1[1] (closed_form) = 2.32074397556 -1.40249864255 absolute error = 1.625 relative error = 59.93 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.50427723588 2.16372367925 absolute error = 2.443 relative error = 92.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5752 1.68 h = 0.003 0.006 y1[1] (numeric) = 1.065165981 -0.372201815388 y1[1] (closed_form) = 2.32926645776 -1.4087442829 absolute error = 1.635 relative error = 60.05 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.51013221384 2.17288312616 absolute error = 2.454 relative error = 92.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13569.4MB, alloc=44.3MB, time=187.44 x[1] = 0.5782 1.686 h = 0.0001 0.005 y1[1] (numeric) = 1.06515601099 -0.373694306672 y1[1] (closed_form) = 2.33777939221 -1.42438479171 absolute error = 1.65 relative error = 60.28 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.52563210571 2.18263459465 absolute error = 2.47 relative error = 92.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13619.1MB, alloc=44.3MB, time=188.10 x[1] = 0.5783 1.691 h = 0.0001 0.003 y1[1] (numeric) = 1.06562689506 -0.374702441208 y1[1] (closed_form) = 2.34856854391 -1.43225021679 absolute error = 1.663 relative error = 60.44 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.53300799431 2.19420760926 absolute error = 2.484 relative error = 92.81 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5784 1.694 h = 0.001 0.001 y1[1] (numeric) = 1.06590143896 -0.375311248733 y1[1] (closed_form) = 2.35500800223 -1.43707581194 absolute error = 1.67 relative error = 60.54 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.53754715843 2.20111950282 absolute error = 2.492 relative error = 92.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13668.8MB, alloc=44.3MB, time=188.76 x[1] = 0.5794 1.695 h = 0.0001 0.004 y1[1] (numeric) = 1.06579994554 -0.375609082323 y1[1] (closed_form) = 2.35567013625 -1.44081683383 absolute error = 1.673 relative error = 60.58 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.54134144367 2.2020358962 absolute error = 2.495 relative error = 92.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13718.3MB, alloc=44.3MB, time=189.42 x[1] = 0.5795 1.699 h = 0.003 0.006 y1[1] (numeric) = 1.06617265952 -0.376417553353 y1[1] (closed_form) = 2.36434242519 -1.44721488298 absolute error = 1.683 relative error = 60.71 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.5473534991 2.21133150775 absolute error = 2.506 relative error = 92.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5825 1.705 h = 0.0001 0.005 y1[1] (numeric) = 1.06616268951 -0.377910044638 y1[1] (closed_form) = 2.37297416562 -1.46319521761 absolute error = 1.699 relative error = 60.93 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.56319063912 2.22117786773 absolute error = 2.523 relative error = 92.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13767.8MB, alloc=44.3MB, time=190.08 x[1] = 0.5826 1.71 h = 0.0001 0.003 y1[1] (numeric) = 1.06663357358 -0.378918179174 y1[1] (closed_form) = 2.38395269894 -1.47125279305 absolute error = 1.711 relative error = 61.09 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.57076458873 2.23292343867 absolute error = 2.537 relative error = 92.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13817.5MB, alloc=44.3MB, time=190.74 x[1] = 0.5827 1.713 h = 0.001 0.001 y1[1] (numeric) = 1.06690811748 -0.379526986699 y1[1] (closed_form) = 2.3905046766 -1.47619571568 absolute error = 1.719 relative error = 61.18 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.57542448052 2.23993774728 absolute error = 2.546 relative error = 92.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5837 1.714 h = 0.001 0.003 y1[1] (numeric) = 1.06680662406 -0.379824820288 y1[1] (closed_form) = 2.3911677124 -1.48001346864 absolute error = 1.722 relative error = 61.22 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.57929342116 2.24085047953 absolute error = 2.548 relative error = 92.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13867.1MB, alloc=44.3MB, time=191.40 x[1] = 0.5847 1.717 h = 0.0001 0.004 y1[1] (numeric) = 1.06690147081 -0.380521980889 y1[1] (closed_form) = 2.39631609492 -1.4870053074 absolute error = 1.73 relative error = 61.33 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.58613768382 2.24654819548 absolute error = 2.557 relative error = 92.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5848 1.721 h = 0.003 0.006 y1[1] (numeric) = 1.06727418479 -0.381330451919 y1[1] (closed_form) = 2.40516226036 -1.49358737879 absolute error = 1.74 relative error = 61.45 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.59233893421 2.25600211037 absolute error = 2.568 relative error = 93.01 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13916.7MB, alloc=44.3MB, time=192.05 x[1] = 0.5878 1.727 h = 0.0001 0.005 y1[1] (numeric) = 1.06726421478 -0.382822943204 y1[1] (closed_form) = 2.41392678264 -1.50997300124 absolute error = 1.756 relative error = 61.68 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.60857818252 2.26595406325 absolute error = 2.585 relative error = 93.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=13966.1MB, alloc=44.3MB, time=192.72 x[1] = 0.5879 1.732 h = 0.0001 0.003 y1[1] (numeric) = 1.06773509885 -0.38383107774 y1[1] (closed_form) = 2.42512514737 -1.51826259798 absolute error = 1.769 relative error = 61.83 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.61639070685 2.27790025707 absolute error = 2.6 relative error = 93.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.588 1.735 h = 0.001 0.001 y1[1] (numeric) = 1.06800964275 -0.384439885265 y1[1] (closed_form) = 2.43180766402 -1.52334712053 absolute error = 1.777 relative error = 61.92 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.62119596411 2.2850335707 absolute error = 2.608 relative error = 93.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14015.8MB, alloc=44.3MB, time=193.38 x[1] = 0.589 1.736 h = 0.001 0.003 y1[1] (numeric) = 1.06790814933 -0.384737718854 y1[1] (closed_form) = 2.43246997698 -1.5272557821 absolute error = 1.78 relative error = 61.96 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.62515340423 2.28594040873 absolute error = 2.611 relative error = 93.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14065.4MB, alloc=44.3MB, time=194.04 x[1] = 0.59 1.739 h = 0.0001 0.004 y1[1] (numeric) = 1.06800299607 -0.385434879455 y1[1] (closed_form) = 2.43770779273 -1.53443060394 absolute error = 1.788 relative error = 62.07 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.63218101513 2.29171483185 absolute error = 2.62 relative error = 93.12 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5901 1.743 h = 0.003 0.006 y1[1] (numeric) = 1.06837571006 -0.386243350485 y1[1] (closed_form) = 2.44673033277 -1.54120176157 absolute error = 1.798 relative error = 62.19 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.6385764926 2.3013299141 absolute error = 2.631 relative error = 93.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14114.9MB, alloc=44.3MB, time=194.70 x[1] = 0.5931 1.749 h = 0.0001 0.005 y1[1] (numeric) = 1.06836574005 -0.38773584177 y1[1] (closed_form) = 2.45562781142 -1.55800218647 absolute error = 1.815 relative error = 62.41 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.65522757402 2.31138820993 absolute error = 2.649 relative error = 93.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14164.6MB, alloc=44.3MB, time=195.36 x[1] = 0.5932 1.754 h = 0.0001 0.003 y1[1] (numeric) = 1.06883662411 -0.388743976306 y1[1] (closed_form) = 2.46704917987 -1.56653019558 absolute error = 1.828 relative error = 62.56 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.66328502103 2.32353865116 absolute error = 2.664 relative error = 93.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5933 1.757 h = 0.001 0.001 y1[1] (numeric) = 1.06911116802 -0.389352783831 y1[1] (closed_form) = 2.47386409643 -1.57176019469 absolute error = 1.836 relative error = 62.65 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.66823949821 2.33079310137 absolute error = 2.672 relative error = 93.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14214.2MB, alloc=44.3MB, time=196.02 x[1] = 0.5943 1.758 h = 0.001 0.003 y1[1] (numeric) = 1.06900967459 -0.38965061742 y1[1] (closed_form) = 2.47452507694 -1.57576170138 absolute error = 1.839 relative error = 62.69 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.67228745359 2.33169353568 absolute error = 2.675 relative error = 93.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5953 1.761 h = 0.0001 0.004 y1[1] (numeric) = 1.06910452134 -0.390347778021 y1[1] (closed_form) = 2.47985304066 -1.58312399903 absolute error = 1.847 relative error = 62.79 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.67950296347 2.33754565971 absolute error = 2.684 relative error = 93.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14263.8MB, alloc=44.3MB, time=196.68 x[1] = 0.5954 1.765 h = 0.003 0.006 y1[1] (numeric) = 1.06947723532 -0.391156249051 y1[1] (closed_form) = 2.48905448974 -1.59008943424 absolute error = 1.858 relative error = 62.91 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.68609782627 2.34732480151 absolute error = 2.696 relative error = 93.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14313.3MB, alloc=44.3MB, time=197.33 x[1] = 0.5984 1.771 h = 0.0001 0.005 y1[1] (numeric) = 1.06946726531 -0.392648740336 y1[1] (closed_form) = 2.49808506317 -1.60731439632 absolute error = 1.875 relative error = 63.13 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.70317067818 2.35749014277 absolute error = 2.714 relative error = 93.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.5985 1.776 h = 0.0001 0.003 y1[1] (numeric) = 1.06993814938 -0.393656874872 y1[1] (closed_form) = 2.50973265372 -1.61608736959 absolute error = 1.889 relative error = 63.27 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.71147955515 2.36984849193 absolute error = 2.729 relative error = 93.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14362.8MB, alloc=44.3MB, time=197.99 x[1] = 0.5986 1.779 h = 0.001 0.001 y1[1] (numeric) = 1.07021269328 -0.394265682397 y1[1] (closed_form) = 2.51668185753 -1.62146681909 absolute error = 1.897 relative error = 63.36 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.71658720296 2.37722623072 absolute error = 2.738 relative error = 93.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14412.4MB, alloc=44.3MB, time=198.65 x[1] = 0.5996 1.78 h = 0.001 0.003 y1[1] (numeric) = 1.07011119986 -0.394563515986 y1[1] (closed_form) = 2.51734087373 -1.62556314942 absolute error = 1.9 relative error = 63.4 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.72072772916 2.37811972779 absolute error = 2.741 relative error = 93.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6006 1.783 h = 0.0001 0.004 y1[1] (numeric) = 1.07020604661 -0.395260676587 y1[1] (closed_form) = 2.52275969753 -1.63311752209 absolute error = 1.908 relative error = 63.5 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.72813579255 2.38405053806 absolute error = 2.75 relative error = 93.39 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14461.9MB, alloc=44.3MB, time=199.31 x[1] = 0.6007 1.787 h = 0.003 0.006 y1[1] (numeric) = 1.07057876059 -0.396069147617 y1[1] (closed_form) = 2.53214262635 -1.64028255652 absolute error = 1.919 relative error = 63.62 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.7349353281 2.3939966599 absolute error = 2.762 relative error = 93.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14511.5MB, alloc=44.3MB, time=199.97 x[1] = 0.6037 1.793 h = 0.0001 0.005 y1[1] (numeric) = 1.07056879058 -0.397561638902 y1[1] (closed_form) = 2.54130639463 -1.65794201514 absolute error = 1.937 relative error = 63.83 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.75244010514 2.40426969951 absolute error = 2.78 relative error = 93.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6038 1.798 h = 0.0001 0.003 y1[1] (numeric) = 1.07103967465 -0.398569773438 y1[1] (closed_form) = 2.55318347168 -1.66696666879 absolute error = 1.951 relative error = 63.98 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.76100708246 2.41683965328 absolute error = 2.795 relative error = 93.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14561.2MB, alloc=44.3MB, time=200.63 x[1] = 0.6039 1.801 h = 0.001 0.001 y1[1] (numeric) = 1.07131421855 -0.399178580963 y1[1] (closed_form) = 2.56026887645 -1.67249964196 absolute error = 1.959 relative error = 64.06 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.76627195022 2.42434285313 absolute error = 2.805 relative error = 93.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6049 1.802 h = 0.0001 0.004 y1[1] (numeric) = 1.07121272513 -0.399476414552 y1[1] (closed_form) = 2.56092527346 -1.67669281725 absolute error = 1.962 relative error = 64.11 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.77050714338 2.42522885468 absolute error = 2.808 relative error = 93.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14610.6MB, alloc=44.3MB, time=201.29 x[1] = 0.605 1.806 h = 0.003 0.006 y1[1] (numeric) = 1.07158543911 -0.400284885583 y1[1] (closed_form) = 2.57046896651 -1.68403181905 absolute error = 1.973 relative error = 64.22 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.77748515239 2.43532359394 absolute error = 2.82 relative error = 93.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14660.2MB, alloc=44.3MB, time=201.95 x[1] = 0.608 1.812 h = 0.0001 0.005 y1[1] (numeric) = 1.0715754691 -0.401777376868 y1[1] (closed_form) = 2.57975277511 -1.70207184033 absolute error = 1.991 relative error = 64.43 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.79536872463 2.44569513399 absolute error = 2.839 relative error = 93.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6081 1.817 h = 0.0001 0.003 y1[1] (numeric) = 1.07204635317 -0.402785511404 y1[1] (closed_form) = 2.5918331456 -1.7113158512 absolute error = 2.005 relative error = 64.57 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.80416075378 2.45845340357 absolute error = 2.854 relative error = 93.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14709.7MB, alloc=44.3MB, time=202.61 x[1] = 0.6082 1.82 h = 0.001 0.001 y1[1] (numeric) = 1.07232089707 -0.403394318928 y1[1] (closed_form) = 2.59903923685 -1.71698265792 absolute error = 2.014 relative error = 64.66 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.80956274074 2.46606829178 absolute error = 2.863 relative error = 93.61 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14759.3MB, alloc=44.3MB, time=203.27 x[1] = 0.6092 1.821 h = 0.001 0.003 y1[1] (numeric) = 1.07221940365 -0.403692152518 y1[1] (closed_form) = 2.59969402399 -1.72126088821 absolute error = 2.017 relative error = 64.7 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.81388122899 2.46694853736 absolute error = 2.866 relative error = 93.61 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6102 1.824 h = 0.0001 0.004 y1[1] (numeric) = 1.07231425039 -0.404389313118 y1[1] (closed_form) = 2.6052862229 -1.72918418071 absolute error = 2.026 relative error = 64.8 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.82165937849 2.47303078503 absolute error = 2.876 relative error = 93.63 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14808.9MB, alloc=44.3MB, time=203.93 x[1] = 0.6103 1.828 h = 0.003 0.006 y1[1] (numeric) = 1.07268696438 -0.405197784149 y1[1] (closed_form) = 2.61501634259 -1.73673300963 absolute error = 2.038 relative error = 64.91 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.82885221773 2.4832980811 absolute error = 2.888 relative error = 93.66 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14858.4MB, alloc=44.3MB, time=204.59 x[1] = 0.6133 1.834 h = 0.0001 0.005 y1[1] (numeric) = 1.07267699437 -0.406690275434 y1[1] (closed_form) = 2.62443354757 -1.75522667293 absolute error = 2.056 relative error = 65.11 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.84718719892 2.49377852267 absolute error = 2.907 relative error = 93.