|\^/| 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_y := proc(x) > return(neg(ln(cos(c(x))))); > end; exact_soln_y := proc(x) return neg(ln(cos(c(x)))) end proc > next_delta := proc() > global glob_nxt, x_delta; > x_delta := [ 0.001 + 0.00004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.0001 + 0.004 * I, > 0.003 + 0.006 * I, > 0.0001 + 0.005 * I, > 0.0001 + 0.003 * I, > 0.001 + 0.001 * I, > 0.001 + 0.003 * I, > 0.000 + 0.000 * I ]; > glob_nxt := glob_nxt + 1; > it := x_delta[glob_nxt]; > return it; > end; Warning, `it` is implicitly declared local to procedure `next_delta` next_delta := proc() local it; global glob_nxt, x_delta; x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 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, 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0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 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. + 0.*I]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it end proc #END USER DEF BLOCK #END BLOCK 3 #END USER FUNCTION BLOCK # before write_aux functions # Begin Function number 2 > display_poles := proc() > local rad_given; > global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ; > if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1 > rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I )); > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," "); > omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," "); > if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and > (float_abs(rad_given) > 0.0)) then # if number 2 > glob_least_given_sing := rad_given; > fi;# end if 2; > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > elif > (glob_type_given_pole = 5) then # if number 3 > omniout_str(ALWAYS,"SOME POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 3; > if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," "); > if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4 > glob_least_ratio_sing := array_rad_test_poles[1,1]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," "); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," "); > if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4 > glob_least_3_sing := array_rad_test_poles[1,2]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 3; > if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," "); > if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4 > glob_least_6_sing := array_rad_test_poles[1,3]; > fi;# end if 4; > omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 3 > ; > 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 end proc # End Function number 2 # Begin Function number 3 > my_check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := glob__1; > else > ret := glob__m1; > fi;# end if 3; > ret;; > end; my_check_sign := proc(x0, xf) local ret; if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret end proc # End Function number 3 # Begin Function number 4 > est_size_answer := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local min_size; > min_size := glob_estimated_size_answer; > if (float_abs(array_y[1]) < min_size) then # if number 3 > min_size := float_abs(array_y[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < glob__1) then # if number 3 > min_size := glob__1; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; min_size := glob_estimated_size_answer; if float_abs(array_y[1]) < min_size then min_size := float_abs(array_y[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < glob__1 then min_size := glob__1; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc # End Function number 4 # Begin Function number 5 > test_suggested_h := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := glob__small; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; max_estimated_step_error := glob__small; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := float_abs(array_y[no_terms - 3] + array_y[no_terms - 2]*hn_div_ho + array_y[no_terms - 1]*hn_div_ho_2 + array_y[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc # End Function number 5 # Begin Function number 6 > track_estimated_error := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > no_terms := ATS_MAX_TERMS; > hn_div_ho := glob__0_5; > hn_div_ho_2 := glob__0_25; > hn_div_ho_3 := glob__0_125; > est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3); > if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3 > est_tmp := c(glob_prec) * c(float_abs(array_y[1])); > fi;# end if 3; > if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3 > array_max_est_error[1] := c(est_tmp); > fi;# end if 3 > ; > end; track_estimated_error := proc() local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; no_terms := ATS_MAX_TERMS; hn_div_ho := glob__0_5; hn_div_ho_2 := glob__0_25; hn_div_ho_3 := glob__0_125; est_tmp := c(float_abs(array_y[no_terms - 3])) + c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho) + c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2) + c(float_abs(array_y[no_terms]))*c(hn_div_ho_3); if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then est_tmp := c(glob_prec)*c(float_abs(array_y[1])) end if; if c(array_max_est_error[1]) <= c(est_tmp) then array_max_est_error[1] := c(est_tmp) end if end proc # End Function number 6 # Begin Function number 7 > reached_interval := proc() > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local ret; > if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; if glob_check_sign*glob_next_display - glob_h/glob__10 <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc # End Function number 7 # Begin Function number 8 > display_alot := proc(iter) > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err; > #TOP DISPLAY ALOT > ind_var := array_x[1]; > omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > omniout_complex(ALWAYS,"h ",33,glob_h,20," "); > omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > closed_form_val_y := evalf(exact_soln_y(ind_var)); > omniout_complex(ALWAYS,"y[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 3 > relerr := abserr/float_abs(closed_form_val_y); > if (float_abs(c(relerr)) > 0.0) then # if number 4 > glob_good_digits := round(-log10(relerr)); > else > relerr := 0.0 ; > glob_good_digits := Digits - 2; > fi;# end if 4; > else > ; > relerr := glob__m1 ; > glob_good_digits := -16; > fi;# end if 3; > if (glob_good_digits < glob_min_good_digits) then # if number 3 > glob_min_good_digits := glob_good_digits; > fi;# end if 3; > 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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ind_var := array_x[1]; omniout_complex(ALWAYS, "x[1] ", 33, ind_var, 20, " "); term_no := 1; numeric_val := array_y[term_no]; omniout_complex(ALWAYS, "h ", 33, glob_h, 20, " "); omniout_complex(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); closed_form_val_y := evalf(exact_soln_y(ind_var)); omniout_complex(ALWAYS, "y[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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := (clock_sec1) - (glob_orig_start_sec); > glob_clock_sec := (clock_sec1) - (glob_clock_start_sec); > left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1); > expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec)); > opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); > percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr((total_clock_sec)); > if (c(percent_done) < glob__100) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr((expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr((glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr((glob_total_exp_sec)); > fi;# end if 3; > #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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := clock_sec1 - glob_orig_start_sec; glob_clock_sec := clock_sec1 - glob_clock_start_sec; left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1; expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, clock_sec1 - glob_orig_start_sec); opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec; glob_optimal_expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec) ; glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec); percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(total_clock_sec); 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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no; > #TOP CHECK FOR POLE > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,1] := glob_larger_float; > array_ord_test_poles[1,1] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 3 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 3; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 4 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 5 > found_sing := 0; > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_rad_test_poles[1,1]) then # if number 6 > array_rad_test_poles[1,1] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,1] := rad_c; > array_ord_test_poles[1,1] := tmp_ord; > fi;# end if 6; > fi;# end if 5; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,2] := glob_larger_float; > array_ord_test_poles[1,2] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 5 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 5; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 6 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 7 > found_sing := 0; > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_rad_test_poles[1,2]) then # if number 8 > array_rad_test_poles[1,2] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,2] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 9 > glob_min_pole_est := rad_c; > fi;# end if 9; > array_ord_test_poles[1,2] := tmp_ord; > fi;# end if 8; > fi;# end if 7; > #BOTTOM general radius test1 > tmp_rad := glob_larger_float; > prev_tmp_rad := glob_larger_float; > tmp_ratio := glob_larger_float; > rad_c := glob_larger_float; > array_rad_test_poles[1,3] := glob_larger_float; > array_ord_test_poles[1,3] := glob_larger_float; > found_sing := 1; > last_no := ATS_MAX_TERMS - 1 - 10; > cnt := 0; > while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1 > tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > if (float_abs(prev_tmp_rad) > glob__0) then # if number 7 > tmp_ratio := tmp_rad / prev_tmp_rad; > else > tmp_ratio := glob_large_float; > fi;# end if 7; > if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7 > rad_c := tmp_rad; > elif > (cnt = 0) then # if number 8 > rad_c := tmp_rad; > elif > (cnt > 0) then # if number 9 > found_sing := 0; > fi;# end if 9; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > last_no := last_no + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 9 > if (rad_c < array_rad_test_poles[1,3]) then # if number 10 > array_rad_test_poles[1,3] := rad_c; > last_no := last_no - 1; > tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no); > array_rad_test_poles[1,3] := rad_c; > if (rad_c < glob_min_pole_est) then # if number 11 > glob_min_pole_est := rad_c; > fi;# end if 11; > array_ord_test_poles[1,3] := tmp_ord; > fi;# end if 10; > fi;# end if 9; > #BOTTOM general radius test1 > ; > if (true) then # if number 9 > display_poles(); > fi;# end if 9 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio, prev_tmp_rad, last_no; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 1] := glob_larger_float; array_ord_test_poles[1, 1] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 1] then array_rad_test_poles[1, 1] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 1] := rad_c; array_ord_test_poles[1, 1] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 2] := glob_larger_float; array_ord_test_poles[1, 2] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do tmp_rad := comp_rad_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 2] then array_rad_test_poles[1, 2] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_three_terms( array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 2] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 2] := tmp_ord end if end if; tmp_rad := glob_larger_float; prev_tmp_rad := glob_larger_float; tmp_ratio := glob_larger_float; rad_c := glob_larger_float; array_rad_test_poles[1, 3] := glob_larger_float; array_ord_test_poles[1, 3] := glob_larger_float; found_sing := 1; last_no := ATS_MAX_TERMS - 11; cnt := 0; while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); if glob__0 < float_abs(prev_tmp_rad) then tmp_ratio := tmp_rad/prev_tmp_rad else tmp_ratio := glob_large_float end if; if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad elif cnt = 0 then rad_c := tmp_rad elif 0 < cnt then found_sing := 0 end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; last_no := last_no + 1 end do; if found_sing = 1 then if rad_c < array_rad_test_poles[1, 3] then array_rad_test_poles[1, 3] := rad_c; last_no := last_no - 1; tmp_ord := comp_ord_from_six_terms( array_y_higher[1, last_no - 5], array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3], array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1], array_y_higher[1, last_no], last_no); array_rad_test_poles[1, 