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6134 1.839 h = 0.0001 0.003 y1[1] (numeric) = 1.07314787843 -0.40769840997 y1[1] (closed_form) = 2.6367496858 -1.76473527215 absolute error = 2.07 relative error = 65.25 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.85625014299 2.50675545639 absolute error = 2.923 relative error = 93.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14908.0MB, alloc=44.3MB, time=205.25 x[1] = 0.6135 1.842 h = 0.001 0.001 y1[1] (numeric) = 1.07342242234 -0.408307217494 y1[1] (closed_form) = 2.64409566034 -1.7705634311 absolute error = 2.079 relative error = 65.34 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.86181712876 2.51449995395 absolute error = 2.933 relative error = 93.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6145 1.843 h = 0.001 0.003 y1[1] (numeric) = 1.07332092891 -0.408605051084 y1[1] (closed_form) = 2.64474657114 -1.77494239249 absolute error = 2.082 relative error = 65.38 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.86623430264 2.51537162289 absolute error = 2.936 relative error = 93.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=14957.6MB, alloc=44.3MB, time=205.91 x[1] = 0.6155 1.846 h = 0.0001 0.004 y1[1] (numeric) = 1.07341577566 -0.409302211684 y1[1] (closed_form) = 2.65043170532 -1.78307151754 absolute error = 2.091 relative error = 65.47 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.87421890424 2.52153538323 absolute error = 2.946 relative error = 93.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15007.1MB, alloc=44.3MB, time=206.57 x[1] = 0.6156 1.85 h = 0.003 0.006 y1[1] (numeric) = 1.07378848965 -0.410110682715 y1[1] (closed_form) = 2.66035092731 -1.79083588452 absolute error = 2.103 relative error = 65.58 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.8816322476 2.53197823971 absolute error = 2.958 relative error = 93.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6186 1.856 h = 0.0001 0.005 y1[1] (numeric) = 1.07377851963 -0.411603174 y1[1] (closed_form) = 2.66990150913 -1.80979381777 absolute error = 2.122 relative error = 65.79 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.9004294413 2.54256808503 absolute error = 2.978 relative error = 93.81 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15056.6MB, alloc=44.3MB, time=207.22 x[1] = 0.6187 1.861 h = 0.0001 0.003 y1[1] (numeric) = 1.0742494037 -0.412611308536 y1[1] (closed_form) = 2.68245681274 -1.81957421288 absolute error = 2.137 relative error = 65.92 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.90977045874 2.55576748572 absolute error = 2.994 relative error = 93.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15106.2MB, alloc=44.3MB, time=207.88 x[1] = 0.6188 1.864 h = 0.001 0.001 y1[1] (numeric) = 1.0745239476 -0.41322011606 y1[1] (closed_form) = 2.68994466053 -1.82556809445 absolute error = 2.146 relative error = 66 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.91550678758 2.5636438252 absolute error = 3.004 relative error = 93.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6198 1.865 h = 0.001 0.003 y1[1] (numeric) = 1.07442245418 -0.41351794965 y1[1] (closed_form) = 2.69059097051 -1.83004993523 absolute error = 2.149 relative error = 66.04 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.92002486427 2.56450628475 absolute error = 3.007 relative error = 93.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15155.7MB, alloc=44.3MB, time=208.54 x[1] = 0.6208 1.868 h = 0.0001 0.004 y1[1] (numeric) = 1.07451730093 -0.41421511025 y1[1] (closed_form) = 2.69636973608 -1.83838992496 absolute error = 2.158 relative error = 66.14 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.92822099582 2.57075250582 absolute error = 3.017 relative error = 93.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15205.1MB, alloc=44.3MB, time=209.20 x[1] = 0.6209 1.872 h = 0.003 0.006 y1[1] (numeric) = 1.07489001491 -0.415023581281 y1[1] (closed_form) = 2.70648077198 -1.84637568328 absolute error = 2.17 relative error = 66.25 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.93586065868 2.58137395491 absolute error = 3.03 relative error = 93.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6239 1.878 h = 0.0001 0.005 y1[1] (numeric) = 1.0748800449 -0.416516072566 y1[1] (closed_form) = 2.71616466365 -1.8658087572 absolute error = 2.19 relative error = 66.45 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.95513110469 2.59207364829 absolute error = 3.05 relative error = 93.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15254.6MB, alloc=44.3MB, time=209.86 x[1] = 0.624 1.883 h = 0.0001 0.003 y1[1] (numeric) = 1.07535092897 -0.417524207102 y1[1] (closed_form) = 2.72896257592 -1.87586833543 absolute error = 2.205 relative error = 66.58 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.96475753262 2.60549935538 absolute error = 3.066 relative error = 93.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6241 1.886 h = 0.001 0.001 y1[1] (numeric) = 1.07562547287 -0.418133014626 y1[1] (closed_form) = 2.73659431297 -1.88203241867 absolute error = 2.214 relative error = 66.66 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.97066765677 2.61350978997 absolute error = 3.076 relative error = 93.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15304.3MB, alloc=44.3MB, time=210.52 x[1] = 0.6251 1.887 h = 0.001 0.003 y1[1] (numeric) = 1.07552397945 -0.418430848216 y1[1] (closed_form) = 2.73723527154 -1.88661933292 absolute error = 2.217 relative error = 66.7 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.97528889729 2.61436237966 absolute error = 3.08 relative error = 93.99 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15353.9MB, alloc=44.3MB, time=211.18 x[1] = 0.6261 1.89 h = 0.0001 0.004 y1[1] (numeric) = 1.07561882619 -0.419128008816 y1[1] (closed_form) = 2.74310835814 -1.89517533745 absolute error = 2.227 relative error = 66.79 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.98370175234 2.62069199775 absolute error = 3.09 relative error = 94 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6262 1.894 h = 0.003 0.006 y1[1] (numeric) = 1.07599154018 -0.419936479847 y1[1] (closed_form) = 2.75341395538 -1.90338848606 absolute error = 2.239 relative error = 66.9 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 1.9915736949 2.63149510032 absolute error = 3.103 relative error = 94.03 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15403.4MB, alloc=44.3MB, time=211.84 x[1] = 0.6292 1.9 h = 0.0001 0.005 y1[1] (numeric) = 1.07598157017 -0.421428971132 y1[1] (closed_form) = 2.76323103987 -1.92330781909 absolute error = 2.259 relative error = 67.09 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.01132867442 2.64230502579 absolute error = 3.123 relative error = 94.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15452.9MB, alloc=44.3MB, time=212.50 x[1] = 0.6293 1.905 h = 0.0001 0.003 y1[1] (numeric) = 1.07645245423 -0.422437105668 y1[1] (closed_form) = 2.77627504959 -1.93365415152 absolute error = 2.274 relative error = 67.23 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.02124803286 2.6559609153 absolute error = 3.14 relative error = 94.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6294 1.908 h = 0.001 0.001 y1[1] (numeric) = 1.07672699814 -0.423045913192 y1[1] (closed_form) = 2.7840527178 -1.93999302664 absolute error = 2.284 relative error = 67.31 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.02733651505 2.6641077188 absolute error = 3.15 relative error = 94.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15502.6MB, alloc=44.3MB, time=213.16 x[1] = 0.6304 1.909 h = 0.0001 0.004 y1[1] (numeric) = 1.07662550471 -0.423343746782 y1[1] (closed_form) = 2.78468754745 -1.94468725514 absolute error = 2.287 relative error = 67.34 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.03206322518 2.66494974958 absolute error = 3.154 relative error = 94.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15552.1MB, alloc=44.3MB, time=213.82 x[1] = 0.6305 1.913 h = 0.003 0.006 y1[1] (numeric) = 1.0769982187 -0.424152217812 y1[1] (closed_form) = 2.7951656526 -1.95309868845 absolute error = 2.3 relative error = 67.45 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.04013777824 2.67591455261 absolute error = 3.167 relative error = 94.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6335 1.919 h = 0.0001 0.005 y1[1] (numeric) = 1.07698824869 -0.425644709097 y1[1] (closed_form) = 2.80510322842 -1.97344408959 absolute error = 2.32 relative error = 67.64 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.06031773176 2.68682558107 absolute error = 3.188 relative error = 94.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15601.6MB, alloc=44.3MB, time=214.48 x[1] = 0.6336 1.924 h = 0.0001 0.003 y1[1] (numeric) = 1.07745913276 -0.426652843633 y1[1] (closed_form) = 2.81836544099 -1.98404046783 absolute error = 2.336 relative error = 67.77 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.07049259424 2.7006863505 absolute error = 3.205 relative error = 94.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6337 1.927 h = 0.001 0.001 y1[1] (numeric) = 1.07773367666 -0.427261651158 y1[1] (closed_form) = 2.82627253532 -1.99053178853 absolute error = 2.345 relative error = 67.85 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.07673667943 2.70895457297 absolute error = 3.216 relative error = 94.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15651.3MB, alloc=44.3MB, time=215.14 x[1] = 0.6347 1.928 h = 0.001 0.003 y1[1] (numeric) = 1.07763218323 -0.427559484747 y1[1] (closed_form) = 2.82690276108 -1.99532030627 absolute error = 2.349 relative error = 67.89 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.08155619299 2.70978823537 absolute error = 3.219 relative error = 94.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15700.8MB, alloc=44.3MB, time=215.80 x[1] = 0.6357 1.931 h = 0.0001 0.004 y1[1] (numeric) = 1.07772702998 -0.428256645348 y1[1] (closed_form) = 2.83295589035 -2.00429124307 absolute error = 2.359 relative error = 67.98 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.09038553051 2.71627821766 absolute error = 3.229 relative error = 94.22 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6358 1.935 h = 0.003 0.006 y1[1] (numeric) = 1.07809974397 -0.429065116378 y1[1] (closed_form) = 2.84363383971 -2.01294159496 absolute error = 2.372 relative error = 68.08 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.09870381384 2.72743052118 absolute error = 3.243 relative error = 94.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15750.4MB, alloc=44.3MB, time=216.45 x[1] = 0.6388 1.941 h = 0.0001 0.005 y1[1] (numeric) = 1.07808977395 -0.430557607663 y1[1] (closed_form) = 2.85370438793 -2.0337946236 absolute error = 2.392 relative error = 68.27 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.11938995023 2.73845246879 absolute error = 3.264 relative error = 94.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15800.1MB, alloc=44.3MB, time=217.13 x[1] = 0.6389 1.946 h = 0.0001 0.003 y1[1] (numeric) = 1.07856065802 -0.431565742199 y1[1] (closed_form) = 2.86721940582 -2.0446923053 absolute error = 2.409 relative error = 68.4 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.12987219074 2.75255082544 absolute error = 3.282 relative error = 94.3 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.639 1.949 h = 0.001 0.001 y1[1] (numeric) = 1.07883520192 -0.432174549724 y1[1] (closed_form) = 2.87527635722 -2.05136723881 absolute error = 2.418 relative error = 68.47 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.1363033996 2.76095976013 absolute error = 3.293 relative error = 94.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15849.7MB, alloc=44.3MB, time=217.79 x[1] = 0.64 1.95 h = 0.001 0.003 y1[1] (numeric) = 1.0787337085 -0.432472383313 y1[1] (closed_form) = 2.87589896058 -2.05626737746 absolute error = 2.422 relative error = 68.51 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.14123280443 2.7617815313 absolute error = 3.296 relative error = 94.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.641 1.953 h = 0.0001 0.004 y1[1] (numeric) = 1.07882855525 -0.433169543914 y1[1] (closed_form) = 2.88204840617 -2.06546972857 absolute error = 2.432 relative error = 68.6 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.15029437445 2.76835758395 absolute error = 3.307 relative error = 94.34 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15899.4MB, alloc=44.3MB, time=218.45 x[1] = 0.6411 1.957 h = 0.003 0.006 y1[1] (numeric) = 1.07920126923 -0.433978014944 y1[1] (closed_form) = 2.89292905064 -2.07436543321 absolute error = 2.446 relative error = 68.7 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.15886278147 2.77970053256 absolute error = 3.321 relative error = 94.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15948.8MB, alloc=44.3MB, time=219.11 x[1] = 0.6441 1.963 h = 0.0001 0.005 y1[1] (numeric) = 1.07919129922 -0.435470506229 y1[1] (closed_form) = 2.90313229937 -2.09573794536 absolute error = 2.466 relative error = 68.88 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.18006710252 2.79083360011 absolute error = 3.343 relative error = 94.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6442 1.968 h = 0.0001 0.003 y1[1] (numeric) = 1.07966218329 -0.436478640765 y1[1] (closed_form) = 2.91690374285 -2.10694505096 absolute error = 2.483 relative error = 69.01 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.19086478813 2.8051735271 absolute error = 3.36 relative error = 94.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=15998.3MB, alloc=44.3MB, time=219.77 x[1] = 0.6443 1.971 h = 0.001 0.001 y1[1] (numeric) = 1.07993672719 -0.43708744829 y1[1] (closed_form) = 2.92511266795 -2.11380851956 absolute error = 2.493 relative error = 69.08 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.19748801392 2.81372550796 absolute error = 3.371 relative error = 94.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16048.0MB, alloc=44.3MB, time=220.43 x[1] = 0.6453 1.972 h = 0.001 0.003 y1[1] (numeric) = 1.07983523377 -0.437385281879 y1[1] (closed_form) = 2.92572678997 -2.1188226584 absolute error = 2.497 relative error = 69.12 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.2025297491 2.81453461294 absolute error = 3.375 relative error = 94.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6463 1.975 h = 0.0001 0.004 y1[1] (numeric) = 1.07993008051 -0.43808244248 y1[1] (closed_form) = 2.93197320939 -2.12826205355 absolute error = 2.507 relative error = 69.21 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.21182921664 2.82119762079 absolute error = 3.386 relative error = 94.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16097.6MB, alloc=44.3MB, time=221.09 x[1] = 0.6464 1.979 h = 0.003 0.006 y1[1] (numeric) = 1.0803027945 -0.43889091351 y1[1] (closed_form) = 2.94305943507 -2.13740970426 absolute error = 2.521 relative error = 69.31 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.22065429926 2.83273438771 absolute error = 3.4 relative error = 94.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16147.0MB, alloc=44.3MB, time=221.75 x[1] = 0.6494 1.985 h = 0.0001 0.005 y1[1] (numeric) = 1.08029282449 -0.440383404795 y1[1] (closed_form) = 2.95339505175 -2.15931382371 absolute error = 2.542 relative error = 69.49 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.24238906894 2.84397870578 absolute error = 3.422 relative error = 94.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6495 1.99 h = 0.0001 0.003 y1[1] (numeric) = 1.08076370856 -0.441391539331 y1[1] (closed_form) = 2.96742658584 -2.17083867453 absolute error = 2.559 relative error = 69.61 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.25351046689 2.8585642228 absolute error = 3.441 relative error = 94.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16196.5MB, alloc=44.3MB, time=222.40 x[1] = 0.6496 1.993 h = 0.001 0.001 y1[1] (numeric) = 1.08103825246 -0.442000346856 y1[1] (closed_form) = 2.97578962661 -2.1778957219 absolute error = 2.57 relative error = 69.68 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.26033072375 2.86726160423 absolute error = 3.452 relative error = 94.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6506 1.994 h = 0.001 0.003 y1[1] (numeric) = 1.08093675903 -0.442298180445 y1[1] (closed_form) = 2.97639437788 -2.18302629022 absolute error = 2.573 relative error = 69.72 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.26548727662 2.86805723608 absolute error = 3.455 relative error = 94.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16246.2MB, alloc=44.3MB, time=223.06 x[1] = 0.6516 1.997 h = 0.0001 0.004 y1[1] (numeric) = 1.08103160578 -0.442995341046 y1[1] (closed_form) = 2.98273841759 -2.19270848981 absolute error = 2.584 relative error = 69.81 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.27503043545 2.87480806816 absolute error = 3.467 relative error = 94.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16295.8MB, alloc=44.3MB, time=223.72 x[1] = 0.6517 2.001 h = 0.003 0.006 y1[1] (numeric) = 1.08140431977 -0.443803812076 y1[1] (closed_form) = 2.99403314555 -2.20211484271 absolute error = 2.598 relative error = 69.9 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.2841189078 2.88654185509 absolute error = 3.481 relative error = 94.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6547 2.007 h = 0.0001 0.005 y1[1] (numeric) = 1.08139434975 -0.445296303361 y1[1] (closed_form) = 3.004500734 -2.2245629665 absolute error = 2.62 relative error = 70.08 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.30639665786 2.89789748129 absolute error = 3.504 relative error = 94.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16345.5MB, alloc=44.3MB, time=224.38 x[1] = 0.6548 2.012 h = 0.0001 0.003 y1[1] (numeric) = 1.08186523382 -0.446304437897 y1[1] (closed_form) = 3.01879606819 -2.23641408938 absolute error = 2.637 relative error = 70.2 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.31785024025 2.91273264451 absolute error = 3.523 relative error = 94.63 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16395.2MB, alloc=44.3MB, time=225.05 x[1] = 0.6549 2.015 h = 0.001 0.001 y1[1] (numeric) = 1.08213977772 -0.446913245422 y1[1] (closed_form) = 3.02731539169 -2.2436698834 absolute error = 2.648 relative error = 70.27 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.32487266608 2.92157780122 absolute error = 3.534 relative error = 94.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6559 2.016 h = 0.0001 0.004 y1[1] (numeric) = 1.0820382843 -0.447211079011 y1[1] (closed_form) = 3.02790985141 -2.24891936138 absolute error = 2.652 relative error = 70.31 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.33014657319 2.9223591201 absolute error = 3.538 relative error = 94.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16444.8MB, alloc=44.3MB, time=225.70 x[1] = 0.656 2.02 h = 0.003 0.006 y1[1] (numeric) = 1.08241099829 -0.448019550042 y1[1] (closed_form) = 3.03938961108 -2.25855140203 absolute error = 2.666 relative error = 70.41 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.33946486648 2.93426833024 absolute error = 3.553 relative error = 94.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16494.3MB, alloc=44.3MB, time=226.36 x[1] = 0.659 2.026 h = 0.0001 0.005 y1[1] (numeric) = 1.08240102827 -0.449512041327 y1[1] (closed_form) = 3.04997711465 -2.28147636217 absolute error = 2.688 relative error = 70.58 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.36221891429 2.94572643125 absolute error = 3.576 relative error = 94.7 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6591 2.031 h = 0.0001 0.003 y1[1] (numeric) = 1.08287191234 -0.450520175863 y1[1] (closed_form) = 3.06450655206 -2.29361211432 absolute error = 2.706 relative error = 70.7 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.37396233396 2.96078385562 absolute error = 3.595 relative error = 94.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16543.8MB, alloc=44.3MB, time=227.02 x[1] = 0.6592 2.034 h = 0.001 0.001 y1[1] (numeric) = 1.08314645624 -0.451128983388 y1[1] (closed_form) = 3.07316460649 -2.30104132084 absolute error = 2.717 relative error = 70.77 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.38116119183 2.96976062332 absolute error = 3.606 relative error = 94.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6602 2.035 h = 0.001 0.003 y1[1] (numeric) = 1.08304496282 -0.451426816977 y1[1] (closed_form) = 3.07375090309 -2.30639531601 absolute error = 2.721 relative error = 70.81 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.38653836777 2.97053036365 absolute error = 3.61 relative error = 94.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16593.5MB, alloc=44.3MB, time=227.68 x[1] = 0.6612 2.038 h = 0.0001 0.004 y1[1] (numeric) = 1.08313980957 -0.452123977577 y1[1] (closed_form) = 3.0802813302 -2.31654392836 absolute error = 2.732 relative error = 70.89 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.39654978262 2.97744994277 absolute error = 3.622 relative error = 94.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16643.0MB, alloc=44.3MB, time=228.33 x[1] = 0.6613 2.042 h = 0.003 0.006 y1[1] (numeric) = 1.08351252355 -0.452932448608 y1[1] (closed_form) = 3.09197520503 -2.32644765329 absolute error = 2.747 relative error = 70.98 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.40614436502 2.98956229076 absolute error = 3.637 relative error = 94.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6643 2.048 h = 0.0001 0.005 y1[1] (numeric) = 1.08350255354 -0.454424939893 y1[1] (closed_form) = 3.10269391883 -2.34994043879 absolute error = 2.769 relative error = 71.16 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.4294654458 3.00113175993 absolute error = 3.66 relative error = 94.8 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16692.5MB, alloc=44.3MB, time=228.99 x[1] = 0.6644 2.053 h = 0.0001 0.003 y1[1] (numeric) = 1.08397343761 -0.455433074429 y1[1] (closed_form) = 3.11749428376 -2.36241884741 absolute error = 2.788 relative error = 71.27 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.44155732697 3.01644658158 absolute error = 3.68 relative error = 94.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16742.0MB, alloc=44.3MB, time=229.65 x[1] = 0.6645 2.056 h = 0.001 0.001 y1[1] (numeric) = 1.08424798151 -0.456041881954 y1[1] (closed_form) = 3.12631278463 -2.37005673069 absolute error = 2.799 relative error = 71.34 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.44896822468 3.02557566194 absolute error = 3.692 relative error = 94.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6655 2.057 h = 0.001 0.003 y1[1] (numeric) = 1.08414648809 -0.456339715543 y1[1] (closed_form) = 3.12688702018 -2.37553440108 absolute error = 2.803 relative error = 71.38 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.45446762002 3.02632946719 absolute error = 3.696 relative error = 94.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16791.4MB, alloc=44.3MB, time=230.31 x[1] = 0.6665 2.06 h = 0.0001 0.004 y1[1] (numeric) = 1.08424133484 -0.457036876143 y1[1] (closed_form) = 3.13351692035 -2.3859430367 absolute error = 2.814 relative error = 71.46 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.4647400278 3.03333933485 absolute error = 3.708 relative error = 94.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16841.0MB, alloc=44.3MB, time=230.96 x[1] = 0.6666 2.064 h = 0.003 0.006 y1[1] (numeric) = 1.08461404882 -0.457845347174 y1[1] (closed_form) = 3.14542793213 -2.39612568846 absolute error = 2.829 relative error = 71.55 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.47461809851 3.04565810536 absolute error = 3.723 relative error = 94.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6696 2.07 h = 0.0001 0.005 y1[1] (numeric) = 1.08460407881 -0.459337838459 y1[1] (closed_form) = 3.15627726413 -2.42019951 absolute error = 2.853 relative error = 71.72 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.49851954307 3.05733877857 absolute error = 3.747 relative error = 94.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16890.5MB, alloc=44.3MB, time=231.62 x[1] = 0.6697 2.075 h = 0.0001 0.003 y1[1] (numeric) = 1.08507496288 -0.460345972995 y1[1] (closed_form) = 3.17135239422 -2.43302971601 absolute error = 2.871 relative error = 71.83 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.5109689704 3.07291515986 absolute error = 3.767 relative error = 94.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6698 2.078 h = 0.001 0.001 y1[1] (numeric) = 1.08534950678 -0.46095478052 y1[1] (closed_form) = 3.18033358079 -2.44088181496 absolute error = 2.883 relative error = 71.9 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.51859741581 3.08219898667 absolute error = 3.779 relative error = 94.94 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16940.2MB, alloc=44.3MB, time=232.28 x[1] = 0.6708 2.079 h = 0.001 0.003 y1[1] (numeric) = 1.08524801336 -0.461252614109 y1[1] (closed_form) = 3.18089473961 -2.44648579188 absolute error = 2.887 relative error = 71.93 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.52422171366 3.08293591796 absolute error = 3.783 relative error = 94.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=16989.8MB, alloc=44.3MB, time=232.94 x[1] = 0.6718 2.082 h = 0.0001 0.004 y1[1] (numeric) = 1.0853428601 -0.461949774709 y1[1] (closed_form) = 3.18762470808 -2.45716074252 absolute error = 2.898 relative error = 72.01 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.5347614326 3.0900368744 absolute error = 3.795 relative error = 94.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6719 2.086 h = 0.003 0.006 y1[1] (numeric) = 1.08571557409 -0.46275824574 y1[1] (closed_form) = 3.19975591253 -2.46762974147 absolute error = 2.914 relative error = 72.1 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.54493036822 3.10256538011 absolute error = 3.811 relative error = 94.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17039.4MB, alloc=44.3MB, time=233.60 x[1] = 0.6749 2.092 h = 0.0001 0.005 y1[1] (numeric) = 1.08570560407 -0.464250737025 y1[1] (closed_form) = 3.21073519475 -2.49229810511 absolute error = 2.937 relative error = 72.27 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.56942579793 3.11435700861 absolute error = 3.836 relative error = 95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17088.9MB, alloc=44.3MB, time=234.26 x[1] = 0.675 2.097 h = 0.0001 0.003 y1[1] (numeric) = 1.08617648814 -0.465258871561 y1[1] (closed_form) = 3.22608897087 -2.50548947387 absolute error = 2.957 relative error = 72.38 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.58224208007 3.13019914772 absolute error = 3.856 relative error = 95.03 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6751 2.1 h = 0.001 0.001 y1[1] (numeric) = 1.08645103204 -0.465867679086 y1[1] (closed_form) = 3.23523510661 -2.51356146302 absolute error = 2.968 relative error = 72.45 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.59009371633 3.13964017461 absolute error = 3.868 relative error = 95.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17138.6MB, alloc=44.3MB, time=234.92 x[1] = 0.6761 2.101 h = 0.001 0.003 y1[1] (numeric) = 1.08634953862 -0.466165512675 y1[1] (closed_form) = 3.2357821376 -2.51929443233 absolute error = 2.972 relative error = 72.48 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.59584565278 3.14035925625 absolute error = 3.873 relative error = 95.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17188.2MB, alloc=44.3MB, time=235.58 x[1] = 0.6771 2.104 h = 0.0001 0.004 y1[1] (numeric) = 1.08644438537 -0.466862673275 y1[1] (closed_form) = 3.24261275313 -2.53024213448 absolute error = 2.984 relative error = 72.56 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.60665914427 3.14755208091 absolute error = 3.885 relative error = 95.06 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6772 2.108 h = 0.003 0.006 y1[1] (numeric) = 1.08681709935 -0.467671144306 y1[1] (closed_form) = 3.25496723959 -2.5410050829 absolute error = 3 relative error = 72.65 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.61712650291 3.16029366225 absolute error = 3.901 relative error = 95.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17237.7MB, alloc=44.3MB, time=236.24 x[1] = 0.6802 2.114 h = 0.0001 0.005 y1[1] (numeric) = 1.08680712934 -0.469163635591 y1[1] (closed_form) = 3.26607572463 -2.56628179607 absolute error = 3.024 relative error = 72.81 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.6422298358 3.17219590936 absolute error = 3.926 relative error = 95.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6803 2.119 h = 0.0001 0.003 y1[1] (numeric) = 1.08727801341 -0.470171770127 y1[1] (closed_form) = 3.28171207045 -2.57984392259 absolute error = 3.044 relative error = 72.92 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.65542251067 3.18830804011 absolute error = 3.947 relative error = 95.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17287.3MB, alloc=44.3MB, time=236.90 x[1] = 0.6804 2.122 h = 0.001 0.001 y1[1] (numeric) = 1.08755255731 -0.470780577652 y1[1] (closed_form) = 3.29102544278 -2.58814161519 absolute error = 3.056 relative error = 72.99 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.66350311932 3.19790874031 absolute error = 3.96 relative error = 95.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17336.9MB, alloc=44.3MB, time=237.55 x[1] = 0.6814 2.123 h = 0.0001 0.004 y1[1] (numeric) = 1.08745106389 -0.471078411241 y1[1] (closed_form) = 3.29155725831 -2.59400631826 absolute error = 3.06 relative error = 73.02 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.66938548452 3.19860895868 absolute error = 3.964 relative error = 95.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6815 2.127 h = 0.003 0.006 y1[1] (numeric) = 1.08782377787 -0.471886882271 y1[1] (closed_form) = 3.30411006594 -2.6050258078 absolute error = 3.076 relative error = 73.11 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.68011331698 3.2115403252 absolute error = 3.981 relative error = 95.