3] := rad_c; if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c end if; array_ord_test_poles[1, 3] := tmp_ord end if end if; 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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > # before write maple main top matter > # before generate constants assign > # before generate globals assign > #END OUTFILE1 > #BEGIN OUTFILE2 > #END OUTFILE2 > #BEGIN ATOMHDR1 > #emit pre tan $eq_no = 1 > array_tmp1_a1[1] := sin(array_x[1]); > array_tmp1_a2[1] := cos(array_x[1]); > array_tmp1[1] := (array_tmp1_a1[1] / array_tmp1_a2[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_y_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_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre tan $eq_no = 1 > array_tmp1_a1[2] := array_tmp1_a2[1] * array_x[2] / c(1); > array_tmp1_a2[2] := neg(array_tmp1_a1[1]) * array_x[2] / c(1); > array_tmp1[2] := (array_tmp1_a1[2] - ats(2,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #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_y_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_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre tan $eq_no = 1 > array_tmp1_a1[3] := array_tmp1_a2[2] * array_x[2] / c(2); > array_tmp1_a2[3] := neg(array_tmp1_a1[2]) * array_x[2] / c(2); > array_tmp1[3] := (array_tmp1_a1[3] - ats(3,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #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_y_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_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre tan $eq_no = 1 > array_tmp1_a1[4] := array_tmp1_a2[3] * array_x[2] / c(3); > array_tmp1_a2[4] := neg(array_tmp1_a1[3]) * array_x[2] / c(3); > array_tmp1[4] := (array_tmp1_a1[4] - ats(4,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #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_y_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_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre tan $eq_no = 1 > array_tmp1_a1[5] := array_tmp1_a2[4] * array_x[2] / c(4); > array_tmp1_a2[5] := neg(array_tmp1_a1[4]) * array_x[2] / c(4); > array_tmp1[5] := (array_tmp1_a1[5] - ats(5,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #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_y_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_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > array_tmp1_a1[kkk] := array_tmp1_a2[kkk-1] * array_x[2] / c(kkk - 1); > array_tmp1_a2[kkk] := neg(array_tmp1_a1[kkk-1]) * array_x[2] / c(kkk - 1); > array_tmp1[kkk] := (array_tmp1_a1[kkk] - ats(kkk ,array_tmp1_a2,array_tmp1,2)) / array_tmp1_a2[1]; > #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_y_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_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; array_tmp1_a1[1] := sin(array_x[1]); array_tmp1_a2[1] := cos(array_x[1]); array_tmp1[1] := array_tmp1_a1[1]/array_tmp1_a2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_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_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1_a1[2] := array_tmp1_a2[1]*array_x[2]/c(1); array_tmp1_a2[2] := neg(array_tmp1_a1[1])*array_x[2]/c(1); array_tmp1[2] := ( array_tmp1_a1[2] - ats(2, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[2] := array_tmp1[2]; if not array_y_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_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp1_a1[3] := array_tmp1_a2[2]*array_x[2]/c(2); array_tmp1_a2[3] := neg(array_tmp1_a1[2])*array_x[2]/c(2); array_tmp1[3] := ( array_tmp1_a1[3] - ats(3, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[3] := array_tmp1[3]; if not array_y_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_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp1_a1[4] := array_tmp1_a2[3]*array_x[2]/c(3); array_tmp1_a2[4] := neg(array_tmp1_a1[3])*array_x[2]/c(3); array_tmp1[4] := ( array_tmp1_a1[4] - ats(4, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[4] := array_tmp1[4]; if not array_y_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_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp1_a1[5] := array_tmp1_a2[4]*array_x[2]/c(4); array_tmp1_a2[5] := neg(array_tmp1_a1[4])*array_x[2]/c(4); array_tmp1[5] := ( array_tmp1_a1[5] - ats(5, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[5] := array_tmp1[5]; if not array_y_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_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp1_a1[kkk] := array_tmp1_a2[kkk - 1]*array_x[2]/c(kkk - 1); array_tmp1_a2[kkk] := neg(array_tmp1_a1[kkk - 1])*array_x[2]/c(kkk - 1); array_tmp1[kkk] := ( array_tmp1_a1[kkk] - ats(kkk, array_tmp1_a2, array_tmp1, 2))/ array_tmp1_a2[1]; array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_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_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 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_y_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_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1_g, > array_tmp1_a1, > array_tmp1_a2, > array_tmp1, > array_tmp2, > array_m1, > array_y_higher, > array_y_higher_work, > array_y_higher_work2, > array_y_set_initial, > array_given_rad_poles, > array_given_ord_poles, > array_rad_test_poles, > array_ord_test_poles, > array_fact_2, > ATS_MAX_TERMS, > glob_last; > ATS_MAX_TERMS := 40; > # before first input block > #BEGIN FIRST INPUT BLOCK > #BEGIN BLOCK 1 > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=40; > #END BLOCK 1 > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > # before generate arrays > array_y_init:= Array(0..(40),[]); > array_norms:= Array(0..(40),[]); > array_fact_1:= Array(0..(40),[]); > array_1st_rel_error:= Array(0..(2),[]); > array_last_rel_error:= Array(0..(2),[]); > array_est_rel_error:= Array(0..(2),[]); > array_max_est_error:= Array(0..(2),[]); > array_type_pole:= Array(0..(2),[]); > array_type_real_pole:= Array(0..(2),[]); > array_type_complex_pole:= Array(0..(2),[]); > array_est_digits:= Array(0..(2),[]); > array_y:= Array(0..(40),[]); > array_x:= Array(0..(40),[]); > array_tmp0:= Array(0..(40),[]); > array_tmp1_g:= Array(0..(40),[]); > array_tmp1_a1:= Array(0..(40),[]); > array_tmp1_a2:= Array(0..(40),[]); > array_tmp1:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_y_higher := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]); > array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]); > array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]); > array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]); > array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]); > array_fact_2 := Array(0..(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_y_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 <= 2) do # do number 1 > array_1st_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_last_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_rel_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_max_est_error[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_real_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_type_complex_pole[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 2) do # do number 1 > array_est_digits[term] := 0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_y[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_tmp0[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1_g[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1_a1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp1_a2[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_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_y_higher[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_higher_work2[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_y_set_initial[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_rad_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 4) do # do number 2 > array_ord_test_poles[ord,term] := c(0.0); > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=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_y); > zero_ats_ar(array_x); > zero_ats_ar(array_tmp0); > zero_ats_ar(array_tmp1_g); > zero_ats_ar(array_tmp1_a1); > zero_ats_ar(array_tmp1_a2); > zero_ats_ar(array_tmp1); > zero_ats_ar(array_tmp2); > 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_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := false; > array_y_set_initial[1,3] := false; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > array_y_set_initial[1,31] := false; > array_y_set_initial[1,32] := false; > array_y_set_initial[1,33] := false; > array_y_set_initial[1,34] := false; > array_y_set_initial[1,35] := false; > array_y_set_initial[1,36] := false; > array_y_set_initial[1,37] := false; > array_y_set_initial[1,38] := false; > array_y_set_initial[1,39] := false; > array_y_set_initial[1,40] := 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 := 1; > 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/tanpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( x ) ; "); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=40;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(1.570796327);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > 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_y := proc(x)"); > omniout_str(ALWAYS,"return(neg(ln(cos(c(x)))));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"next_delta := proc()"); > omniout_str(ALWAYS,"global glob_nxt, x_delta;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.004 * I,"); > omniout_str(ALWAYS,"0.003 + 0.006 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.005 * I,"); > omniout_str(ALWAYS,"0.0001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.001 + 0.001 * I,"); > omniout_str(ALWAYS,"0.001 + 0.003 * I,"); > omniout_str(ALWAYS,"0.000 + 0.000 * I ];"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;"); > omniout_str(ALWAYS,"it := x_delta[glob_nxt];"); > omniout_str(ALWAYS,"return it;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := glob__0; > glob_smallish_float := glob__0; > glob_large_float := c(1.0e100); > glob_larger_float := c( 1.1e100); > glob_almost_1 := c( 0.99); > # before second block > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #BEGIN BLOCK 2 > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1 + 0.1 * I; > x_end := 99.0 + 99.0 * I; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_look_poles := true; > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(1.570796327); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.0); > array_given_ord_poles[1,2] := c(0.0); > #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 9 > h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius; > omniout_str(ALWAYS,"SETTING H FOR POLE"); > glob_h_reason := 6; > if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 10; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 9; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > found_h := true; > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := c(x_start); > array_x[2] := c(glob_h); > glob_next_display := c(x_start); > glob_min_pole_est := glob_larger_float; > glob_least_given_sing := glob_larger_float; > glob_least_ratio_sing := glob_larger_float; > glob_least_3_sing := glob_larger_float; > glob_least_6_sing := glob_larger_float; > order_diff := 1; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1)); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > if (term_no < ATS_MAX_TERMS) then # if number 10 > array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1))); > fi;# end if 10; > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > 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 10 > 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 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 1 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 10; > #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 10 > omniout_str(INFO," "); > fi;# end if 10; > 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 10 > 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 11 > omniout_str(ALWAYS,"SETTING H FOR MIN H"); > h_new := glob_min_h; > glob_h_reason := 5; > fi;# end if 11; > term := 1; > ratio := c(1.0); > while (term <= ATS_MAX_TERMS) do # do number 2 > array_y[term] := array_y[term]* ratio; > array_y_higher[1,term] := array_y_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / float_abs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 10; > #BOTTOM ADJUST ALL SERIES > #END OPTIMIZE CODE > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > atomall(); > if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10 > display_alot(current_iter); > fi;# end if 10; > if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10 > check_for_pole(); > fi;# end if 10; > if (true) then # if number 10 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 10; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1)); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := glob__0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := ATS_MAX_TERMS; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := ATS_MAX_TERMS; > while (term_no >= 1) do # do number 2 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 10 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 10; > if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 10; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = tan ( x ) ; "); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 10 > logstart(html_log_file); > logitem_str(html_log_file,"2017-11-26T16:51:35-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"tan") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( x ) ; ") > ; > logitem_complex(html_log_file,x_start) > ; > logitem_complex(html_log_file,x_end) > ; > logitem_complex(html_log_file,array_x[1]) > ; > logitem_complex(html_log_file,glob_h) > ; > logitem_h_reason(html_log_file) > ; > logitem_integer(html_log_file,Digits) > ; > ; > glob_desired_digits_correct := 0.0; > logitem_float(html_log_file,glob_desired_digits_correct) > ; > if (array_est_digits[1] <> -16) then # if number 11 > logitem_integer(html_log_file,array_est_digits[1]) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_min_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_min_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > if (glob_good_digits <> -16) then # if number 11 > logitem_integer(html_log_file,glob_good_digits) > ; > else > logitem_str(html_log_file,"Unknown") > ; > fi;# end if 11; > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > logitem_integer(html_log_file,ATS_MAX_TERMS) > ; > if (glob_type_given_pole = 0) then # if number 11 > logitem_str(html_log_file,"Not Given") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 4) then # if number 12 > logitem_str(html_log_file,"No Solution") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 5) then # if number 13 > logitem_str(html_log_file,"Some Pole") > ; > logitem_str(html_log_file,"????") > ; > elif > (glob_type_given_pole = 3) then # if number 14 > logitem_str(html_log_file,"No Pole") > ; > logitem_str(html_log_file,"NA") > ; > elif > (glob_type_given_pole = 1) then # if number 15 > logitem_str(html_log_file,"Real Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > elif > (glob_type_given_pole = 2) then # if number 16 > logitem_str(html_log_file,"Complex Sing") > ; > logitem_float(html_log_file,glob_least_given_sing) > ; > fi;# end if 16; > if (glob_least_ratio_sing < glob_large_float) then # if number 16 > glob_least_ratio_sing := 0; > logitem_float(html_log_file,glob_least_ratio_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_3_sing < glob_large_float) then # if number 16 > logitem_float(html_log_file,glob_least_3_sing) > ; > else > logitem_str(html_log_file,"NONE") > ; > fi;# end if 16; > if (glob_least_6_sing < glob_large_float) then # if number 16 > 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 16; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,(glob_clock_sec)) > ; > if (c(glob_percent_done) < glob__100) then # if number 16 > logitem_time(html_log_file,(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 16; > log_revs(html_log_file," 309 ") > ; > logitem_str(html_log_file,"tan diffeq.mxt") > ; > logitem_str(html_log_file,"tan maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > 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_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1_g, array_tmp1_a1, array_tmp1_a2, array_tmp1, array_tmp2, array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2, array_y_set_initial, array_given_rad_poles, array_given_ord_poles, array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last; ATS_MAX_TERMS := 40; Digits := 32; max_terms := 40; glob_html_log := true; array_y_init := Array(0 .. 40, []); array_norms := Array(0 .. 40, []); array_fact_1 := Array(0 .. 40, []); array_1st_rel_error := Array(0 .. 2, []); array_last_rel_error := Array(0 .. 2, []); array_est_rel_error := Array(0 .. 2, []); array_max_est_error := Array(0 .. 2, []); array_type_pole := Array(0 .. 2, []); array_type_real_pole := Array(0 .. 2, []); array_type_complex_pole := Array(0 .. 2, []); array_est_digits := Array(0 .. 2, []); array_y := Array(0 .. 40, []); array_x := Array(0 .. 40, []); array_tmp0 := Array(0 .. 40, []); array_tmp1_g := Array(0 .. 40, []); array_tmp1_a1 := Array(0 .. 40, []); array_tmp1_a2 := Array(0 .. 40, []); array_tmp1 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_y_higher := Array(0 .. 2, 0 .. 41, []); array_y_higher_work := Array(0 .. 2, 0 .. 41, []); array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []); array_y_set_initial := Array(0 .. 2, 0 .. 41, []); array_given_rad_poles := Array(0 .. 2, 0 .. 4, []); array_given_ord_poles := Array(0 .. 2, 0 .. 4, []); array_rad_test_poles := Array(0 .. 2, 0 .. 5, []); array_ord_test_poles := Array(0 .. 2, 0 .. 5, []); array_fact_2 := Array(0 .. 40, 0 .. 41, []); term := 1; while term <= 40 do array_y_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 <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_last_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1 end do; term := 1; while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_real_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1 end do; term := 1; while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do ; term := 1; while term <= 40 do array_y[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_tmp0[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1_a1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp1_a2[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_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_higher_work2[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_y_set_initial[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_rad_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 4 do array_ord_test_poles[ord, term] := c(0.); term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_y); zero_ats_ar(array_x); zero_ats_ar(array_tmp0); zero_ats_ar(array_tmp1_g); zero_ats_ar(array_tmp1_a1); zero_ats_ar(array_tmp1_a2); zero_ats_ar(array_tmp1); zero_ats_ar(array_tmp2); 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_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := false; array_y_set_initial[1, 3] := false; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 30] := false; array_y_set_initial[1, 31] := false; array_y_set_initial[1, 32] := false; array_y_set_initial[1, 33] := false; array_y_set_initial[1, 34] := false; array_y_set_initial[1, 35] := false; array_y_set_initial[1, 36] := false; array_y_set_initial[1, 37] := false; array_y_set_initial[1, 38] := false; array_y_set_initial[1, 39] := false; array_y_set_initial[1, 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 := 1; 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/tanpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( x ) ; ") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=40;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(1.570796327);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); 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_y := proc(x)"); omniout_str(ALWAYS, "return(neg(ln(cos(c(x)))));"); omniout_str(ALWAYS, "end;"); 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,"); 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omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 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(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 0.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(1.570796327); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.); array_given_ord_poles[1, 2] := c(0.); 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_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; if 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_y[term_no] := array_y_init[term_no]* expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1)); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; if term_no < ATS_MAX_TERMS then array_y_higher[r_order, term_no] := array_y_init[it]* expt(glob_h, c(term_no - 1))/ c(factorial_1(term_no - 1)) end if; term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; 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_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; 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_y[term] := array_y[term]*ratio; array_y_higher[1, term] := array_y_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/float_abs(glob_h); term := term + 1 end do; glob_h := h_new end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); atomall(); 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_y_higher_work[2, iii] := array_y_higher[2, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 2; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 2; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( expt(glob_h, c(calc_term - 1))* c(factorial_3(iii - calc_term, iii - 1))); iii := iii - 1 end do; temp_sum := glob__0; ord := 1; calc_term := 1; iii := ATS_MAX_TERMS; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, c(calc_term - 1))/ c(factorial_1(calc_term - 1)); term_no := ATS_MAX_TERMS; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = tan ( x ) ; "); 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, "2017-11-26T16:51:35-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "tan"); logitem_str(html_log_file, "diff ( y , x , 1 ) = tan ( x ) ; "); logitem_complex(html_log_file, x_start); logitem_complex(html_log_file, x_end); logitem_complex(html_log_file, array_x[1]); logitem_complex(html_log_file, glob_h); logitem_h_reason(html_log_file); logitem_integer(html_log_file, Digits); glob_desired_digits_correct := 0.; logitem_float(html_log_file, glob_desired_digits_correct); if array_est_digits[1] <> -16 then logitem_integer(html_log_file, array_est_digits[1]) else logitem_str(html_log_file, "Unknown") end if; if glob_min_good_digits <> -16 then logitem_integer(html_log_file, glob_min_good_digits) else logitem_str(html_log_file, "Unknown") end if; if glob_good_digits <> -16 then logitem_integer(html_log_file, glob_good_digits) else logitem_str(html_log_file, "Unknown") end if; logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); logitem_integer(html_log_file, ATS_MAX_TERMS); if glob_type_given_pole = 0 then logitem_str(html_log_file, "Not Given"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 4 then logitem_str(html_log_file, "No Solution"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 5 then logitem_str(html_log_file, "Some Pole"); logitem_str(html_log_file, "????") elif glob_type_given_pole = 3 then logitem_str(html_log_file, "No Pole"); logitem_str(html_log_file, "NA") elif glob_type_given_pole = 1 then logitem_str(html_log_file, "Real Sing"); logitem_float(html_log_file, glob_least_given_sing) elif glob_type_given_pole = 2 then logitem_str(html_log_file, "Complex Sing"); logitem_float(html_log_file, glob_least_given_sing) end if; if glob_least_ratio_sing < glob_large_float then glob_least_ratio_sing := 0; logitem_float(html_log_file, glob_least_ratio_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_3_sing < glob_large_float then logitem_float(html_log_file, glob_least_3_sing) else logitem_str(html_log_file, "NONE") end if; if glob_least_6_sing < glob_large_float then glob_least_6_sing := 0.; logitem_float(html_log_file, glob_least_6_sing) else logitem_str(html_log_file, "NONE") end if; logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, glob_clock_sec); if c(glob_percent_done) < glob__100 then logitem_time(html_log_file, glob_total_exp_sec); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 309 "); logitem_str(html_log_file, "tan diffeq.mxt"); logitem_str(html_log_file, "tan maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.9MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/tanpostcpx.cpx################# diff ( y , x , 1 ) = tan ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1 + 0.1 * I; x_end := 99.0 + 99.0 * I; array_y_init[0 + 1] := exact_soln_y(x_start); glob_look_poles := true; glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(1.570796327); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.0); array_given_ord_poles[1,2] := c(0.0); #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_y := proc(x) return(neg(ln(cos(c(x))))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 0.1 h = 0.0001 0.005 y[1] (numeric) = -3.33322540155e-05 0.00999982222922 y[1] (closed_form) = -3.33322540155e-05 0.00999982222922 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = -0.000536704658607 0.010506775804 y[1] (closed_form) = -0.000539203489427 0.010506774275 absolute error = 2.499e-06 relative error = 0.02375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=27.1MB, alloc=40.3MB, time=0.34 x[1] = 0.1002 0.108 h = 0.001 0.001 y[1] (numeric) = -0.000851241578742 0.0108155577935 y[1] (closed_form) = -0.000850743859916 0.0108155210131 absolute error = 4.991e-07 relative error = 0.0046 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.475 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1012 0.109 h = 0.001 0.003 y[1] (numeric) = -0.000862017510831 0.0110250910589 y[1] (closed_form) = -0.000860060860379 0.0110245372686 absolute error = 2.034e-06 relative error = 0.01839 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = -0.00109175188357 0.0114377547048 y[1] (closed_form) = -0.00109281126202 0.0114381315217 absolute error = 1.124e-06 relative error = 0.009786 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1023 0.116 h = 0.003 0.006 y[1] (numeric) = -0.00153837878743 0.011856103966 y[1] (closed_form) = -0.00154143631153 0.0118546880918 absolute error = 3.369e-06 relative error = 0.02819 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = -0.0019466094645 0.0128197973194 y[1] (closed_form) = -0.00195159758719 0.0128299946396 absolute error = 1.135e-05 relative error = 0.08747 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = -0.0025648560088 0.0133600269442 y[1] (closed_form) = -0.0025673068923 0.0133630229164 absolute error = 3.871e-06 relative error = 0.02845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1055 0.13 h = 0.001 0.001 y[1] (numeric) = -0.00294504665573 0.013685249961 y[1] (closed_form) = -0.00294451331622 0.01368822796 absolute error = 3.025e-06 relative error = 0.02161 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1065 0.131 h = 0.001 0.003 y[1] (numeric) = -0.00297312336596 0.0139215518241 y[1] (closed_form) = -0.00297113432326 0.0139240233992 absolute error = 3.173e-06 relative error = 0.02228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=72.1MB, alloc=52.3MB, time=0.92 x[1] = 0.