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17386.4MB, alloc=44.3MB, time=238.21 x[1] = 0.6845 2.133 h = 0.0001 0.005 y1[1] (numeric) = 1.08781380786 -0.473379373556 y1[1] (closed_form) = 3.31533657891 -2.63083593381 absolute error = 3.101 relative error = 73.27 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.70574997848 3.22354492242 absolute error = 4.006 relative error = 95.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17436.1MB, alloc=44.3MB, time=238.87 x[1] = 0.6846 2.138 h = 0.0001 0.003 y1[1] (numeric) = 1.08828469193 -0.474387508092 y1[1] (closed_form) = 3.33122390201 -2.64472162856 absolute error = 3.121 relative error = 73.38 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.71927117089 3.23989751282 absolute error = 4.027 relative error = 95.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6847 2.141 h = 0.001 0.001 y1[1] (numeric) = 1.08855923583 -0.474996315617 y1[1] (closed_form) = 3.34068586119 -2.65321633288 absolute error = 3.133 relative error = 73.44 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.72755166663 3.24964047368 absolute error = 4.04 relative error = 95.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17485.8MB, alloc=44.3MB, time=239.53 x[1] = 0.6857 2.142 h = 0.001 0.003 y1[1] (numeric) = 1.08845774241 -0.475294149207 y1[1] (closed_form) = 3.34120529479 -2.65919686588 absolute error = 3.138 relative error = 73.48 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.73354881869 3.25032521366 absolute error = 4.044 relative error = 95.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17535.4MB, alloc=44.3MB, time=240.19 x[1] = 0.6867 2.145 h = 0.0001 0.004 y1[1] (numeric) = 1.08855258916 -0.475991309807 y1[1] (closed_form) = 3.34822810674 -2.67066852026 absolute error = 3.15 relative error = 73.55 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.74488832222 3.25769443183 absolute error = 4.057 relative error = 95.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6868 2.149 h = 0.003 0.006 y1[1] (numeric) = 1.08892530314 -0.476799780837 y1[1] (closed_form) = 3.36101012897 -2.68199656613 absolute error = 3.166 relative error = 73.64 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.75592909872 3.27084525826 absolute error = 4.074 relative error = 95.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17584.8MB, alloc=44.3MB, time=240.84 x[1] = 0.6898 2.155 h = 0.0001 0.005 y1[1] (numeric) = 1.08891533313 -0.478292272122 y1[1] (closed_form) = 3.37236440364 -2.70844156856 absolute error = 3.192 relative error = 73.79 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.78220037947 3.28295977621 absolute error = 4.1 relative error = 95.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6899 2.16 h = 0.0001 0.003 y1[1] (numeric) = 1.0893862172 -0.479300406658 y1[1] (closed_form) = 3.38854183088 -2.72271645667 absolute error = 3.212 relative error = 73.9 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.79611628948 3.29959045042 absolute error = 4.122 relative error = 95.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17634.6MB, alloc=44.3MB, time=241.52 x[1] = 0.69 2.163 h = 0.001 0.001 y1[1] (numeric) = 1.0896607611 -0.479909214183 y1[1] (closed_form) = 3.39817541883 -2.73144803379 absolute error = 3.225 relative error = 73.96 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.8046368652 3.30949781107 absolute error = 4.135 relative error = 95.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17684.0MB, alloc=44.3MB, time=242.18 x[1] = 0.691 2.164 h = 0.001 0.003 y1[1] (numeric) = 1.08955926768 -0.480207047773 y1[1] (closed_form) = 3.39867754629 -2.73756556681 absolute error = 3.229 relative error = 73.99 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.81076979837 3.31016173178 absolute error = 4.139 relative error = 95.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.692 2.167 h = 0.0001 0.004 y1[1] (numeric) = 1.08965411442 -0.480904208373 y1[1] (closed_form) = 3.40580264144 -2.74932920702 absolute error = 3.242 relative error = 74.07 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.82240236914 3.31762500551 absolute error = 4.153 relative error = 95.33 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17733.6MB, alloc=44.3MB, time=242.83 x[1] = 0.6921 2.171 h = 0.003 0.006 y1[1] (numeric) = 1.09002682841 -0.481712679403 y1[1] (closed_form) = 3.41881706399 -2.76097395494 absolute error = 3.259 relative error = 74.15 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.83376419042 3.3309987127 absolute error = 4.17 relative error = 95.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17783.1MB, alloc=44.3MB, time=243.49 x[1] = 0.6951 2.177 h = 0.0001 0.005 y1[1] (numeric) = 1.09001685839 -0.483205170688 y1[1] (closed_form) = 3.43029810959 -2.78806853868 absolute error = 3.285 relative error = 74.31 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.86068489341 3.34322254774 absolute error = 4.197 relative error = 95.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6952 2.182 h = 0.0001 0.003 y1[1] (numeric) = 1.09048774246 -0.484213305224 y1[1] (closed_form) = 3.44676968746 -2.80274290125 absolute error = 3.306 relative error = 74.41 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.87500574417 3.36013564263 absolute error = 4.219 relative error = 95.4 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17832.7MB, alloc=44.3MB, time=244.15 x[1] = 0.6953 2.185 h = 0.001 0.001 y1[1] (numeric) = 1.09076228636 -0.484822112749 y1[1] (closed_form) = 3.45657726001 -2.81171757882 absolute error = 3.318 relative error = 74.47 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.88377259517 3.37020993292 absolute error = 4.232 relative error = 95.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17882.2MB, alloc=44.3MB, time=244.81 x[1] = 0.6963 2.186 h = 0.001 0.003 y1[1] (numeric) = 1.09066079294 -0.485119946339 y1[1] (closed_form) = 3.45706088354 -2.81797501809 absolute error = 3.323 relative error = 74.5 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.89004426043 3.37085190674 absolute error = 4.237 relative error = 95.42 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.6973 2.189 h = 0.0001 0.004 y1[1] (numeric) = 1.09075563969 -0.485817106939 y1[1] (closed_form) = 3.4642887669 -2.83003766916 absolute error = 3.336 relative error = 74.58 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.90197694255 3.3784099258 absolute error = 4.25 relative error = 95.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17931.6MB, alloc=44.3MB, time=245.46 x[1] = 0.6974 2.193 h = 0.003 0.006 y1[1] (numeric) = 1.09112835367 -0.486625577969 y1[1] (closed_form) = 3.47753880757 -2.84200746342 absolute error = 3.353 relative error = 74.66 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.91366810771 3.39200996135 absolute error = 4.268 relative error = 95.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7004 2.199 h = 0.0001 0.005 y1[1] (numeric) = 1.09111838366 -0.488118069254 y1[1] (closed_form) = 3.48914553964 -2.86976665909 absolute error = 3.38 relative error = 74.81 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.94125335754 3.40434240822 absolute error = 4.295 relative error = 95.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=17981.1MB, alloc=44.3MB, time=246.12 x[1] = 0.7005 2.204 h = 0.0001 0.003 y1[1] (numeric) = 1.09158926773 -0.48912620379 y1[1] (closed_form) = 3.50591535558 -2.88485102796 absolute error = 3.401 relative error = 74.91 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.95598962268 3.42154229498 absolute error = 4.318 relative error = 95.49 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18030.7MB, alloc=44.3MB, time=246.78 x[1] = 0.7006 2.207 h = 0.001 0.001 y1[1] (numeric) = 1.09186381163 -0.489735011315 y1[1] (closed_form) = 3.51589929116 -2.89407518505 absolute error = 3.414 relative error = 74.97 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.96500909546 3.43178606341 absolute error = 4.331 relative error = 95.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7016 2.208 h = 0.001 0.003 y1[1] (numeric) = 1.09176231821 -0.490032844905 y1[1] (closed_form) = 3.51636317192 -2.90047549626 absolute error = 3.419 relative error = 75 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.97142250193 3.43240492037 absolute error = 4.336 relative error = 95.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18080.3MB, alloc=44.3MB, time=247.44 x[1] = 0.7026 2.211 h = 0.0001 0.004 y1[1] (numeric) = 1.09185716496 -0.490730005505 y1[1] (closed_form) = 3.52369432562 -2.91284434349 absolute error = 3.432 relative error = 75.08 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.98366249845 3.44005834772 absolute error = 4.35 relative error = 95.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18129.7MB, alloc=44.3MB, time=248.10 x[1] = 0.7027 2.215 h = 0.003 0.006 y1[1] (numeric) = 1.09222987894 -0.491538476536 y1[1] (closed_form) = 3.53718323384 -2.92514773154 absolute error = 3.45 relative error = 75.16 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 2.99569150953 3.45388818561 absolute error = 4.368 relative error = 95.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7057 2.221 h = 0.0001 0.005 y1[1] (numeric) = 1.09221990893 -0.49303096782 y1[1] (closed_form) = 3.54891447021 -2.95358690209 absolute error = 3.477 relative error = 75.31 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.02395675907 3.46632843357 absolute error = 4.396 relative error = 95.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18179.2MB, alloc=44.3MB, time=248.76 x[1] = 0.7058 2.226 h = 0.0001 0.003 y1[1] (numeric) = 1.092690793 -0.494039102356 y1[1] (closed_form) = 3.56598665203 -2.96909206559 absolute error = 3.499 relative error = 75.41 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.03911916851 3.48381951727 absolute error = 4.419 relative error = 95.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18228.9MB, alloc=44.3MB, time=249.42 x[1] = 0.7059 2.229 h = 0.001 0.001 y1[1] (numeric) = 1.0929653369 -0.494647909881 y1[1] (closed_form) = 3.57614935132 -2.97857223612 absolute error = 3.512 relative error = 75.47 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.04839776429 3.49423533072 absolute error = 4.433 relative error = 95.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7069 2.23 h = 0.0001 0.004 y1[1] (numeric) = 1.09286384348 -0.494945743471 y1[1] (closed_form) = 3.57659220813 -2.98511844552 absolute error = 3.517 relative error = 75.5 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.05495598031 3.49482985725 absolute error = 4.437 relative error = 95.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18278.2MB, alloc=44.3MB, time=250.07 x[1] = 0.707 2.234 h = 0.003 0.006 y1[1] (numeric) = 1.09323655746 -0.495754214501 y1[1] (closed_form) = 3.59029346757 -2.99771308444 absolute error = 3.535 relative error = 75.58 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.0672799703 3.50886446915 absolute error = 4.456 relative error = 95.61 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.71 2.24 h = 0.0001 0.005 y1[1] (numeric) = 1.09322658745 -0.497246705786 y1[1] (closed_form) = 3.60213920402 -3.02674865359 absolute error = 3.563 relative error = 75.72 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.09614190196 3.52140513292 absolute error = 4.484 relative error = 95.63 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18327.7MB, alloc=44.3MB, time=250.73 x[1] = 0.7101 2.245 h = 0.0001 0.003 y1[1] (numeric) = 1.09369747152 -0.498254840322 y1[1] (closed_form) = 3.61948018034 -3.04262119282 absolute error = 3.585 relative error = 75.82 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.11167637371 3.53915567722 absolute error = 4.508 relative error = 95.66 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18377.3MB, alloc=44.3MB, time=251.39 x[1] = 0.7102 2.248 h = 0.001 0.001 y1[1] (numeric) = 1.09397201542 -0.498863647847 y1[1] (closed_form) = 3.629801851 -3.0523249155 absolute error = 3.599 relative error = 75.88 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.12118124933 3.54972484552 absolute error = 4.522 relative error = 95.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7112 2.249 h = 0.001 0.003 y1[1] (numeric) = 1.093870522 -0.499161481436 y1[1] (closed_form) = 3.63022734005 -3.05899945153 absolute error = 3.604 relative error = 75.91 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.12786692601 3.55029919905 absolute error = 4.527 relative error = 95.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18426.9MB, alloc=44.3MB, time=252.05 x[1] = 0.7122 2.252 h = 0.0001 0.004 y1[1] (numeric) = 1.09396536874 -0.499858642037 y1[1] (closed_form) = 3.63775571172 -3.07195650298 absolute error = 3.618 relative error = 75.98 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.140697339 3.55813569684 absolute error = 4.541 relative error = 95.68 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18476.4MB, alloc=44.3MB, time=252.71 x[1] = 0.7123 2.256 h = 0.003 0.006 y1[1] (numeric) = 1.09433808273 -0.500667113067 y1[1] (closed_form) = 3.65170207525 -3.08490115762 absolute error = 3.636 relative error = 76.06 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.15337550936 3.57240675136 absolute error = 4.56 relative error = 95.7 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7153 2.262 h = 0.0001 0.005 y1[1] (numeric) = 1.09432811271 -0.502159604352 y1[1] (closed_form) = 3.66367003471 -3.11464621317 absolute error = 3.664 relative error = 76.2 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.18294710516 3.58505360689 absolute error = 4.589 relative error = 95.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18525.9MB, alloc=44.3MB, time=253.37 x[1] = 0.7154 2.267 h = 0.0001 0.003 y1[1] (numeric) = 1.09479899678 -0.503167738888 y1[1] (closed_form) = 3.68132129898 -3.1309602742 absolute error = 3.687 relative error = 76.3 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.19892833616 3.60310376864 absolute error = 4.613 relative error = 95.74 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18575.5MB, alloc=44.3MB, time=254.03 x[1] = 0.7155 2.27 h = 0.001 0.001 y1[1] (numeric) = 1.09507354069 -0.503776546413 y1[1] (closed_form) = 3.69182634043 -3.14093256362 absolute error = 3.701 relative error = 76.35 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.20870482494 3.6138498879 absolute error = 4.628 relative error = 95.75 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7165 2.271 h = 0.001 0.003 y1[1] (numeric) = 1.09497204726 -0.504074380002 y1[1] (closed_form) = 3.69222834229 -3.1477588103 absolute error = 3.706 relative error = 76.38 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.21554119788 3.61439757069 absolute error = 4.632 relative error = 95.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18625.1MB, alloc=44.3MB, time=254.69 x[1] = 0.7175 2.274 h = 0.0001 0.004 y1[1] (numeric) = 1.09506689401 -0.504771540603 y1[1] (closed_form) = 3.69986131634 -3.16104352451 absolute error = 3.72 relative error = 76.45 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.22870043347 3.6223313053 absolute error = 4.647 relative error = 95.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7176 2.278 h = 0.003 0.006 y1[1] (numeric) = 1.09543960799 -0.505580011633 y1[1] (closed_form) = 3.71405612351 -3.17434734917 absolute error = 3.739 relative error = 76.53 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.24174189274 3.63684235217 absolute error = 4.667 relative error = 95.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18674.5MB, alloc=44.3MB, time=255.34 x[1] = 0.7206 2.284 h = 0.0001 0.005 y1[1] (numeric) = 1.09542963798 -0.507072502918 y1[1] (closed_form) = 3.72614482537 -3.20481824371 absolute error = 3.768 relative error = 76.67 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.27203958452 3.64959426883 absolute error = 4.696 relative error = 95.8 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18724.0MB, alloc=44.3MB, time=256.00 x[1] = 0.7207 2.289 h = 0.0001 0.003 y1[1] (numeric) = 1.09590052205 -0.508080637454 y1[1] (closed_form) = 3.74411062047 -3.22158538107 absolute error = 3.792 relative error = 76.76 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.28847907059 3.66794855041 absolute error = 4.721 relative error = 95.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7208 2.292 h = 0.001 0.001 y1[1] (numeric) = 1.09617506595 -0.508689444979 y1[1] (closed_form) = 3.7548014965 -3.23183323381 absolute error = 3.806 relative error = 76.82 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.29853413604 3.67887423997 absolute error = 4.735 relative error = 95.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18773.6MB, alloc=44.3MB, time=256.66 x[1] = 0.7218 2.293 h = 0.001 0.003 y1[1] (numeric) = 1.09607357253 -0.508987278568 y1[1] (closed_form) = 3.75517860244 -3.23881439712 absolute error = 3.811 relative error = 76.85 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.30552444982 3.67939390737 absolute error = 4.74 relative error = 95.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18823.1MB, alloc=44.3MB, time=257.32 x[1] = 0.7228 2.296 h = 0.0001 0.004 y1[1] (numeric) = 1.09616841928 -0.509684439169 y1[1] (closed_form) = 3.76291656069 -3.25243461104 absolute error = 3.825 relative error = 76.91 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.3190203579 3.68742542701 absolute error = 4.755 relative error = 95.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7229 2.3 h = 0.003 0.006 y1[1] (numeric) = 1.09654113326 -0.510492910199 y1[1] (closed_form) = 3.77736318055 -3.26610698172 absolute error = 3.845 relative error = 76.99 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.33243443621 3.70218004064 absolute error = 4.775 relative error = 95.87 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18872.5MB, alloc=44.3MB, time=257.98 x[1] = 0.7259 2.306 h = 0.0001 0.005 y1[1] (numeric) = 1.09653116325 -0.511985401484 y1[1] (closed_form) = 3.78957102997 -3.29732042692 absolute error = 3.874 relative error = 77.13 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.36347501135 3.71503576636 absolute error = 4.805 relative error = 95.89 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18922.1MB, alloc=44.3MB, time=258.63 x[1] = 0.726 2.311 h = 0.0001 0.003 y1[1] (numeric) = 1.09700204732 -0.51299353602 y1[1] (closed_form) = 3.80785563652 -3.31455247509 absolute error = 3.898 relative error = 77.22 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.38038452816 3.73369870192 absolute error = 4.831 relative error = 95.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7261 2.314 h = 0.001 0.001 y1[1] (numeric) = 1.09727659122 -0.513602343545 y1[1] (closed_form) = 3.81873483136 -3.32508305667 absolute error = 3.913 relative error = 77.28 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.39072530268 3.74480659804 absolute error = 4.846 relative error = 95.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=18971.6MB, alloc=44.3MB, time=259.29 x[1] = 0.7271 2.315 h = 0.001 0.003 y1[1] (numeric) = 1.0971750978 -0.513900177134 y1[1] (closed_form) = 3.81908558519 -3.33222240742 absolute error = 3.918 relative error = 77.3 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.39787286554 3.74529685671 absolute error = 4.851 relative error = 95.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7281 2.318 h = 0.0001 0.004 y1[1] (numeric) = 1.09726994454 -0.514597337735 y1[1] (closed_form) = 3.82692887907 -3.34618613546 absolute error = 3.933 relative error = 77.37 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.4117134723 3.75342667564 absolute error = 4.866 relative error = 95.93 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19021.3MB, alloc=44.3MB, time=259.95 x[1] = 0.7282 2.322 h = 0.003 0.006 y1[1] (numeric) = 1.09764265853 -0.515405808765 y1[1] (closed_form) = 3.84163070952 -3.36023665491 absolute error = 3.953 relative error = 77.44 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.42550972647 3.76842845461 absolute error = 4.886 relative error = 95.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19070.8MB, alloc=44.3MB, time=260.61 x[1] = 0.7312 2.328 h = 0.0001 0.005 y1[1] (numeric) = 1.09763268851 -0.51689830005 y1[1] (closed_form) = 3.85395599281 -3.39220972878 absolute error = 3.983 relative error = 77.58 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.45731033525 3.78138661138 absolute error = 4.917 relative error = 95.97 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7313 2.333 h = 0.0001 0.003 y1[1] (numeric) = 1.09810357258 -0.517906434586 y1[1] (closed_form) = 3.87256372837 -3.40991880852 absolute error = 4.008 relative error = 77.67 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.47470194478 3.80036276619 absolute error = 4.943 relative error = 95.99 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19120.4MB, alloc=44.3MB, time=261.27 x[1] = 0.7314 2.336 h = 0.001 0.001 y1[1] (numeric) = 1.09837811649 -0.518515242111 y1[1] (closed_form) = 3.88363374616 -3.42073945729 absolute error = 4.023 relative error = 77.72 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.48533573352 3.81165552156 absolute error = 4.958 relative error = 96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19170.1MB, alloc=44.3MB, time=261.93 x[1] = 0.7324 2.337 h = 0.0001 0.004 y1[1] (numeric) = 1.09827662306 -0.5188130757 y1[1] (closed_form) = 3.88395664278 -3.42804033229 absolute error = 4.028 relative error = 77.75 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.49264391854 3.81211492808 absolute error = 4.964 relative error = 96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7325 2.341 h = 0.003 0.006 y1[1] (numeric) = 1.09864933705 -0.519621546731 y1[1] (closed_form) = 3.89888555695 -3.4424211205 absolute error = 4.048 relative error = 77.82 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.50677396371 3.82733707006 absolute error = 4.984 relative error = 96.02 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19219.6MB, alloc=44.3MB, time=262.59 x[1] = 0.7355 2.347 h = 0.0001 0.005 y1[1] (numeric) = 1.09863936704 -0.521114038015 y1[1] (closed_form) = 3.91131978934 -3.47506064936 absolute error = 4.079 relative error = 77.96 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.53924160482 3.84039153148 absolute error = 5.016 relative error = 96.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19269.2MB, alloc=44.3MB, time=263.25 x[1] = 0.7356 2.352 h = 0.0001 0.003 y1[1] (numeric) = 1.0991102511 -0.522122172551 y1[1] (closed_form) = 3.93021503283 -3.49318635163 absolute error = 4.104 relative error = 78.05 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.55705426037 3.85964691757 absolute error = 5.042 relative error = 96.06 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7357 2.355 h = 0.001 0.001 y1[1] (numeric) = 1.09938479501 -0.522730980076 y1[1] (closed_form) = 3.94145490224 -3.50426037774 absolute error = 4.119 relative error = 78.1 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.56794400523 3.87110454209 absolute error = 5.058 relative error = 96.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19318.8MB, alloc=44.3MB, time=263.91 x[1] = 0.7367 2.356 h = 0.001 0.003 y1[1] (numeric) = 1.09928330158 -0.523028813666 y1[1] (closed_form) = 3.94175455604 -3.51170336784 absolute error = 4.125 relative error = 78.13 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.57539359175 3.87153816619 absolute error = 5.063 relative error = 96.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7377 2.359 h = 0.0001 0.004 y1[1] (numeric) = 1.09937814833 -0.523725974266 y1[1] (closed_form) = 3.94979900496 -3.52632698638 absolute error = 4.14 relative error = 78.19 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.58989640024 3.87985648306 absolute error = 5.079 relative error = 96.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19368.3MB, alloc=44.3MB, time=264.56 x[1] = 0.7378 2.363 h = 0.003 0.006 y1[1] (numeric) = 1.09975086232 -0.524534445297 y1[1] (closed_form) = 3.96498964784 -3.5411043719 absolute error = 4.16 relative error = 78.26 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.60442698199 3.89533266915 absolute error = 5.1 relative error = 96.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19417.8MB, alloc=44.3MB, time=265.22 x[1] = 0.7408 2.369 h = 0.0001 0.005 y1[1] (numeric) = 1.0997408923 -0.526026936581 y1[1] (closed_form) = 3.97753800665 -3.57453633202 absolute error = 4.192 relative error = 78.39 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.63768758129 3.90848686124 absolute error = 5.132 relative error = 96.12 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7409 2.374 h = 0.0001 0.003 y1[1] (numeric) = 1.10021177637 -0.527035071117 y1[1] (closed_form) = 3.99676466115 -3.59316235189 absolute error = 4.218 relative error = 78.48 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.65600550335 3.92806419373 absolute error = 5.159 relative error = 96.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19467.4MB, alloc=44.3MB, time=265.88 x[1] = 0.741 2.377 h = 0.001 0.001 y1[1] (numeric) = 1.10048632027 -0.527643878642 y1[1] (closed_form) = 4.00820015667 -3.6045405433 absolute error = 4.233 relative error = 78.53 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.66720229697 3.93971174765 absolute error = 5.175 relative error = 96.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19517.1MB, alloc=44.3MB, time=266.54 x[1] = 0.742 2.378 h = 0.001 0.003 y1[1] (numeric) = 1.10038482685 -0.527941712232 y1[1] (closed_form) = 4.00846905904 -3.61215146563 absolute error = 4.239 relative error = 78.56 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.67481897751 3.94011173752 absolute error = 5.18 relative error = 96.15 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.743 2.381 h = 0.0001 0.004 y1[1] (numeric) = 1.1004796736 -0.528638872832 y1[1] (closed_form) = 4.01661976859 -3.62714253643 absolute error = 4.255 relative error = 78.62 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.68969044881 3.94852972558 absolute error = 5.197 relative error = 96.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19566.6MB, alloc=44.3MB, time=267.19 x[1] = 0.7431 2.385 h = 0.003 0.006 y1[1] (numeric) = 1.10085238758 -0.529447343863 y1[1] (closed_form) = 4.03207561959 -3.64232679934 absolute error = 4.276 relative error = 78.69 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.70463180129 3.96426362292 absolute error = 5.218 relative error = 96.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19616.0MB, alloc=44.3MB, time=267.85 x[1] = 0.7461 2.391 h = 0.0001 0.005 y1[1] (numeric) = 1.10084241757 -0.530939835147 y1[1] (closed_form) = 4.04473602897 -3.6765693596 absolute error = 4.308 relative error = 78.82 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.73870359082 3.97751578603 absolute error = 5.251 relative error = 96.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7462 2.396 h = 0.0001 0.003 y1[1] (numeric) = 1.10131330164 -0.531947969683 y1[1] (closed_form) = 4.06429851642 -3.69570867311 absolute error = 4.335 relative error = 78.91 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.75753969674 3.99741971861 absolute error = 5.279 relative error = 96.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19665.7MB, alloc=44.3MB, time=268.51 x[1] = 0.7463 2.399 h = 0.001 0.001 y1[1] (numeric) = 1.10158784554 -0.532556777208 y1[1] (closed_form) = 4.07593219817 -3.70739888433 absolute error = 4.35 relative error = 78.96 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.7690513604 4.00925990101 absolute error = 5.295 relative error = 96.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7473 2.4 h = 0.001 0.003 y1[1] (numeric) = 1.10148635212 -0.532854610798 y1[1] (closed_form) = 4.07616869672 -3.71518127161 absolute error = 4.356 relative error = 78.98 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.77683870086 4.00962466268 absolute error = 5.301 relative error = 96.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19715.3MB, alloc=44.3MB, time=269.17 x[1] = 0.7483 2.403 h = 0.0001 0.004 y1[1] (numeric) = 1.10158119886 -0.533551771398 y1[1] (closed_form) = 4.08442588679 -3.73054853033 absolute error = 4.372 relative error = 79.04 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.79208757843 4.0181426916 absolute error = 5.317 relative error = 96.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19764.7MB, alloc=44.3MB, time=269.83 x[1] = 0.7484 2.407 h = 0.003 0.006 y1[1] (numeric) = 1.10195391285 -0.534360242429 y1[1] (closed_form) = 4.10015045135 -3.74615019805 absolute error = 4.394 relative error = 79.11 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.80745018317 4.03413798905 absolute error = 5.339 relative error = 96.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7514 2.413 h = 0.0001 0.005 y1[1] (numeric) = 1.10194394284 -0.535852733713 y1[1] (closed_form) = 4.1129206975 -3.78122192305 absolute error = 4.427 relative error = 79.24 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.84235178768 4.04748621898 absolute error = 5.373 relative error = 96.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19814.4MB, alloc=44.3MB, time=270.49 x[1] = 0.7515 2.418 h = 0.0001 0.003 y1[1] (numeric) = 1.1024148269 -0.536860868249 y1[1] (closed_form) = 4.13282347327 -3.80088781856 absolute error = 4.454 relative error = 79.32 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.86171930723 4.0677214334 absolute error = 5.401 relative error = 96.29 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19863.9MB, alloc=44.3MB, time=271.15 x[1] = 0.7516 2.421 h = 0.001 0.001 y1[1] (numeric) = 1.10268937081 -0.537469675774 y1[1] (closed_form) = 4.14465791893 -3.81289809262 absolute error = 4.47 relative error = 79.37 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.8735538507 4.07975695777 absolute error = 5.418 relative error = 96.3 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7526 2.422 h = 0.001 0.003 y1[1] (numeric) = 1.10258787738 -0.537767509364 y1[1] (closed_form) = 4.14486030649 -3.82085554816 absolute error = 4.476 relative error = 79.4 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.88151548658 4.08008484139 absolute error = 5.423 relative error = 96.3 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19913.5MB, alloc=44.3MB, time=271.81 x[1] = 0.7536 2.425 h = 0.0001 0.004 y1[1] (numeric) = 1.10268272413 -0.538464669964 y1[1] (closed_form) = 4.15322415781 -3.83660792681 absolute error = 4.493 relative error = 79.46 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.89715070929 4.08870323842 absolute error = 5.44 relative error = 96.