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = -0.00326425891823 0.0143704410954 y[1] (closed_form) = -0.00326527840077 0.0143738217512 absolute error = 3.531e-06 relative error = 0.02396 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.469 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1076 0.138 h = 0.003 0.006 y[1] (numeric) = -0.00379853907702 0.0148097941984 y[1] (closed_form) = -0.00380153726303 0.0148113783882 absolute error = 3.391e-06 relative error = 0.02218 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = -0.00432478961223 0.0158675664594 y[1] (closed_form) = -0.00432977863135 0.0158806981654 absolute error = 1.405e-05 relative error = 0.08534 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.467 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = -0.00505257458748 0.0164330603091 y[1] (closed_form) = -0.00505499454673 0.0164390416678 absolute error = 6.452e-06 relative error = 0.03752 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1108 0.152 h = 0.001 0.001 y[1] (numeric) = -0.00549821233092 0.0167742588475 y[1] (closed_form) = -0.00549766317022 0.0167802406718 absolute error = 6.007e-06 relative error = 0.03402 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1118 0.153 h = 0.001 0.003 y[1] (numeric) = -0.00554366752058 0.0170370999961 y[1] (closed_form) = -0.00554166704904 0.0170425870101 absolute error = 5.840e-06 relative error = 0.03259 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.467 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = -0.00589613323631 0.0175216750007 y[1] (closed_form) = -0.00589713132476 0.0175280475771 absolute error = 6.450e-06 relative error = 0.03488 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.466 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1129 0.16 h = 0.003 0.006 y[1] (numeric) = -0.00651776759669 0.0179813952695 y[1] (closed_form) = -0.00652072242709 0.017985968535 absolute error = 5.445e-06 relative error = 0.02846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.467 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=117.1MB, alloc=52.3MB, time=1.46 x[1] = 0.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = -0.00716201514211 0.0191320468353 y[1] (closed_form) = -0.00716702347115 0.0191480904599 absolute error = 1.681e-05 relative error = 0.08221 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.116 0.171 h = 0.0001 0.003 y[1] (numeric) = -0.0079989147434 0.0197219714772 y[1] (closed_form) = -0.00800132198376 0.0197309233363 absolute error = 9.270e-06 relative error = 0.04354 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1161 0.174 h = 0.001 0.001 y[1] (numeric) = -0.00850973803291 0.020078640838 y[1] (closed_form) = -0.00850919400808 0.020087612669 absolute error = 8.988e-06 relative error = 0.0412 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1171 0.175 h = 0.001 0.003 y[1] (numeric) = -0.00857264307543 0.020367760876 y[1] (closed_form) = -0.00857065329922 0.0203762504879 absolute error = 8.720e-06 relative error = 0.03945 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = -0.00898632405025 0.0208874258787 y[1] (closed_form) = -0.0089873204047 0.0208967756462 absolute error = 9.403e-06 relative error = 0.04134 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1182 0.182 h = 0.003 0.006 y[1] (numeric) = -0.00969493980887 0.021366825847 y[1] (closed_form) = -0.00969786850054 0.0213743744356 absolute error = 8.097e-06 relative error = 0.0345 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = -0.0104570856741 0.0226090285193 y[1] (closed_form) = -0.0104621326035 0.0226279590115 absolute error = 1.959e-05 relative error = 0.07859 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = -0.0114025835194 0.0232224895803 y[1] (closed_form) = -0.0114049973364 0.0232343943067 absolute error = 1.215e-05 relative error = 0.04693 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=162.2MB, alloc=52.3MB, time=2.01 x[1] = 0.1214 0.196 h = 0.001 0.001 y[1] (numeric) = -0.0119782760129 0.023594088157 y[1] (closed_form) = -0.0119777591373 0.0236060333285 absolute error = 1.196e-05 relative error = 0.04517 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.463 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = -0.0120586952632 0.0239091964437 y[1] (closed_form) = -0.0120567393629 0.0239206729097 absolute error = 1.164e-05 relative error = 0.04346 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1225 0.201 h = 0.003 0.006 y[1] (numeric) = -0.0128381460393 0.0244040118154 y[1] (closed_form) = -0.0128420029758 0.0244135951794 absolute error = 1.033e-05 relative error = 0.03745 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = -0.0137027033129 0.0257224592001 y[1] (closed_form) = -0.0137087343519 0.0257433386498 absolute error = 2.173e-05 relative error = 0.07452 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = -0.0147414598621 0.0263541363953 y[1] (closed_form) = -0.0147448312996 0.0263680530621 absolute error = 1.432e-05 relative error = 0.0474 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1257 0.215 h = 0.001 0.001 y[1] (numeric) = -0.0153728630818 0.0267373589115 y[1] (closed_form) = -0.0153733239364 0.0267513340505 absolute error = 1.398e-05 relative error = 0.04532 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1267 0.216 h = 0.001 0.003 y[1] (numeric) = -0.0154687079542 0.0270743723643 y[1] (closed_form) = -0.0154677366811 0.0270878910239 absolute error = 1.355e-05 relative error = 0.04345 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = -0.0159962366484 0.0276568410287 y[1] (closed_form) = -0.0159982214902 0.0276711681531 absolute error = 1.446e-05 relative error = 0.04525 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=207.4MB, alloc=52.3MB, time=2.55 x[1] = 0.1278 0.223 h = 0.003 0.006 y[1] (numeric) = -0.0168656737765 0.0281698476702 y[1] (closed_form) = -0.0168695393518 0.0281823732521 absolute error = 1.311e-05 relative error = 0.03991 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = -0.0178477186394 0.029577053454 y[1] (closed_form) = -0.0178538257674 0.0296007662448 absolute error = 2.449e-05 relative error = 0.07084 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = -0.0189938557778 0.0302304636805 y[1] (closed_form) = -0.0189972719661 0.0302472929565 absolute error = 1.717e-05 relative error = 0.04808 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.459 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.131 0.237 h = 0.001 0.001 y[1] (numeric) = -0.0196893874868 0.0306275233231 y[1] (closed_form) = -0.0196899186096 0.0306444330237 absolute error = 1.692e-05 relative error = 0.04645 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.459 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.132 0.238 h = 0.001 0.003 y[1] (numeric) = -0.0198028409787 0.0309899065495 y[1] (closed_form) = -0.0198019488698 0.0310063748244 absolute error = 1.649e-05 relative error = 0.04483 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.133 0.241 h = 0.0001 0.004 y[1] (numeric) = -0.0203910002123 0.031605478047 y[1] (closed_form) = -0.0203930447724 0.0316227246625 absolute error = 1.737e-05 relative error = 0.04616 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1331 0.245 h = 0.003 0.006 y[1] (numeric) = -0.0213459381626 0.0321359536894 y[1] (closed_form) = -0.0213498325856 0.0321513999633 absolute error = 1.593e-05 relative error = 0.04127 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=252.5MB, alloc=52.3MB, time=3.10 x[1] = 0.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = -0.0224451442866 0.0336302523753 y[1] (closed_form) = -0.0224513486663 0.0336567664226 absolute error = 2.723e-05 relative error = 0.06731 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = -0.02369788376 0.0343043517034 y[1] (closed_form) = -0.0237013665102 0.0343240683023 absolute error = 2.002e-05 relative error = 0.048 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1363 0.259 h = 0.001 0.001 y[1] (numeric) = -0.0244570727315 0.0347146162532 y[1] (closed_form) = -0.024457698503 0.0347344358766 absolute error = 1.983e-05 relative error = 0.04668 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1373 0.26 h = 0.001 0.003 y[1] (numeric) = -0.024588174954 0.0351019978948 y[1] (closed_form) = -0.0245873875368 0.0351213918869 absolute error = 1.941e-05 relative error = 0.04527 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = -0.0252366756357 0.0357498859144 y[1] (closed_form) = -0.0252388030383 0.0357700267185 absolute error = 2.025e-05 relative error = 0.04626 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1384 0.267 h = 0.003 0.006 y[1] (numeric) = -0.0262764607813 0.03629697946 y[1] (closed_form) = -0.0262804051192 0.0363153222668 absolute error = 1.876e-05 relative error = 0.04185 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = -0.0274924201108 0.0378765992606 y[1] (closed_form) = -0.0274987433467 0.0379058801776 absolute error = 2.996e-05 relative error = 0.06397 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = -0.0288508945266 0.0385703002227 y[1] (closed_form) = -0.0288544663227 0.0385928762904 absolute error = 2.286e-05 relative error = 0.04743 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=297.6MB, alloc=52.3MB, time=3.65 x[1] = 0.1416 0.281 h = 0.001 0.001 y[1] (numeric) = -0.0296732168519 0.0389931110663 y[1] (closed_form) = -0.0296739622567 0.0390158132862 absolute error = 2.271e-05 relative error = 0.04634 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1426 0.282 h = 0.001 0.003 y[1] (numeric) = -0.0298219982493 0.0394050938526 y[1] (closed_form) = -0.0298213416419 0.0394273869056 absolute error = 2.230e-05 relative error = 0.04512 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = -0.0305305058359 0.0400844699754 y[1] (closed_form) = -0.0305327398298 0.0401074770506 absolute error = 2.312e-05 relative error = 0.04586 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1437 0.289 h = 0.003 0.006 y[1] (numeric) = -0.0316544141929 0.04064729693 y[1] (closed_form) = -0.0316584302582 0.0406685095322 absolute error = 2.159e-05 relative error = 0.04189 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = -0.0329866359245 0.0423103666685 y[1] (closed_form) = -0.0329930999449 0.0423423778574 absolute error = 3.266e-05 relative error = 0.06084 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = -0.0344498903565 0.0430225433305 y[1] (closed_form) = -0.0344535742358 0.0430479485133 absolute error = 2.567e-05 relative error = 0.04656 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1469 0.303 h = 0.001 0.001 y[1] (numeric) = -0.0353347704107 0.0434572185169 y[1] (closed_form) = -0.0353356609093 0.0434827733847 absolute error = 2.557e-05 relative error = 0.04564 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = -0.0355012511131 0.0438933806351 y[1] (closed_form) = -0.0355007518916 0.0439185433979 absolute error = 2.517e-05 relative error = 0.04457 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=342.7MB, alloc=52.3MB, time=4.20 x[1] = 0.148 0.308 h = 0.003 0.006 y[1] (numeric) = -0.0366933928617 0.0444682673353 y[1] (closed_form) = -0.0366983614619 0.0444914033163 absolute error = 2.366e-05 relative error = 0.04103 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.151 0.314 h = 0.0001 0.005 y[1] (numeric) = -0.0381261946462 0.0462002236772 y[1] (closed_form) = -0.0381336685993 0.0462340297413 absolute error = 3.462e-05 relative error = 0.05777 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = -0.03967901133 0.0469261453996 y[1] (closed_form) = -0.0396836827704 0.0469534356215 absolute error = 2.769e-05 relative error = 0.04504 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1512 0.322 h = 0.001 0.001 y[1] (numeric) = -0.0406173693016 0.0473697365118 y[1] (closed_form) = -0.0406192779354 0.0473971964738 absolute error = 2.753e-05 relative error = 0.0441 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1522 0.323 h = 0.001 0.003 y[1] (numeric) = -0.0407993735252 0.0478261449949 y[1] (closed_form) = -0.0407999041077 0.0478532277949 absolute error = 2.709e-05 relative error = 0.04308 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = -0.0416188443269 0.048561075011 y[1] (closed_form) = -0.0416222138727 0.048588808324 absolute error = 2.794e-05 relative error = 0.04367 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1533 0.33 h = 0.003 0.006 y[1] (numeric) = -0.0428972856496 0.0491497483332 y[1] (closed_form) = -0.0429023677571 0.0491756974459 absolute error = 2.644e-05 relative error = 0.04052 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = -0.044445189222 0.050961441619 y[1] (closed_form) = -0.0444528447256 0.0509979040489 absolute error = 3.726e-05 relative error = 0.05507 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=387.9MB, alloc=52.3MB, time=4.74 x[1] = 0.