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=19963.1MB, alloc=44.3MB, time=272.46 x[1] = 0.7537 2.429 h = 0.003 0.006 y1[1] (numeric) = 1.10305543812 -0.539273140995 y1[1] (closed_form) = 4.16922096653 -3.85263777975 absolute error = 4.514 relative error = 79.52 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.91294530083 4.10496364577 absolute error = 5.463 relative error = 96.33 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7567 2.435 h = 0.0001 0.005 y1[1] (numeric) = 1.1030454681 -0.540765632279 y1[1] (closed_form) = 4.18209869235 -3.88855763774 absolute error = 4.548 relative error = 79.65 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.9486957458 4.11840588862 absolute error = 5.497 relative error = 96.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20012.7MB, alloc=44.3MB, time=273.15 x[1] = 0.7568 2.44 h = 0.0001 0.003 y1[1] (numeric) = 1.10351635217 -0.541773766815 y1[1] (closed_form) = 4.20234624412 -3.90876372305 absolute error = 4.576 relative error = 79.73 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.96860822827 4.13897709372 absolute error = 5.526 relative error = 96.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7569 2.443 h = 0.001 0.001 y1[1] (numeric) = 1.10379089607 -0.54238257434 y1[1] (closed_form) = 4.21438404829 -3.92110229572 absolute error = 4.593 relative error = 79.78 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.98077385409 4.1512106873 absolute error = 5.543 relative error = 96.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20062.3MB, alloc=44.3MB, time=273.81 x[1] = 0.7579 2.444 h = 0.0001 0.004 y1[1] (numeric) = 1.10368940265 -0.54268040793 y1[1] (closed_form) = 4.21455056131 -3.9292384947 absolute error = 4.599 relative error = 79.81 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 3.98891349174 4.15149998556 absolute error = 5.549 relative error = 96.38 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20111.9MB, alloc=44.3MB, time=274.47 x[1] = 0.758 2.448 h = 0.003 0.006 y1[1] (numeric) = 1.10406211664 -0.54348887896 y1[1] (closed_form) = 4.23078983459 -3.94564244459 absolute error = 4.621 relative error = 79.87 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.00508549799 4.1679969014 absolute error = 5.572 relative error = 96.39 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.761 2.454 h = 0.0001 0.005 y1[1] (numeric) = 1.10405214662 -0.544981370245 y1[1] (closed_form) = 4.24376849244 -3.98230661128 absolute error = 4.655 relative error = 79.99 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.04158105993 4.18152873184 absolute error = 5.607 relative error = 96.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20161.5MB, alloc=44.3MB, time=275.12 x[1] = 0.7611 2.459 h = 0.0001 0.003 y1[1] (numeric) = 1.10452303069 -0.545989504781 y1[1] (closed_form) = 4.26432309479 -4.00298463969 absolute error = 4.683 relative error = 80.08 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.06196964844 4.20239965448 absolute error = 5.636 relative error = 96.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20211.0MB, alloc=44.3MB, time=275.78 x[1] = 0.7612 2.462 h = 0.001 0.001 y1[1] (numeric) = 1.10479757459 -0.546598312306 y1[1] (closed_form) = 4.27654208106 -4.01561008144 absolute error = 4.7 relative error = 80.13 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.07442457383 4.21481001383 absolute error = 5.653 relative error = 96.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7622 2.463 h = 0.001 0.003 y1[1] (numeric) = 1.10469608117 -0.546896145895 y1[1] (closed_form) = 4.27667844812 -4.02390359262 absolute error = 4.706 relative error = 80.15 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.08272094089 4.21506686865 absolute error = 5.659 relative error = 96.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20260.7MB, alloc=44.3MB, time=276.44 x[1] = 0.7632 2.466 h = 0.0001 0.004 y1[1] (numeric) = 1.10479092792 -0.547593306496 y1[1] (closed_form) = 4.28524595773 -4.04039577849 absolute error = 4.724 relative error = 80.21 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.09909833683 4.22387760788 absolute error = 5.677 relative error = 96.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20310.3MB, alloc=44.3MB, time=277.11 x[1] = 0.7633 2.47 h = 0.003 0.006 y1[1] (numeric) = 1.1051636419 -0.548401777526 y1[1] (closed_form) = 4.30176424445 -4.05724862373 absolute error = 4.747 relative error = 80.27 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.11572295287 4.24064672483 absolute error = 5.7 relative error = 96.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7663 2.476 h = 0.0001 0.005 y1[1] (numeric) = 1.10515367189 -0.549894268811 y1[1] (closed_form) = 4.31484583329 -4.09479735344 absolute error = 4.782 relative error = 80.39 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.15310388095 4.25426856759 absolute error = 5.736 relative error = 96.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20359.9MB, alloc=44.3MB, time=277.77 x[1] = 0.7664 2.481 h = 0.0001 0.003 y1[1] (numeric) = 1.10562455596 -0.550902403347 y1[1] (closed_form) = 4.33575381577 -4.11604171347 absolute error = 4.811 relative error = 80.47 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.17406346318 4.27548448233 absolute error = 5.766 relative error = 96.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7665 2.484 h = 0.001 0.001 y1[1] (numeric) = 1.10589909986 -0.551511210872 y1[1] (closed_form) = 4.34818113459 -4.1290112753 absolute error = 4.828 relative error = 80.52 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.18686522919 4.28809812329 absolute error = 5.784 relative error = 96.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20409.5MB, alloc=44.3MB, time=278.43 x[1] = 0.7675 2.485 h = 0.001 0.003 y1[1] (numeric) = 1.10579760644 -0.551809044461 y1[1] (closed_form) = 4.34827823564 -4.13749058687 absolute error = 4.834 relative error = 80.54 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.19534670977 4.28831310346 absolute error = 5.79 relative error = 96.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20459.0MB, alloc=44.3MB, time=279.08 x[1] = 0.7685 2.488 h = 0.0001 0.004 y1[1] (numeric) = 1.10589245318 -0.552506205062 y1[1] (closed_form) = 4.35695280356 -4.15439456609 absolute error = 4.852 relative error = 80.6 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.21213713737 4.2972250099 absolute error = 5.808 relative error = 96.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7686 2.492 h = 0.003 0.006 y1[1] (numeric) = 1.10626516717 -0.553314676092 y1[1] (closed_form) = 4.37375370439 -4.17170784264 absolute error = 4.875 relative error = 80.66 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.2292258536 4.31427009622 absolute error = 5.832 relative error = 96.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20508.4MB, alloc=44.3MB, time=279.74 x[1] = 0.7716 2.498 h = 0.0001 0.005 y1[1] (numeric) = 1.10625519716 -0.554807167377 y1[1] (closed_form) = 4.38693543138 -4.21016130555 absolute error = 4.912 relative error = 80.78 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.26751236748 4.32797944392 absolute error = 5.868 relative error = 96.55 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20558.0MB, alloc=44.3MB, time=280.40 x[1] = 0.7717 2.503 h = 0.0001 0.003 y1[1] (numeric) = 1.10672608123 -0.555815301913 y1[1] (closed_form) = 4.40820137187 -4.23198655909 absolute error = 4.941 relative error = 80.86 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.28905744732 4.34954513542 absolute error = 5.899 relative error = 96.57 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7718 2.506 h = 0.001 0.001 y1[1] (numeric) = 1.10700062513 -0.556424109438 y1[1] (closed_form) = 4.42083966439 -4.24530905239 absolute error = 4.959 relative error = 80.9 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.30221483229 4.36236482324 absolute error = 5.917 relative error = 96.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20607.6MB, alloc=44.3MB, time=281.06 x[1] = 0.7728 2.507 h = 0.001 0.003 y1[1] (numeric) = 1.1068991317 -0.556721943027 y1[1] (closed_form) = 4.42089556618 -4.25397805291 absolute error = 4.965 relative error = 80.93 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.31088534343 4.36253604875 absolute error = 5.923 relative error = 96.58 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20657.1MB, alloc=44.3MB, time=281.72 x[1] = 0.7738 2.51 h = 0.0001 0.004 y1[1] (numeric) = 1.10699397845 -0.557419103628 y1[1] (closed_form) = 4.42967720503 -4.27130355544 absolute error = 4.983 relative error = 80.98 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.32809853624 4.3715492697 absolute error = 5.942 relative error = 96.59 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7739 2.514 h = 0.003 0.006 y1[1] (numeric) = 1.10736669244 -0.558227574658 y1[1] (closed_form) = 4.44676434213 -4.28908907509 absolute error = 5.007 relative error = 81.04 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.34566311902 4.38887411125 absolute error = 5.967 relative error = 96.6 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20706.7MB, alloc=44.3MB, time=282.38 x[1] = 0.7769 2.52 h = 0.0001 0.005 y1[1] (numeric) = 1.10735672242 -0.559720065943 y1[1] (closed_form) = 4.46004324909 -4.32846787721 absolute error = 5.044 relative error = 81.16 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.38487587165 4.4026682852 absolute error = 6.004 relative error = 96.62 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.777 2.525 h = 0.0001 0.003 y1[1] (numeric) = 1.10782760649 -0.560728200479 y1[1] (closed_form) = 4.48167175317 -4.35088893449 absolute error = 5.074 relative error = 81.24 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.40702130149 4.42458856106 absolute error = 6.035 relative error = 96.64 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20756.2MB, alloc=44.3MB, time=283.04 x[1] = 0.7771 2.528 h = 0.001 0.001 y1[1] (numeric) = 1.10810215039 -0.561337008004 y1[1] (closed_form) = 4.49452367445 -4.36457338078 absolute error = 5.092 relative error = 81.28 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.42054329395 4.437617072 absolute error = 6.054 relative error = 96.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20805.9MB, alloc=44.3MB, time=283.70 x[1] = 0.7781 2.529 h = 0.001 0.003 y1[1] (numeric) = 1.10800065697 -0.561634841593 y1[1] (closed_form) = 4.4945363807 -4.37343603567 absolute error = 5.099 relative error = 81.31 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.42940682867 4.4377425988 absolute error = 6.06 relative error = 96.65 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7791 2.532 h = 0.0001 0.004 y1[1] (numeric) = 1.10809550372 -0.562332002194 y1[1] (closed_form) = 4.50342505361 -4.39119300865 absolute error = 5.117 relative error = 81.36 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.44705273663 4.44685722917 absolute error = 6.079 relative error = 96.66 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20855.6MB, alloc=44.3MB, time=284.36 x[1] = 0.7792 2.536 h = 0.003 0.006 y1[1] (numeric) = 1.1084682177 -0.563140473224 y1[1] (closed_form) = 4.52080206949 -4.40946286523 absolute error = 5.142 relative error = 81.42 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.4651052345 4.46446562837 absolute error = 6.104 relative error = 96.67 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20905.1MB, alloc=44.3MB, time=285.02 x[1] = 0.7822 2.542 h = 0.0001 0.005 y1[1] (numeric) = 1.10845824769 -0.564632964509 y1[1] (closed_form) = 4.53417502675 -4.44978805715 absolute error = 5.18 relative error = 81.53 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.50526532093 4.47834177253 absolute error = 6.142 relative error = 96.69 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7823 2.547 h = 0.0001 0.003 y1[1] (numeric) = 1.10892913176 -0.565641099045 y1[1] (closed_form) = 4.55617072636 -4.47282018459 absolute error = 5.211 relative error = 81.61 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.52802630956 4.500621462 absolute error = 6.174 relative error = 96.7 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=20954.8MB, alloc=44.3MB, time=285.68 x[1] = 0.7824 2.55 h = 0.001 0.001 y1[1] (numeric) = 1.10920367566 -0.56624990657 y1[1] (closed_form) = 4.56923894442 -4.48687582019 absolute error = 5.229 relative error = 81.65 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.54192211298 4.51386158248 absolute error = 6.193 relative error = 96.71 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21004.4MB, alloc=44.3MB, time=286.34 x[1] = 0.7834 2.551 h = 0.0001 0.004 y1[1] (numeric) = 1.10910218224 -0.566547740159 y1[1] (closed_form) = 4.569206394 -4.49593617312 absolute error = 5.236 relative error = 81.68 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.55098274163 4.51393940066 absolute error = 6.199 relative error = 96.72 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7835 2.555 h = 0.003 0.006 y1[1] (numeric) = 1.10947489622 -0.56735621119 y1[1] (closed_form) = 4.58684183022 -4.51462932283 absolute error = 5.261 relative error = 81.74 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.56946164922 4.53180094627 absolute error = 6.225 relative error = 96.73 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21054.0MB, alloc=44.3MB, time=287.00 x[1] = 0.7865 2.561 h = 0.0001 0.005 y1[1] (numeric) = 1.10946492621 -0.568848702475 y1[1] (closed_form) = 4.60030472411 -4.55578527193 absolute error = 5.299 relative error = 81.85 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.61045347874 4.54575685561 absolute error = 6.264 relative error = 96.75 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7866 2.566 h = 0.0001 0.003 y1[1] (numeric) = 1.10993581028 -0.569856837011 y1[1] (closed_form) = 4.62262775489 -4.57935144144 absolute error = 5.331 relative error = 81.92 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.63375241674 4.56835738485 absolute error = 6.296 relative error = 96.76 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21103.6MB, alloc=44.3MB, time=287.66 x[1] = 0.7867 2.569 h = 0.001 0.001 y1[1] (numeric) = 1.11021035418 -0.570465644535 y1[1] (closed_form) = 4.63588887513 -4.59373152826 absolute error = 5.349 relative error = 81.97 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.6479749557 4.5817864963 absolute error = 6.316 relative error = 96.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21153.3MB, alloc=44.3MB, time=288.32 x[1] = 0.7877 2.57 h = 0.001 0.003 y1[1] (numeric) = 1.11010886076 -0.570763478125 y1[1] (closed_form) = 4.63581808986 -4.60296592558 absolute error = 5.356 relative error = 81.99 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.65720915791 4.58182400259 absolute error = 6.322 relative error = 96.77 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7887 2.573 h = 0.0001 0.004 y1[1] (numeric) = 1.1102037075 -0.571460638725 y1[1] (closed_form) = 4.64491108064 -4.62155173022 absolute error = 5.376 relative error = 82.04 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.675686282 4.59113284055 absolute error = 6.342 relative error = 96.78 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21202.7MB, alloc=44.3MB, time=288.98 x[1] = 0.7888 2.577 h = 0.003 0.006 y1[1] (numeric) = 1.11057642149 -0.572269109756 y1[1] (closed_form) = 4.662843376 -4.64075244941 absolute error = 5.401 relative error = 82.1 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.69467625157 4.60928521134 absolute error = 6.368 relative error = 96.79 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21252.3MB, alloc=44.3MB, time=289.64 x[1] = 0.7918 2.583 h = 0.0001 0.005 y1[1] (numeric) = 1.11056645148 -0.573761601041 y1[1] (closed_form) = 4.67639428196 -4.68289521457 absolute error = 5.441 relative error = 82.21 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.7366559145 4.62331754718 absolute error = 6.408 relative error = 96.81 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7919 2.588 h = 0.0001 0.003 y1[1] (numeric) = 1.11103733555 -0.574769735577 y1[1] (closed_form) = 4.6990933846 -4.70710178134 absolute error = 5.473 relative error = 82.28 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.76059962959 4.64628672066 absolute error = 6.441 relative error = 96.83 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21301.9MB, alloc=44.3MB, time=290.30 x[1] = 0.792 2.591 h = 0.001 0.001 y1[1] (numeric) = 1.11131187945 -0.575378543101 y1[1] (closed_form) = 4.71257591381 -4.72187080051 absolute error = 5.492 relative error = 82.33 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.7752136603 4.65993276648 absolute error = 6.461 relative error = 96.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21351.6MB, alloc=44.3MB, time=290.96 x[1] = 0.793 2.592 h = 0.001 0.003 y1[1] (numeric) = 1.11121038603 -0.575676376691 y1[1] (closed_form) = 4.71245590789 -4.73131065948 absolute error = 5.499 relative error = 82.35 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.78465276695 4.65991869324 absolute error = 6.468 relative error = 96.84 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.794 2.595 h = 0.0001 0.004 y1[1] (numeric) = 1.11130523277 -0.576373537291 y1[1] (closed_form) = 4.72165566033 -4.75035763365 absolute error = 5.519 relative error = 82.4 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.80359230784 4.66932902964 absolute error = 6.488 relative error = 96.85 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21401.2MB, alloc=44.3MB, time=291.62 x[1] = 0.7941 2.599 h = 0.003 0.006 y1[1] (numeric) = 1.11167794676 -0.577182008322 y1[1] (closed_form) = 4.73988851263 -4.77007885849 absolute error = 5.545 relative error = 82.45 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.8231062308 4.68777607288 absolute error = 6.515 relative error = 96.86 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7971 2.605 h = 0.0001 0.005 y1[1] (numeric) = 1.11166797674 -0.578674499607 y1[1] (closed_form) = 4.7535237804 -4.81323081388 absolute error = 5.585 relative error = 82.56 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.86609613921 4.70188144249 absolute error = 6.555 relative error = 96.88 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21450.8MB, alloc=44.3MB, time=292.28 x[1] = 0.7972 2.61 h = 0.0001 0.003 y1[1] (numeric) = 1.11213886081 -0.579682634143 y1[1] (closed_form) = 4.77660365853 -4.83809410807 absolute error = 5.618 relative error = 82.63 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.8907009047 4.72522414828 absolute error = 6.589 relative error = 96.89 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21500.4MB, alloc=44.3MB, time=292.94 x[1] = 0.7973 2.613 h = 0.001 0.001 y1[1] (numeric) = 1.11241340471 -0.580291441667 y1[1] (closed_form) = 4.7903102993 -4.85326193749 absolute error = 5.638 relative error = 82.68 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.90571627253 4.73908994177 absolute error = 6.609 relative error = 96.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.7983 2.614 h = 0.001 0.003 y1[1] (numeric) = 1.11231191129 -0.580589275257 y1[1] (closed_form) = 4.79013881649 -4.86291153396 absolute error = 5.645 relative error = 82.7 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.91536458383 4.7390220812 absolute error = 6.616 relative error = 96.9 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21549.9MB, alloc=44.3MB, time=293.60 x[1] = 0.7993 2.617 h = 0.0001 0.004 y1[1] (numeric) = 1.11240675804 -0.581286435857 y1[1] (closed_form) = 4.79944508287 -4.88243050716 absolute error = 5.665 relative error = 82.75 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.93477737115 4.7485337894 absolute error = 6.637 relative error = 96.91 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21599.4MB, alloc=44.3MB, time=294.26 x[1] = 0.7994 2.621 h = 0.003 0.006 y1[1] (numeric) = 1.11277947202 -0.582094906888 y1[1] (closed_form) = 4.81798220554 -4.90268548123 absolute error = 5.692 relative error = 82.8 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.95482844652 4.76727936453 absolute error = 6.664 relative error = 96.92 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8024 2.627 h = 0.0001 0.005 y1[1] (numeric) = 1.11276950201 -0.583587398173 y1[1] (closed_form) = 4.83169798794 -4.94686948078 absolute error = 5.733 relative error = 82.91 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 4.99885149012 4.78145417285 absolute error = 6.706 relative error = 96.94 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21649.0MB, alloc=44.3MB, time=294.93 x[1] = 0.8025 2.632 h = 0.0001 0.003 y1[1] (numeric) = 1.11324038608 -0.584595532709 y1[1] (closed_form) = 4.85516336565 -4.97240622076 absolute error = 5.767 relative error = 82.98 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.02413396781 4.80517531515 absolute error = 6.74 relative error = 96.95 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21698.6MB, alloc=44.3MB, time=295.59 x[1] = 0.8026 2.635 h = 0.001 0.001 y1[1] (numeric) = 1.11351492998 -0.585204340233 y1[1] (closed_form) = 4.86909682974 -4.98798297243 absolute error = 5.787 relative error = 83.02 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.03956075235 4.8192636762 absolute error = 6.761 relative error = 96.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8036 2.636 h = 0.001 0.003 y1[1] (numeric) = 1.11341343656 -0.585502173823 y1[1] (closed_form) = 4.86887154139 -4.99784666588 absolute error = 5.794 relative error = 83.04 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.04942265138 4.81913974721 absolute error = 6.768 relative error = 96.96 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21748.2MB, alloc=44.3MB, time=296.25 x[1] = 0.8046 2.639 h = 0.0001 0.004 y1[1] (numeric) = 1.1135082833 -0.586199334423 y1[1] (closed_form) = 4.87828401249 -5.01784870764 absolute error = 5.815 relative error = 83.09 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.06931975414 4.8287526364 absolute error = 6.789 relative error = 96.97 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8047 2.643 h = 0.003 0.006 y1[1] (numeric) = 1.11388099729 -0.587007805454 y1[1] (closed_form) = 4.8971291332 -5.03865098882 absolute error = 5.842 relative error = 83.15 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.08992149547 4.8478006137 absolute error = 6.817 relative error = 96.98 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21797.7MB, alloc=44.3MB, time=296.91 x[1] = 0.8077 2.649 h = 0.0001 0.005 y1[1] (numeric) = 1.11387102728 -0.588500296739 y1[1] (closed_form) = 4.91092137908 -5.0838903758 absolute error = 5.884 relative error = 83.25 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.13500105118 4.86204105638 absolute error = 6.859 relative error = 97 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21847.3MB, alloc=44.3MB, time=297.57 x[1] = 0.8078 2.654 h = 0.0001 0.003 y1[1] (numeric) = 1.11434191135 -0.589508431275 y1[1] (closed_form) = 4.93477699914 -5.11011767691 absolute error = 5.919 relative error = 83.32 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.16097830013 4.88614555389 absolute error = 6.895 relative error = 97.01 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8079 2.657 h = 0.001 0.001 y1[1] (numeric) = 1.11461645525 -0.590117238799 y1[1] (closed_form) = 4.94894000637 -5.12611370214 absolute error = 5.939 relative error = 83.36 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.17682682046 4.9004593079 absolute error = 6.916 relative error = 97.02 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21896.8MB, alloc=44.3MB, time=298.23 x[1] = 0.8089 2.658 h = 0.0001 0.004 y1[1] (numeric) = 1.11451496183 -0.590415072389 y1[1] (closed_form) = 4.94865850938 -5.13619593711 absolute error = 5.947 relative error = 83.38 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.18690677457 4.90027695402 absolute error = 6.923 relative error = 97.03 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21946.2MB, alloc=44.3MB, time=298.88 x[1] = 0.809 2.662 h = 0.003 0.006 y1[1] (numeric) = 1.11488767581 -0.591223543419 y1[1] (closed_form) = 4.96777848464 -5.15747669446 absolute error = 5.975 relative error = 83.43 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.2079899123 4.91959512004 absolute error = 6.952 relative error = 97.04 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.812 2.668 h = 0.0001 0.005 y1[1] (numeric) = 1.1148777058 -0.592716034704 y1[1] (closed_form) = 4.98164610199 -5.20364275591 absolute error = 6.018 relative error = 83.53 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.25399726109 4.93390182046 absolute error = 6.995 relative error = 97.05 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=21995.8MB, alloc=44.3MB, time=299.54 x[1] = 0.8121 2.673 h = 0.0001 0.003 y1[1] (numeric) = 1.11534858987 -0.59372416924 y1[1] (closed_form) = 5.00584995144 -5.23047375838 absolute error = 6.053 relative error = 83.6 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.28058186978 4.95834880607 absolute error = 7.031 relative error = 97.07 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22045.3MB, alloc=44.3MB, time=300.20 x[1] = 0.8122 2.676 h = 0.001 0.001 y1[1] (numeric) = 1.11562313377 -0.594332976765 y1[1] (closed_form) = 5.0202178917 -5.24683637754 absolute error = 6.074 relative error = 83.64 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.2967991255 4.97286403226 absolute error = 7.053 relative error = 97.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8132 2.677 h = 0.001 0.003 y1[1] (numeric) = 1.11552164035 -0.594630810354 y1[1] (closed_form) = 5.01988870634 -5.25711106081 absolute error = 6.081 relative error = 83.66 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.30707115256 4.97263211355 absolute error = 7.06 relative error = 97.08 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22094.9MB, alloc=44.3MB, time=300.86 x[1] = 0.8142 2.68 h = 0.0001 0.004 y1[1] (numeric) = 1.11561648709 -0.595327970955 y1[1] (closed_form) = 5.02950383166 -5.27804103198 absolute error = 6.103 relative error = 83.71 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.32789855818 4.98243863019 absolute error = 7.082 relative error = 97.09 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8143 2.684 h = 0.003 0.006 y1[1] (numeric) = 1.11598920108 -0.596136441985 y1[1] (closed_form) = 5.04893894482 -5.29989514059 absolute error = 6.131 relative error = 83.76 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.34955832249 5.00206659423 absolute error = 7.111 relative error = 97.1 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22144.3MB, alloc=44.3MB, time=301.52 x[1] = 0.8173 2.69 h = 0.0001 0.005 y1[1] (numeric) = 1.11597923106 -0.59762893327 y1[1] (closed_form) = 5.06287521165 -5.34716141582 absolute error = 6.175 relative error = 83.86 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.39666706431 5.01643156087 absolute error = 7.155 relative error = 97.11 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22193.9MB, alloc=44.3MB, time=302.18 x[1] = 0.8174 2.695 h = 0.0001 0.003 y1[1] (numeric) = 1.11645011513 -0.598637067806 y1[1] (closed_form) = 5.08747838755 -5.37471585724 absolute error = 6.211 relative error = 83.93 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.42397921622 5.04127130155 absolute error = 7.192 relative error = 97.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8175 2.698 h = 0.001 0.001 y1[1] (numeric) = 1.11672465903 -0.599245875331 y1[1] (closed_form) = 5.10208107952 -5.39151763422 absolute error = 6.233 relative error = 83.97 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.44063803121 5.05601731886 absolute error = 7.214 relative error = 97.13 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22243.5MB, alloc=44.3MB, time=302.84 x[1] = 0.8185 2.699 h = 0.001 0.003 y1[1] (numeric) = 1.11662316561 -0.59954370892 y1[1] (closed_form) = 5.10169106379 -5.40201939152 absolute error = 6.241 relative error = 83.99 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.45113668585 5.05572243817 absolute error = 7.222 relative error = 97.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22293.1MB, alloc=44.3MB, time=303.50 x[1] = 0.8195 2.702 h = 0.0001 0.004 y1[1] (numeric) = 1.11671801236 -0.600240869521 y1[1] (closed_form) = 5.11141128666 -5.42346547546 absolute error = 6.263 relative error = 84.03 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.47248144514 5.06562935333 absolute error = 7.244 relative error = 97.14 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8196 2.706 h = 0.003 0.006 y1[1] (numeric) = 1.11709072634 -0.601049340551 y1[1] (closed_form) = 5.13116530188 -5.44590743172 absolute error = 6.292 relative error = 84.09 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.49473228881 5.08557101277 absolute error = 7.274 relative error = 97.16 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22342.6MB, alloc=44.3MB, time=304.15 x[1] = 0.8226 2.712 h = 0.0001 0.005 y1[1] (numeric) = 1.11708075633 -0.602541831836 y1[1] (closed_form) = 5.1451655487 -5.49429872069 absolute error = 6.337 relative error = 84.18 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.54296725175 5.09998980836 absolute error = 7.319 relative error = 97.17 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22392.3MB, alloc=44.3MB, time=304.81 x[1] = 0.8227 2.717 h = 0.0001 0.003 y1[1] (numeric) = 1.1175516404 -0.603549966372 y1[1] (closed_form) = 5.17017284203 -5.52259490165 absolute error = 6.373 relative error = 84.25 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.5710251922 5.12522725943 absolute error = 7.357 relative error = 97.18 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8228 2.72 h = 0.001 0.001 y1[1] (numeric) = 1.1178261843 -0.604158773897 y1[1] (closed_form) = 5.18501302493 -5.53984690238 absolute error = 6.396 relative error = 84.29 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.58813660063 5.14020690578 absolute error = 7.38 relative error = 97.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22442.0MB, alloc=44.3MB, time=305.47 x[1] = 0.8238 2.721 h = 0.001 0.003 y1[1] (numeric) = 1.11772469088 -0.604456607486 y1[1] (closed_form) = 5.18455955181 -5.55058043075 absolute error = 6.403 relative error = 84.31 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.59886660064 5.13984648019 absolute error = 7.387 relative error = 97.19 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8248 2.724 h = 0.0001 0.004 y1[1] (numeric) = 1.11781953763 -0.605153768087 y1[1] (closed_form) = 5.19438430229 -5.57255467213 absolute error = 6.426 relative error = 84.35 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.62074075564 5.14985333268 absolute error = 7.41 relative error = 97.2 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22491.6MB, alloc=44.3MB, time=306.13 x[1] = 0.8249 2.728 h = 0.003 0.006 y1[1] (numeric) = 1.11819225161 -0.605962239117 y1[1] (closed_form) = 5.21446099201 -5.59559931484 absolute error = 6.456 relative error = 84.4 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.64359747407 5.1701125901 absolute error = 7.44 relative error = 97.21 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22541.1MB, alloc=44.3MB, time=306.79 x[1] = 0.8279 2.734 h = 0.0001 0.005 y1[1] (numeric) = 1.1181822816 -0.607454730402 y1[1] (closed_form) = 5.22852031616 -5.64514094534 absolute error = 6.502 relative error = 84.5 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.69298401229 5.18458053924 absolute error = 7.487 relative error = 97.23 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.828 2.739 h = 0.0001 0.003 y1[1] (numeric) = 1.11865316567 -0.608462864938 y1[1] (closed_form) = 5.25393652914 -5.67419759885 absolute error = 6.539 relative error = 84.56 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.72180641933 5.21022066343 absolute error = 7.525 relative error = 97.24 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22590.7MB, alloc=44.3MB, time=307.45 x[1] = 0.8281 2.742 h = 0.001 0.001 y1[1] (numeric) = 1.11892770957 -0.609071672463 y1[1] (closed_form) = 5.26901694548 -5.6919111499 absolute error = 6.562 relative error = 84.6 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.7393817162 5.22543677769 absolute error = 7.548 relative error = 97.