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = -0.0461007685655 0.0517036732713 y[1] (closed_form) = -0.046105595581 0.0517337294586 absolute error = 3.044e-05 relative error = 0.04393 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1565 0.344 h = 0.001 0.001 y[1] (numeric) = -0.047100470935 0.052157816734 y[1] (closed_form) = -0.0471025724298 0.0521880665918 absolute error = 3.032e-05 relative error = 0.04313 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1575 0.345 h = 0.001 0.003 y[1] (numeric) = -0.0473001767515 0.0526375594598 y[1] (closed_form) = -0.0473009145072 0.0526674501152 absolute error = 2.990e-05 relative error = 0.04224 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = -0.0481784364148 0.0534014119001 y[1] (closed_form) = -0.0481819823912 0.0534319175251 absolute error = 3.071e-05 relative error = 0.04269 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1586 0.352 h = 0.003 0.006 y[1] (numeric) = -0.0495385431303 0.0540031523818 y[1] (closed_form) = -0.0495437620052 0.0540318808919 absolute error = 2.920e-05 relative error = 0.03983 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = -0.0512008169298 0.0558924693405 y[1] (closed_form) = -0.0512086761645 0.0559315457816 absolute error = 3.986e-05 relative error = 0.05256 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = -0.0529579649184 0.056649805078 y[1] (closed_form) = -0.0529629714232 0.0566825901761 absolute error = 3.317e-05 relative error = 0.04275 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1618 0.366 h = 0.001 0.001 y[1] (numeric) = -0.0540182948849 0.0571137703031 y[1] (closed_form) = -0.0540206153096 0.057146773054 absolute error = 3.308e-05 relative error = 0.04207 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=433.2MB, alloc=52.3MB, time=5.29 x[1] = 0.1628 0.367 h = 0.001 0.003 y[1] (numeric) = -0.0542356894428 0.0576163636993 y[1] (closed_form) = -0.054236661483 0.0576490255867 absolute error = 3.268e-05 relative error = 0.04128 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = -0.0551722296814 0.0584081811408 y[1] (closed_form) = -0.0551759770412 0.05844142178 absolute error = 3.345e-05 relative error = 0.04162 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1639 0.374 h = 0.003 0.006 y[1] (numeric) = -0.05661302111 0.0590220154816 y[1] (closed_form) = -0.0566184002925 0.0590534873716 absolute error = 3.193e-05 relative error = 0.03903 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = -0.0583888496792 0.0609867731199 y[1] (closed_form) = -0.0583969347008 0.0610284194231 absolute error = 4.242e-05 relative error = 0.05023 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.167 0.385 h = 0.0001 0.003 y[1] (numeric) = -0.0602462938446 0.0617579892086 y[1] (closed_form) = -0.0602515038306 0.0617934640057 absolute error = 3.586e-05 relative error = 0.04154 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1671 0.388 h = 0.001 0.001 y[1] (numeric) = -0.061366488313 0.06223103465 y[1] (closed_form) = -0.0613690537065 0.0622667510122 absolute error = 3.581e-05 relative error = 0.04096 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1681 0.389 h = 0.001 0.003 y[1] (numeric) = -0.061601546348 0.0627559766267 y[1] (closed_form) = -0.0616027797214 0.0627913707662 absolute error = 3.542e-05 relative error = 0.04026 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = -0.0625958153066 0.0635747771299 memory used=478.5MB, alloc=52.3MB, time=5.84 y[1] (closed_form) = -0.0625997890131 0.0636107132845 absolute error = 3.616e-05 relative error = 0.04051 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1692 0.396 h = 0.003 0.006 y[1] (numeric) = -0.0641162494059 0.0641997192758 y[1] (closed_form) = -0.064121812593 0.0642338963411 absolute error = 3.463e-05 relative error = 0.03815 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = -0.0660047338551 0.0662376730803 y[1] (closed_form) = -0.0660130664839 0.0662818434234 absolute error = 4.495e-05 relative error = 0.04805 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.455 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = -0.0679611263104 0.0670215332934 y[1] (closed_form) = -0.0679665637249 0.067059656527 absolute error = 3.851e-05 relative error = 0.04033 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1724 0.41 h = 0.001 0.001 y[1] (numeric) = -0.0691403776967 0.0675029096891 y[1] (closed_form) = -0.0691432139388 0.0675412982112 absolute error = 3.849e-05 relative error = 0.03982 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = -0.0693930611152 0.0680496813376 y[1] (closed_form) = -0.0693945826751 0.0680877665024 absolute error = 3.812e-05 relative error = 0.03921 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1735 0.415 h = 0.003 0.006 y[1] (numeric) = -0.0709778278391 0.068682847113 y[1] (closed_form) = -0.0709843595312 0.0687187937775 absolute error = 3.654e-05 relative error = 0.03698 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = -0.0729633343442 0.0707806416934 y[1] (closed_form) = -0.072972686164 0.0708264193093 absolute error = 4.672e-05 relative error = 0.04595 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=523.8MB, alloc=52.3MB, time=6.39 x[1] = 0.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = -0.0750038941339 0.0715732345262 y[1] (closed_form) = -0.0750103367572 0.0716130756664 absolute error = 4.036e-05 relative error = 0.03892 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1767 0.429 h = 0.001 0.001 y[1] (numeric) = -0.0762333875423 0.0720604888091 y[1] (closed_form) = -0.0762372681008 0.072100614872 absolute error = 4.031e-05 relative error = 0.03842 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.459 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1777 0.43 h = 0.001 0.003 y[1] (numeric) = -0.0765014530887 0.0726254145315 y[1] (closed_form) = -0.076504034865 0.0726652533757 absolute error = 3.992e-05 relative error = 0.03784 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = -0.0776018203656 0.0734910725344 y[1] (closed_form) = -0.077607071661 0.0735313846547 absolute error = 4.065e-05 relative error = 0.03803 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1788 0.437 h = 0.003 0.006 y[1] (numeric) = -0.0792675821302 0.0741331167687 y[1] (closed_form) = -0.0792743414091 0.0741716917734 absolute error = 3.916e-05 relative error = 0.03607 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.459 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = -0.0813638247895 0.0762998087449 y[1] (closed_form) = -0.0813734632479 0.0763480208657 absolute error = 4.917e-05 relative error = 0.04406 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.458 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = -0.0835006206974 0.0771027483513 y[1] (closed_form) = -0.0835073342401 0.0771451558058 absolute error = 4.294e-05 relative error = 0.03777 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.459 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.182 0.451 h = 0.001 0.001 y[1] (numeric) = -0.0847875477199 0.0775969405626 y[1] (closed_form) = -0.0847917458837 0.0776396559879 absolute error = 4.292e-05 relative error = 0.03733 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=569.0MB, alloc=52.3MB, time=6.94 x[1] = 0.183 0.452 h = 0.001 0.003 y[1] (numeric) = -0.0850731258993 0.0781826924199 y[1] (closed_form) = -0.0850760443222 0.0782251396967 absolute error = 4.255e-05 relative error = 0.03681 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.184 0.455 h = 0.0001 0.004 y[1] (numeric) = -0.0862293986887 0.0790724314671 y[1] (closed_form) = -0.0862349461498 0.0791153146672 absolute error = 4.324e-05 relative error = 0.03695 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1841 0.459 h = 0.003 0.006 y[1] (numeric) = -0.0879714945842 0.0797227450545 y[1] (closed_form) = -0.0879785049048 0.0797639045315 absolute error = 4.175e-05 relative error = 0.03516 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = -0.0901773411069 0.0819559608287 y[1] (closed_form) = -0.0901872867709 0.0820065575554 absolute error = 5.156e-05 relative error = 0.0423 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = -0.0924088286206 0.0827680051109 y[1] (closed_form) = -0.0924158362349 0.0828129324033 absolute error = 4.547e-05 relative error = 0.03664 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1873 0.473 h = 0.001 0.001 y[1] (numeric) = -0.0937522657553 0.0832683818397 y[1] (closed_form) = -0.0937568062499 0.0833136396458 absolute error = 4.548e-05 relative error = 0.03626 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1883 0.474 h = 0.001 0.003 y[1] (numeric) = -0.0940552799484 0.0838744026371 y[1] (closed_form) = -0.0940585605933 0.0839194113753 absolute error = 4.513e-05 relative error = 0.0358 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.461 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = -0.0952667477377 0.0847871824426 y[1] (closed_form) = -0.0952726152065 0.0848325898139 absolute error = 4.578e-05 relative error = 0.03589 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=614.2MB, alloc=52.3MB, time=7.49 x[1] = 0.1894 0.481 h = 0.003 0.006 y[1] (numeric) = -0.0970839241561 0.0854447703625 y[1] (closed_form) = -0.0970912086727 0.085488468691 absolute error = 4.430e-05 relative error = 0.03425 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.463 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = -0.0993981639859 0.0877421069022 y[1] (closed_form) = -0.099408436811 0.0877950371641 absolute error = 5.392e-05 relative error = 0.04065 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.462 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = -0.101722737288 0.0885620211574 y[1] (closed_form) = -0.101730061644 0.088609420231 absolute error = 4.796e-05 relative error = 0.03555 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.463 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1926 0.495 h = 0.001 0.001 y[1] (numeric) = -0.103121724919 0.0890678332154 y[1] (closed_form) = -0.103126631854 0.0891155847404 absolute error = 4.800e-05 relative error = 0.03522 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1936 0.496 h = 0.001 0.003 y[1] (numeric) = -0.103442084741 0.0896935557431 y[1] (closed_form) = -0.103445752519 0.0897410772199 absolute error = 4.766e-05 relative error = 0.0348 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = -0.104707999268 0.0906283299095 y[1] (closed_form) = -0.104714210028 0.0906762129322 absolute error = 4.828e-05 relative error = 0.03486 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1947 0.503 h = 0.003 0.006 y[1] (numeric) = -0.106598955253 0.0912922044171 y[1] (closed_form) = -0.10660653671 0.0913383943486 absolute error = 4.681e-05 relative error = 0.03334 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.465 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = -0.109020301724 0.0936512374156 y[1] (closed_form) = -0.109030920972 0.0937064491055 absolute error = 5.622e-05 relative error = 0.03911 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.464 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=659.5MB, alloc=52.3MB, time=8.04 x[1] = 0.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = -0.111436297844 0.09447779909 y[1] (closed_form) = -0.111443961028 0.0945276204405 absolute error = 5.041e-05 relative error = 0.03449 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.466 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1979 0.517 h = 0.001 0.001 y[1] (numeric) = -0.112889842697 0.0949883043639 y[1] (closed_form) = -0.112895139462 0.0950384994042 absolute error = 5.047e-05 relative error = 0.0342 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.467 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = -0.113227443933 0.0956331531673 y[1] (closed_form) = -0.113231522983 0.0956831370501 absolute error = 5.015e-05 relative error = 0.03383 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.466 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.199 0.522 h = 0.003 0.006 y[1] (numeric) = -0.115177748246 0.0963013304684 y[1] (closed_form) = -0.115186300285 0.096349105433 absolute error = 4.853e-05 relative error = 0.03232 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.468 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.202 0.528 h = 0.0001 0.005 y[1] (numeric) = -0.117690897324 0.0987102644304 y[1] (closed_form) = -0.117702524193 0.0987668762778 absolute error = 5.779e-05 relative error = 0.03761 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.467 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = -0.120184274719 0.0995405205173 y[1] (closed_form) = -0.120192943029 0.0995918650772 absolute error = 5.207e-05 relative error = 0.03336 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.469 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2022 0.536 h = 0.001 0.001 y[1] (numeric) = -0.12168400547 0.100053845488 y[1] (closed_form) = -0.121690352439 0.100105580767 absolute error = 5.212e-05 relative error = 0.03308 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2032 0.537 h = 0.001 0.003 y[1] (numeric) = -0.12203657192 0.100714488309 y[1] (closed_form) = -0.122041720412 0.100766028271 absolute error = 5.180e-05 relative error = 0.03273 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.469 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=704.8MB, alloc=52.3MB, time=8.59 x[1] = 0.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = -0.123401917776 0.101686771972 y[1] (closed_form) = -0.123409523293 0.10173860603 absolute error = 5.239e-05 relative error = 0.03276 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.469 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2043 0.544 h = 0.003 0.006 y[1] (numeric) = -0.125426597353 0.102358915451 y[1] (closed_form) = -0.125435486608 0.102409089961 absolute error = 5.096e-05 relative error = 0.03147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = -0.128044235963 0.104825022754 y[1] (closed_form) = -0.128056242353 0.104883816568 absolute error = 6.001e-05 relative error = 0.03625 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.47 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = -0.130625790521 0.105659720224 y[1] (closed_form) = -0.130634836259 0.105713391317 absolute error = 5.443e-05 relative error = 0.03239 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.472 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2075 0.558 h = 0.001 0.001 y[1] (numeric) = -0.132178140958 0.10617639818 y[1] (closed_form) = -0.132184918401 0.106230479693 absolute error = 5.450e-05 relative error = 0.03214 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2085 0.559 h = 0.001 0.003 y[1] (numeric) = -0.132547711183 0.106855082157 y[1] (closed_form) = -0.132553312839 0.106908986826 absolute error = 5.419e-05 relative error = 0.03182 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = -0.133965157613 0.107846375048 y[1] (closed_form) = -0.13397316843 0.107900538044 absolute error = 5.475e-05 relative error = 0.03183 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2096 0.566 h = 0.003 0.006 y[1] (numeric) = -0.136059652905 0.10852206924 y[1] (closed_form) = -0.136068900378 0.10857459213 absolute error = 5.333e-05 relative error = 0.03064 % Correct digits = 4 memory used=750.2MB, alloc=52.3MB, time=9.19 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = -0.138780291505 0.1110429089 y[1] (closed_form) = -0.138792694297 0.111103830367 absolute error = 6.217e-05 relative error = 0.03497 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.474 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = -0.141448221345 0.111880884543 y[1] (closed_form) = -0.141457664418 0.11193682929 absolute error = 5.674e-05 relative error = 0.03145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.476 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2128 0.58 h = 0.001 0.001 y[1] (numeric) = -0.143052116469 0.112400208353 y[1] (closed_form) = -0.143059345193 0.112456582299 absolute error = 5.684e-05 relative error = 0.03123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.477 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2138 0.581 h = 0.001 0.003 y[1] (numeric) = -0.143438546985 0.113096344183 y[1] (closed_form) = -0.143444623203 0.113152559452 absolute error = 5.654e-05 relative error = 0.03095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.476 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = -0.144907216738 0.114105609468 y[1] (closed_form) = -0.144915653077 0.114162047977 absolute error = 5.707e-05 relative error = 0.03093 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.476 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2149 0.588 h = 0.003 0.006 y[1] (numeric) = -0.147070076735 0.114783928296 y[1] (closed_form) = -0.147079702654 0.114838747291 absolute error = 5.566e-05 relative error = 0.02983 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.478 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = -0.149892161041 0.117357067555 y[1] (closed_form) = -0.149904976175 0.117420061844 absolute error = 6.428e-05 relative error = 0.03376 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.478 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=795.6MB, alloc=52.3MB, time=9.74 x[1] = 0.218 0.599 h = 0.0001 0.003 y[1] (numeric) = -0.152644624499 0.118197186221 y[1] (closed_form) = -0.152654483906 0.118255350835 absolute error = 5.899e-05 relative error = 0.03055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.479 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2181 0.602 h = 0.001 0.001 y[1] (numeric) = -0.15429896593 0.118718465381 y[1] (closed_form) = -0.154306665696 0.118777076983 absolute error = 5.912e-05 relative error = 0.03036 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.481 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2191 0.603 h = 0.001 0.003 y[1] (numeric) = -0.154702099908 0.119431462094 y[1] (closed_form) = -0.154708670981 0.119489932824 absolute error = 5.884e-05 relative error = 0.0301 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = -0.156221087221 0.120457673127 y[1] (closed_form) = -0.156229968323 0.1205163328 absolute error = 5.933e-05 relative error = 0.03007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.48 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2202 0.61 h = 0.003 0.006 y[1] (numeric) = -0.158450830859 0.121137713905 y[1] (closed_form) = -0.158460854601 0.121194775759 absolute error = 5.794e-05 relative error = 0.02904 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.482 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = -0.161372745431 0.123760735166 y[1] (closed_form) = -0.161385987861 0.123825747062 absolute error = 6.635e-05 relative error = 0.03262 % Correct digits = 3 Radius of convergence (given) for eq 1 = 1.482 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = -0.16420786575 0.124601893194 y[1] (closed_form) = -0.164218159519 0.124662223111 absolute error = 6.120e-05 relative error = 0.02968 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.484 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2234 0.624 h = 0.001 0.001 y[1] (numeric) = -0.165911534504 0.125124455875 y[1] (closed_form) = -0.16591972396 0.125185249529 absolute error = 6.134e-05 relative error = 0.02951 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.485 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=841.0MB, alloc=52.3MB, time=10.29 x[1] = 0.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = -0.166331202068 0.125853722423 y[1] (closed_form) = -0.166338287119 0.125914392601 absolute error = 6.108e-05 relative error = 0.02928 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.484 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2245 0.629 h = 0.003 0.006 y[1] (numeric) = -0.168614526147 0.126534417776 y[1] (closed_form) = -0.16862550486 0.126592862569 absolute error = 5.947e-05 relative error = 0.0282 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.486 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = -0.171621589224 0.129197294364 y[1] (closed_form) = -0.171635805669 0.129263493892 absolute error = 6.771e-05 relative error = 0.03151 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.486 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = -0.174526326783 0.130037535958 y[1] (closed_form) = -0.174537604871 0.130099180741 absolute error = 6.267e-05 relative error = 0.02879 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.488 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2277 0.643 h = 0.001 0.001 y[1] (numeric) = -0.176271549906 0.130560111985 y[1] (closed_form) = -0.176280771881 0.130622233383 absolute error = 6.280e-05 relative error = 0.02862 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.489 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2287 0.644 h = 0.001 0.003 y[1] (numeric) = -0.176705487561 0.131302716885 y[1] (closed_form) = -0.176713626568 0.131364729123 absolute error = 6.254e-05 relative error = 0.0284 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.489 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = -0.178315778606 0.132357201604 y[1] (closed_form) = -0.178326131677 0.132419342008 absolute error = 6.300e-05 relative error = 0.02836 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.489 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2298 0.651 h = 0.003 0.006 y[1] (numeric) = -0.180665944201 0.133037380975 y[1] (closed_form) = -0.180677353638 0.133097967243 absolute error = 6.165e-05 relative error = 0.02747 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.491 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=886.4MB, alloc=52.3MB, time=10.84 x[1] = 0.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = -0.183769653982 0.135745724363 y[1] (closed_form) = -0.183784322139 0.13581383802 absolute error = 6.968e-05 relative error = 0.03049 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.491 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = -0.186753466842 0.136585068935 y[1] (closed_form) = -0.186765209399 0.136648775732 absolute error = 6.478e-05 relative error = 0.02799 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.493 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.233 0.665 h = 0.001 0.001 y[1] (numeric) = -0.188545882435 0.137107748081 y[1] (closed_form) = -0.188555624984 0.137171946178 absolute error = 6.493e-05 relative error = 0.02785 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.234 0.666 h = 0.001 0.003 y[1] (numeric) = -0.188995997181 0.137865530381 y[1] (closed_form) = -0.189004681764 0.137929635832 absolute error = 6.469e-05 relative error = 0.02765 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.235 0.669 h = 0.0001 0.004 y[1] (numeric) = -0.190653865577 0.138934116901 y[1] (closed_form) = -0.190664711827 0.138998318985 absolute error = 6.511e-05 relative error = 0.0276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2351 0.673 h = 0.003 0.006 y[1] (numeric) = -0.193066535746 0.139613606019 y[1] (closed_form) = -0.193078392486 0.139676278523 absolute error = 6.378e-05 relative error = 0.02677 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.496 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = -0.196265124017 0.142365077527 y[1] (closed_form) = -0.196280255842 0.142435049706 absolute error = 7.159e-05 relative error = 0.02952 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.496 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = -0.199326061567 0.143202527673 y[1] (closed_form) = -0.199338283555 0.14326824049 absolute error = 6.684e-05 relative error = 0.02723 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.498 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=931.7MB, alloc=52.3MB, time=11.39 x[1] = 0.2383 0.687 h = 0.001 0.001 y[1] (numeric) = -0.201164507379 0.143724701265 y[1] (closed_form) = -0.201174785696 0.143790918916 absolute error = 6.701e-05 relative error = 0.0271 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.499 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2393 0.688 h = 0.001 0.003 y[1] (numeric) = -0.201630594307 0.144497078057 y[1] (closed_form) = -0.201639839961 0.144563219047 absolute error = 6.678e-05 relative error = 0.02692 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.499 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = -0.203335045726 0.145578804643 y[1] (closed_form) = -0.203346400084 0.145645011842 absolute error = 6.717e-05 relative error = 0.02686 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.499 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2404 0.695 h = 0.003 0.006 y[1] (numeric) = -0.205808658879 0.146256813659 y[1] (closed_form) = -0.205820978428 0.146321516722 absolute error = 6.587e-05 relative error = 0.02608 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = -0.209100312074 0.149049112889 y[1] (closed_form) = -0.209115918434 0.149120888075 absolute error = 7.345e-05 relative error = 0.0286 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.501 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = -0.212236406771 0.149883712744 y[1] (closed_form) = -0.212249122009 0.149951375345 absolute error = 6.885e-05 relative error = 0.02649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.503 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2436 0.709 h = 0.001 0.001 y[1] (numeric) = -0.214119710673 0.150404796839 y[1] (closed_form) = -0.21413053868 0.150472976631 absolute error = 6.903e-05 relative error = 0.02638 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.505 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2446 0.71 h = 0.001 0.003 y[1] (numeric) = -0.214601553587 0.151191190646 y[1] (closed_form) = -0.214611374477 0.151259309203 absolute error = 6.882e-05 relative error = 0.02621 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.504 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=977.0MB, alloc=52.3MB, time=11.94 x[1] = 0.