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22640.3MB, alloc=44.3MB, time=308.11 x[1] = 0.8291 2.743 h = 0.001 0.003 y1[1] (numeric) = 1.11882621615 -0.609369506052 y1[1] (closed_form) = 5.26849730497 -5.70288123724 absolute error = 6.57 relative error = 84.62 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.75034786959 5.22500814045 absolute error = 7.556 relative error = 97.25 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8301 2.746 h = 0.0001 0.004 y1[1] (numeric) = 1.11892106289 -0.610066666653 y1[1] (closed_form) = 5.27842593761 -5.72539594593 absolute error = 6.593 relative error = 84.66 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.77276372699 5.23511439119 absolute error = 7.579 relative error = 97.26 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22689.8MB, alloc=44.3MB, time=308.77 x[1] = 0.8302 2.75 h = 0.003 0.006 y1[1] (numeric) = 1.11929377688 -0.610875137683 y1[1] (closed_form) = 5.29882908083 -5.7490584639 absolute error = 6.623 relative error = 84.71 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.7962414659 5.25569515265 absolute error = 7.611 relative error = 97.27 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22739.4MB, alloc=44.3MB, time=309.43 x[1] = 0.8332 2.756 h = 0.0001 0.005 y1[1] (numeric) = 1.11928380686 -0.612367628968 y1[1] (closed_form) = 5.31294233828 -5.79977630198 absolute error = 6.671 relative error = 84.81 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.84680547002 5.27020733379 absolute error = 7.658 relative error = 97.28 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8333 2.761 h = 0.0001 0.003 y1[1] (numeric) = 1.11975469093 -0.613375763504 y1[1] (closed_form) = 5.33877228222 -5.82961260316 absolute error = 6.709 relative error = 84.87 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.87641146419 5.29625509912 absolute error = 7.697 relative error = 97.3 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22789.0MB, alloc=44.3MB, time=310.09 x[1] = 0.8334 2.764 h = 0.001 0.001 y1[1] (numeric) = 1.12002923483 -0.613984571029 y1[1] (closed_form) = 5.35409567639 -5.84779929756 absolute error = 6.732 relative error = 84.91 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.89446221115 5.31171051979 absolute error = 7.721 relative error = 97.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8344 2.765 h = 0.0001 0.004 y1[1] (numeric) = 1.11992774141 -0.614282404618 y1[1] (closed_form) = 5.35350707316 -5.85901082419 absolute error = 6.74 relative error = 84.93 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.90566941767 5.31121091797 absolute error = 7.729 relative error = 97.31 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22838.5MB, alloc=44.3MB, time=310.75 x[1] = 0.8345 2.769 h = 0.003 0.006 y1[1] (numeric) = 1.1203004554 -0.615090875649 y1[1] (closed_form) = 5.37420185945 -5.88321367434 absolute error = 6.771 relative error = 84.98 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.92969021871 5.33207919841 absolute error = 7.761 relative error = 97.32 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22887.9MB, alloc=44.3MB, time=311.41 x[1] = 0.8375 2.775 h = 0.0001 0.005 y1[1] (numeric) = 1.12029048538 -0.616583366934 y1[1] (closed_form) = 5.38837167173 -5.93496452987 absolute error = 6.819 relative error = 85.07 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 5.98128845384 5.34663977373 absolute error = 7.809 relative error = 97.33 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8376 2.78 h = 0.0001 0.003 y1[1] (numeric) = 1.12076136945 -0.61759150147 y1[1] (closed_form) = 5.41457120588 -5.96548261899 absolute error = 6.858 relative error = 85.13 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.01157965358 5.37305205608 absolute error = 7.849 relative error = 97.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22937.4MB, alloc=44.3MB, time=312.06 x[1] = 0.8377 2.783 h = 0.001 0.001 y1[1] (numeric) = 1.12103591335 -0.618200308995 y1[1] (closed_form) = 5.43011177435 -5.98408313177 absolute error = 6.882 relative error = 85.17 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.03004622173 5.38872159145 absolute error = 7.873 relative error = 97.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=22987.0MB, alloc=44.3MB, time=312.73 x[1] = 0.8387 2.784 h = 0.001 0.003 y1[1] (numeric) = 1.12093441993 -0.618498142584 y1[1] (closed_form) = 5.42946446183 -5.99550732948 absolute error = 6.89 relative error = 85.18 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.04146580517 5.38816158624 absolute error = 7.881 relative error = 97.35 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8397 2.787 h = 0.0001 0.004 y1[1] (numeric) = 1.12102926668 -0.619195303184 y1[1] (closed_form) = 5.43959120208 -6.01906020041 absolute error = 6.914 relative error = 85.23 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.06492216352 5.39845789084 absolute error = 7.905 relative error = 97.36 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23036.6MB, alloc=44.3MB, time=313.39 x[1] = 0.8398 2.791 h = 0.003 0.006 y1[1] (numeric) = 1.12140198066 -0.620003774215 y1[1] (closed_form) = 5.46061967601 -6.04391010203 absolute error = 6.946 relative error = 85.28 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.08959308038 5.41965513748 absolute error = 7.938 relative error = 97.37 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23086.0MB, alloc=44.3MB, time=314.04 x[1] = 0.8428 2.797 h = 0.0001 0.005 y1[1] (numeric) = 1.12139201065 -0.6214962655 y1[1] (closed_form) = 5.4748335023 -6.09688683325 absolute error = 6.995 relative error = 85.37 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.14241848831 5.43425042725 absolute error = 7.987 relative error = 97.39 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8429 2.802 h = 0.0001 0.003 y1[1] (numeric) = 1.12186289472 -0.622504400036 y1[1] (closed_form) = 5.50145597772 -6.12822140352 absolute error = 7.035 relative error = 85.43 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.17353000635 5.46107984225 absolute error = 8.028 relative error = 97.4 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23135.6MB, alloc=44.3MB, time=314.70 x[1] = 0.843 2.805 h = 0.001 0.001 y1[1] (numeric) = 1.12213743862 -0.623113207561 y1[1] (closed_form) = 5.51724477656 -6.14731732849 absolute error = 7.059 relative error = 85.46 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.19249423448 5.47699410547 absolute error = 8.053 relative error = 97.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.844 2.806 h = 0.001 0.003 y1[1] (numeric) = 1.1220359452 -0.62341104115 y1[1] (closed_form) = 5.51652312522 -6.15899233383 absolute error = 7.068 relative error = 85.48 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.20416427337 5.47635783654 absolute error = 8.061 relative error = 97.41 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23185.3MB, alloc=44.3MB, time=315.36 x[1] = 0.845 2.809 h = 0.0001 0.004 y1[1] (numeric) = 1.12213079195 -0.62410820175 y1[1] (closed_form) = 5.5267516131 -6.1831224124 absolute error = 7.092 relative error = 85.52 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.22819906164 5.48675169636 absolute error = 8.086 relative error = 97.42 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23234.8MB, alloc=44.3MB, time=316.02 x[1] = 0.8451 2.813 h = 0.003 0.006 y1[1] (numeric) = 1.12250350593 -0.624916672781 y1[1] (closed_form) = 5.54811756659 -6.20863559935 absolute error = 7.125 relative error = 85.57 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.25353628592 5.50828181982 absolute error = 8.119 relative error = 97.43 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8481 2.819 h = 0.0001 0.005 y1[1] (numeric) = 1.12249353592 -0.626409164066 y1[1] (closed_form) = 5.56236953219 -6.26286567447 absolute error = 7.175 relative error = 85.66 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.30761635484 5.52290615854 absolute error = 8.169 relative error = 97.44 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23284.4MB, alloc=44.3MB, time=316.68 x[1] = 0.8482 2.824 h = 0.0001 0.003 y1[1] (numeric) = 1.12296441999 -0.627417298602 y1[1] (closed_form) = 5.58941977889 -6.29503722088 absolute error = 7.216 relative error = 85.72 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.33956863273 5.55015768259 absolute error = 8.211 relative error = 97.45 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23334.0MB, alloc=44.3MB, time=317.34 x[1] = 0.8483 2.827 h = 0.001 0.001 y1[1] (numeric) = 1.12323896389 -0.628026106127 y1[1] (closed_form) = 5.60545955307 -6.31464094651 absolute error = 7.241 relative error = 85.75 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.35904287855 5.56631950654 absolute error = 8.236 relative error = 97.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8493 2.828 h = 0.001 0.003 y1[1] (numeric) = 1.12313747047 -0.628323939716 y1[1] (closed_form) = 5.60466051108 -6.32657191409 absolute error = 7.249 relative error = 85.77 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.37096854513 5.56560396213 absolute error = 8.245 relative error = 97.46 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23383.7MB, alloc=44.3MB, time=318.00 x[1] = 0.8503 2.831 h = 0.0001 0.004 y1[1] (numeric) = 1.12323231721 -0.629021100317 y1[1] (closed_form) = 5.61498978241 -6.35129258722 absolute error = 7.275 relative error = 85.81 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.39559514537 5.57609451064 absolute error = 8.27 relative error = 97.47 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23433.2MB, alloc=44.3MB, time=318.66 x[1] = 0.8504 2.835 h = 0.003 0.006 y1[1] (numeric) = 1.1236050312 -0.629829571347 y1[1] (closed_form) = 5.63669700657 -6.37748567446 absolute error = 7.308 relative error = 85.86 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.4216152501 5.5979614179 absolute error = 8.304 relative error = 97.48 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8534 2.841 h = 0.0001 0.005 y1[1] (numeric) = 1.12359506118 -0.631322062632 y1[1] (closed_form) = 5.65098096186 -6.43299714202 absolute error = 7.359 relative error = 85.95 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.476978047 5.61260886071 absolute error = 8.355 relative error = 97.49 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23482.7MB, alloc=44.3MB, time=319.32 x[1] = 0.8535 2.846 h = 0.0001 0.003 y1[1] (numeric) = 1.12406594525 -0.632330197168 y1[1] (closed_form) = 5.67846380969 -6.4660266409 absolute error = 7.401 relative error = 86 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.50979200805 5.64028746655 absolute error = 8.398 relative error = 97.5 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8536 2.849 h = 0.001 0.001 y1[1] (numeric) = 1.12434048915 -0.632939004693 y1[1] (closed_form) = 5.69475730016 -6.48615084575 absolute error = 7.426 relative error = 86.04 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.52978891953 5.65669967804 absolute error = 8.424 relative error = 97.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23532.4MB, alloc=44.3MB, time=319.98 x[1] = 0.8546 2.85 h = 0.001 0.003 y1[1] (numeric) = 1.12423899573 -0.633236838282 y1[1] (closed_form) = 5.69387772071 -6.49834302882 absolute error = 7.435 relative error = 86.06 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.54197548411 5.65590175065 absolute error = 8.433 relative error = 97.51 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23581.9MB, alloc=44.3MB, time=320.64 x[1] = 0.8556 2.853 h = 0.0001 0.004 y1[1] (numeric) = 1.12433384248 -0.633933998883 y1[1] (closed_form) = 5.70430671956 -6.52366797619 absolute error = 7.461 relative error = 86.1 % Correct digits = 0 h = 0.0001 0.004 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.56720757073 5.66648802736 absolute error = 8.459 relative error = 97.52 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8557 2.857 h = 0.003 0.006 y1[1] (numeric) = 1.12470655646 -0.634742469913 y1[1] (closed_form) = 5.72635900251 -6.55055796825 absolute error = 7.495 relative error = 86.14 % Correct digits = 0 h = 0.003 0.006 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.59392751882 5.6886956197 absolute error = 8.494 relative error = 97.53 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23631.5MB, alloc=44.3MB, time=321.29 x[1] = 0.8587 2.863 h = 0.0001 0.005 y1[1] (numeric) = 1.12469658645 -0.636234961198 y1[1] (closed_form) = 5.7406685136 -6.60737946846 absolute error = 7.547 relative error = 86.23 % Correct digits = 0 h = 0.0001 0.005 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.65060170089 5.70335993312 absolute error = 8.546 relative error = 97.54 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23681.1MB, alloc=44.3MB, time=321.95 x[1] = 0.8588 2.868 h = 0.0001 0.003 y1[1] (numeric) = 1.12516747052 -0.637243095734 y1[1] (closed_form) = 5.76858878956 -6.6412883882 absolute error = 7.59 relative error = 86.28 % Correct digits = 0 h = 0.0001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.68429876088 5.73147058725 absolute error = 8.59 relative error = 97.55 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 x[1] = 0.8589 2.871 h = 0.001 0.001 y1[1] (numeric) = 1.12544201442 -0.637851903259 y1[1] (closed_form) = 5.78513873158 -6.66194604729 absolute error = 7.616 relative error = 86.32 % Correct digits = 0 h = 0.001 0.001 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.7048312827 5.74813600536 absolute error = 8.616 relative error = 97.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23730.8MB, alloc=44.3MB, time=322.62 x[1] = 0.8599 2.872 h = 0.001 0.003 y1[1] (numeric) = 1.125340521 -0.638149736848 y1[1] (closed_form) = 5.78417537021 -6.6744047994 absolute error = 7.625 relative error = 86.33 % Correct digits = 0 h = 0.001 0.003 y2[1] (numeric) = 0.199663505514 0.0981700839054 y2[1] (closed_form) = 6.71728411532 5.74725248906 absolute error = 8.625 relative error = 97.56 % Correct digits = 0 NO POLE (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO POLE (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 memory used=23780.6MB, alloc=44.3MB, time=323.29 Finished! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = neg ( y2 ) ; diff ( y2 , x , 1 ) = y1 ; Iterations = 754 Total Elapsed Time = 5 Minutes 23 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 5 Minutes 23 Seconds > quit memory used=23781.4MB, alloc=44.3MB, time=323.30