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = -0.216351576471 0.152285117892 y[1] (closed_form) = -0.216363452659 0.152353273404 absolute error = 6.918e-05 relative error = 0.02614 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.505 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2457 0.717 h = 0.003 0.006 y[1] (numeric) = -0.218884559087 0.15296089063 y[1] (closed_form) = -0.218897355843 0.153027568272 absolute error = 6.789e-05 relative error = 0.02542 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.507 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = -0.222267422701 0.155791760435 y[1] (closed_form) = -0.222283513371 0.155865283313 absolute error = 7.526e-05 relative error = 0.02772 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.507 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = -0.225476694645 0.156622597485 y[1] (closed_form) = -0.225489915787 0.156692153517 absolute error = 7.080e-05 relative error = 0.02578 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.509 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2489 0.731 h = 0.001 0.001 y[1] (numeric) = -0.227403677333 0.157142033954 y[1] (closed_form) = -0.227415067662 0.157212118343 absolute error = 7.100e-05 relative error = 0.02568 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.511 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = -0.227901049328 0.157941873966 y[1] (closed_form) = -0.22791145827 0.158011911959 absolute error = 7.081e-05 relative error = 0.02553 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.51 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.25 0.736 h = 0.003 0.006 y[1] (numeric) = -0.230481405277 0.15861519121 y[1] (closed_form) = -0.230495122511 0.158683045281 absolute error = 6.923e-05 relative error = 0.02474 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.512 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.253 0.742 h = 0.0001 0.005 y[1] (numeric) = -0.233941690557 0.161476434418 y[1] (closed_form) = -0.233958701464 0.161550939322 absolute error = 7.642e-05 relative error = 0.02688 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.512 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1022.5MB, alloc=52.3MB, time=12.50 x[1] = 0.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = -0.237212300672 0.162302496599 y[1] (closed_form) = -0.237226464593 0.162373158739 absolute error = 7.207e-05 relative error = 0.02507 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.515 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2532 0.75 h = 0.001 0.001 y[1] (numeric) = -0.23917590454 0.162819587185 y[1] (closed_form) = -0.239188286216 0.162890785669 absolute error = 7.227e-05 relative error = 0.02497 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2542 0.751 h = 0.001 0.003 y[1] (numeric) = -0.239686605101 0.163630368977 y[1] (closed_form) = -0.239698027808 0.16370153304 absolute error = 7.207e-05 relative error = 0.02483 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = -0.241518804638 0.164744068977 y[1] (closed_form) = -0.241532182188 0.164815219481 absolute error = 7.240e-05 relative error = 0.02476 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.516 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = -0.244157999825 0.165413126042 y[1] (closed_form) = -0.244172217341 0.16548285002 absolute error = 7.116e-05 relative error = 0.02412 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.518 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2554 0.762 h = 0.003 0.006 y[1] (numeric) = -0.246807474126 0.166078032352 y[1] (closed_form) = -0.246821691642 0.166147756329 absolute error = 7.116e-05 relative error = 0.02392 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.52 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = -0.250371584016 0.168976350559 y[1] (closed_form) = -0.250389084897 0.169052462609 absolute error = 7.810e-05 relative error = 0.02585 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.521 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = -0.2537232517 0.169793569031 y[1] (closed_form) = -0.25373794243 0.169866004795 absolute error = 7.391e-05 relative error = 0.02421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.523 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1067.9MB, alloc=52.3MB, time=13.04 x[1] = 0.2586 0.776 h = 0.001 0.001 y[1] (numeric) = -0.255735264986 0.170306051541 y[1] (closed_form) = -0.255748239476 0.170379031944 absolute error = 7.412e-05 relative error = 0.02412 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2596 0.777 h = 0.001 0.003 y[1] (numeric) = -0.256264066891 0.17113077897 y[1] (closed_form) = -0.256276113299 0.171203739978 absolute error = 7.395e-05 relative error = 0.02399 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = -0.258146455383 0.17225417578 y[1] (closed_form) = -0.258160392387 0.172327095272 absolute error = 7.424e-05 relative error = 0.02392 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.525 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2607 0.784 h = 0.003 0.006 y[1] (numeric) = -0.260849624753 0.172916268221 y[1] (closed_form) = -0.260864353363 0.172987795901 absolute error = 7.303e-05 relative error = 0.02333 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.527 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = -0.264499013522 0.175846714404 y[1] (closed_form) = -0.264517019042 0.175924408355 absolute error = 7.975e-05 relative error = 0.02511 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.527 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = -0.267917785036 0.176657778 y[1] (closed_form) = -0.267933010061 0.176731936375 absolute error = 7.571e-05 relative error = 0.02359 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.53 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2639 0.798 h = 0.001 0.001 y[1] (numeric) = -0.269969859725 0.177167143895 y[1] (closed_form) = -0.269983424091 0.177241854472 absolute error = 7.593e-05 relative error = 0.02351 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.531 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2649 0.799 h = 0.001 0.003 y[1] (numeric) = -0.270513417035 0.178003650735 y[1] (closed_form) = -0.270526079228 0.178078354849 absolute error = 7.577e-05 relative error = 0.02339 % Correct digits = 4 memory used=1113.4MB, alloc=52.3MB, time=13.60 Radius of convergence (given) for eq 1 = 1.531 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = -0.272437130794 0.179135772813 y[1] (closed_form) = -0.272451629663 0.179210411295 absolute error = 7.603e-05 relative error = 0.02332 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.532 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.266 0.806 h = 0.003 0.006 y[1] (numeric) = -0.275193244689 0.179793021794 y[1] (closed_form) = -0.275208494114 0.179866297304 absolute error = 7.485e-05 relative error = 0.02277 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.534 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.269 0.812 h = 0.0001 0.005 y[1] (numeric) = -0.278925941593 0.182753555475 y[1] (closed_form) = -0.278944457185 0.182832777905 absolute error = 8.136e-05 relative error = 0.02439 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.534 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = -0.282409833576 0.183557737994 y[1] (closed_form) = -0.282425600777 0.183633563437 absolute error = 7.745e-05 relative error = 0.02299 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.537 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2692 0.82 h = 0.001 0.001 y[1] (numeric) = -0.284500788816 0.18406354025 y[1] (closed_form) = -0.284514950466 0.184139924285 absolute error = 7.769e-05 relative error = 0.02292 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.538 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2702 0.821 h = 0.001 0.003 y[1] (numeric) = -0.28505883864 0.184911293713 y[1] (closed_form) = -0.285072123988 0.184987683565 absolute error = 7.754e-05 relative error = 0.02282 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.538 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = -0.287022817171 0.186051338566 y[1] (closed_form) = -0.287037885415 0.186127640002 absolute error = 7.778e-05 relative error = 0.02273 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.539 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1158.9MB, alloc=52.3MB, time=14.15 x[1] = 0.2713 0.828 h = 0.003 0.006 y[1] (numeric) = -0.289830296584 0.186703172358 y[1] (closed_form) = -0.289846075377 0.186778140132 absolute error = 7.661e-05 relative error = 0.02222 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.541 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = -0.29364431286 0.189691814253 y[1] (closed_form) = -0.293663342918 0.18977251242 absolute error = 8.291e-05 relative error = 0.02371 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.542 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = -0.297191350688 0.190488436976 y[1] (closed_form) = -0.297207666776 0.190565874404 absolute error = 7.914e-05 relative error = 0.02242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.544 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2745 0.842 h = 0.001 0.001 y[1] (numeric) = -0.2993200109 0.190990256922 y[1] (closed_form) = -0.299334775978 0.191068258179 absolute error = 7.939e-05 relative error = 0.02235 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.546 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2755 0.843 h = 0.001 0.003 y[1] (numeric) = -0.299892283115 0.191848735725 y[1] (closed_form) = -0.299906197672 0.191926754419 absolute error = 7.925e-05 relative error = 0.02226 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.545 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = -0.301895462946 0.192995931255 y[1] (closed_form) = -0.301911106861 0.193073840091 absolute error = 7.946e-05 relative error = 0.02217 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.546 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2766 0.85 h = 0.003 0.006 y[1] (numeric) = -0.304752737051 0.193641816026 y[1] (closed_form) = -0.304769052598 0.193718420906 absolute error = 7.832e-05 relative error = 0.02169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.548 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = -0.30864607033 0.196656650317 y[1] (closed_form) = -0.308665618231 0.196738772235 absolute error = 8.442e-05 relative error = 0.02306 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.549 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1204.3MB, alloc=52.3MB, time=14.70 x[1] = 0.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = -0.312254291778 0.197445082018 y[1] (closed_form) = -0.312271162315 0.197524076903 absolute error = 8.078e-05 relative error = 0.02186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.552 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2798 0.864 h = 0.001 0.001 y[1] (numeric) = -0.314419488823 0.197942529355 y[1] (closed_form) = -0.314434862232 0.198022092177 absolute error = 8.103e-05 relative error = 0.02181 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.553 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = -0.315005706807 0.198811224415 y[1] (closed_form) = -0.31502025534 0.198890815633 absolute error = 8.091e-05 relative error = 0.02172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.553 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2809 0.869 h = 0.003 0.006 y[1] (numeric) = -0.317902534119 0.199451799407 y[1] (closed_form) = -0.317919702116 0.199529335522 absolute error = 7.941e-05 relative error = 0.02116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.555 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = -0.321862812359 0.202486782748 y[1] (closed_form) = -0.321883190862 0.20256965532 absolute error = 8.534e-05 relative error = 0.02244 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.556 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.284 0.88 h = 0.0001 0.003 y[1] (numeric) = -0.325522032437 0.203266997201 y[1] (closed_form) = -0.325539768272 0.203346855192 absolute error = 8.180e-05 relative error = 0.02131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.559 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2841 0.883 h = 0.001 0.001 y[1] (numeric) = -0.327717693058 0.203759973302 y[1] (closed_form) = -0.327733977585 0.203840401254 absolute error = 8.206e-05 relative error = 0.02126 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.561 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2851 0.884 h = 0.001 0.003 y[1] (numeric) = -0.328315802856 0.20463690275 y[1] (closed_form) = -0.328331284557 0.204717367698 absolute error = 8.194e-05 relative error = 0.02118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.56 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1249.8MB, alloc=52.3MB, time=15.26 x[1] = 0.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = -0.330389160441 0.205795018649 y[1] (closed_form) = -0.330406272631 0.205875338032 absolute error = 8.212e-05 relative error = 0.02109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.561 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2862 0.891 h = 0.003 0.006 y[1] (numeric) = -0.333334865675 0.206427992701 y[1] (closed_form) = -0.333352580489 0.206507064657 absolute error = 8.103e-05 relative error = 0.02066 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.563 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = -0.33737069254 0.209485802587 y[1] (closed_form) = -0.337391591976 0.209570004407 absolute error = 8.676e-05 relative error = 0.02184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.564 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = -0.341087483516 0.210256799737 y[1] (closed_form) = -0.341105780534 0.210338115475 absolute error = 8.335e-05 relative error = 0.0208 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.567 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2894 0.905 h = 0.001 0.001 y[1] (numeric) = -0.343317530184 0.21074476556 y[1] (closed_form) = -0.343334428324 0.210826653357 absolute error = 8.361e-05 relative error = 0.02075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.569 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2904 0.906 h = 0.001 0.003 y[1] (numeric) = -0.343929050584 0.21163100191 y[1] (closed_form) = -0.343945171161 0.211712936436 absolute error = 8.351e-05 relative error = 0.02068 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.569 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = -0.346038561934 0.212794245165 y[1] (closed_form) = -0.346056260687 0.212876016495 absolute error = 8.366e-05 relative error = 0.02059 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.569 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2915 0.913 h = 0.003 0.006 y[1] (numeric) = -0.349029633209 0.213419969084 y[1] (closed_form) = -0.349047899003 0.213500523436 absolute error = 8.260e-05 relative error = 0.02019 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.572 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1295.3MB, alloc=52.3MB, time=15.81 x[1] = 0.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = -0.353138991695 0.21649888018 y[1] (closed_form) = -0.353160412722 0.216584361797 absolute error = 8.812e-05 relative error = 0.02127 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.573 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = -0.356911445778 0.21726016231 y[1] (closed_form) = -0.3569303064 0.217342883349 absolute error = 8.484e-05 relative error = 0.0203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.576 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2947 0.927 h = 0.001 0.001 y[1] (numeric) = -0.359174742825 0.217742807392 y[1] (closed_form) = -0.359192256118 0.217826101553 absolute error = 8.512e-05 relative error = 0.02026 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2957 0.928 h = 0.001 0.003 y[1] (numeric) = -0.359799382888 0.218637879569 y[1] (closed_form) = -0.359816143624 0.218721229541 absolute error = 8.502e-05 relative error = 0.02019 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.577 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = -0.361943993152 0.219805599811 y[1] (closed_form) = -0.36196228034 0.219888770265 absolute error = 8.516e-05 relative error = 0.02011 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.578 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2968 0.935 h = 0.003 0.006 y[1] (numeric) = -0.364978916904 0.220423683601 y[1] (closed_form) = -0.364997736764 0.220505667658 absolute error = 8.412e-05 relative error = 0.01973 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.58 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = -0.369159792409 0.223522039034 y[1] (closed_form) = -0.3691817348 0.223608751986 absolute error = 8.945e-05 relative error = 0.02072 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.581 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = -0.372986026393 0.224273153775 y[1] (closed_form) = -0.373005452 0.224357228538 absolute error = 8.629e-05 relative error = 0.01982 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.584 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1340.6MB, alloc=52.3MB, time=16.36 x[1] = 0.3 0.949 h = 0.001 0.001 y[1] (numeric) = -0.375281452777 0.224750194804 y[1] (closed_form) = -0.375299581667 0.224834842757 absolute error = 8.657e-05 relative error = 0.01979 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.586 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.301 0.95 h = 0.001 0.003 y[1] (numeric) = -0.375918917929 0.225653645798 y[1] (closed_form) = -0.37593631897 0.225738358001 absolute error = 8.648e-05 relative error = 0.01972 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.586 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.302 0.953 h = 0.0001 0.004 y[1] (numeric) = -0.378097579084 0.226825224539 y[1] (closed_form) = -0.378116455515 0.226909742188 absolute error = 8.660e-05 relative error = 0.01964 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.587 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3021 0.957 h = 0.003 0.006 y[1] (numeric) = -0.381174862186 0.227435314114 y[1] (closed_form) = -0.381194238154 0.227518676015 absolute error = 8.558e-05 relative error = 0.01928 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.589 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = -0.385425246283 0.230551525897 y[1] (closed_form) = -0.385447708968 0.230639422758 absolute error = 9.072e-05 relative error = 0.0202 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.59 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = -0.389303404167 0.231292065231 y[1] (closed_form) = -0.389323395147 0.231377443068 absolute error = 8.769e-05 relative error = 0.01936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.593 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3053 0.971 h = 0.001 0.001 y[1] (numeric) = -0.391629855024 0.231763245456 y[1] (closed_form) = -0.391648598898 0.231849195601 absolute error = 8.797e-05 relative error = 0.01933 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.595 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = -0.392279847773 0.232674632612 y[1] (closed_form) = -0.392297888174 0.232760654815 absolute error = 8.789e-05 relative error = 0.01927 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.595 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1386.1MB, alloc=52.3MB, time=16.91 x[1] = 0.3064 0.976 h = 0.003 0.006 y[1] (numeric) = -0.395390666274 0.233277882844 y[1] (closed_form) = -0.395410826291 0.23336199671 absolute error = 8.650e-05 relative error = 0.01884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.597 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = -0.399699468377 0.236407450228 y[1] (closed_form) = -0.399722679715 0.236495936281 absolute error = 9.148e-05 relative error = 0.0197 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.599 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = -0.403620725148 0.237138003894 y[1] (closed_form) = -0.403641506001 0.237224070297 absolute error = 8.854e-05 relative error = 0.01891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.602 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3096 0.99 h = 0.001 0.001 y[1] (numeric) = -0.405972935994 0.237603601538 y[1] (closed_form) = -0.405992511582 0.237690238186 absolute error = 8.882e-05 relative error = 0.01888 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.603 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3106 0.991 h = 0.001 0.003 y[1] (numeric) = -0.406633559779 0.238521332171 y[1] (closed_form) = -0.406652452669 0.238608046817 absolute error = 8.875e-05 relative error = 0.01882 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.603 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = -0.408872852901 0.239698176456 y[1] (closed_form) = -0.408893128025 0.239784672487 absolute error = 8.884e-05 relative error = 0.01874 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.604 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3117 0.998 h = 0.003 0.006 y[1] (numeric) = -0.412024957549 0.240292103979 y[1] (closed_form) = -0.41204567422 0.240377501626 absolute error = 8.787e-05 relative error = 0.01842 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.607 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = -0.416399542668 0.243436779915 y[1] (closed_form) = -0.416423269667 0.243526364547 absolute error = 9.267e-05 relative error = 0.01921 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.608 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1431.5MB, alloc=52.3MB, time=17.46 x[1] = 0.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = -0.420369346536 0.244156134144 y[1] (closed_form) = -0.420390690395 0.244243412072 absolute error = 8.985e-05 relative error = 0.01848 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.611 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3149 1.012 h = 0.001 0.001 y[1] (numeric) = -0.422750571413 0.244615474195 y[1] (closed_form) = -0.422770757622 0.244703319847 absolute error = 9.014e-05 relative error = 0.01845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.613 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3159 1.013 h = 0.001 0.003 y[1] (numeric) = -0.423423158992 0.245540359808 y[1] (closed_form) = -0.423442686173 0.245628290135 absolute error = 9.007e-05 relative error = 0.0184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.613 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = -0.42569355149 0.246719479503 y[1] (closed_form) = -0.425714412121 0.246807179688 absolute error = 9.015e-05 relative error = 0.01832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.614 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.317 1.02 h = 0.003 0.006 y[1] (numeric) = -0.428883871272 0.247304606968 y[1] (closed_form) = -0.42890514387 0.247391239266 absolute error = 8.921e-05 relative error = 0.01802 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.616 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.32 1.026 h = 0.0001 0.005 y[1] (numeric) = -0.43332226867 0.250462999912 y[1] (closed_form) = -0.433346508092 0.250553638862 absolute error = 9.382e-05 relative error = 0.01874 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.618 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = -0.437338854403 0.251170866305 y[1] (closed_form) = -0.437360759052 0.251259308081 absolute error = 9.111e-05 relative error = 0.01806 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.621 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3202 1.034 h = 0.001 0.001 y[1] (numeric) = -0.439748042366 0.251623763756 y[1] (closed_form) = -0.439768835855 0.251712769918 absolute error = 9.140e-05 relative error = 0.01804 % Correct digits = 4 memory used=1476.9MB, alloc=52.3MB, time=18.01 Radius of convergence (given) for eq 1 = 1.623 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3212 1.035 h = 0.001 0.003 y[1] (numeric) = -0.440432291877 0.252555403734 y[1] (closed_form) = -0.440452449593 0.25264450066 absolute error = 9.135e-05 relative error = 0.01799 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.623 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = -0.44273277773 0.253736300766 y[1] (closed_form) = -0.44275422101 0.253825157183 absolute error = 9.141e-05 relative error = 0.01791 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3223 1.042 h = 0.003 0.006 y[1] (numeric) = -0.445959916085 0.254312403528 y[1] (closed_form) = -0.445981742991 0.2544002224 absolute error = 9.049e-05 relative error = 0.01762 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.626 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = -0.450460174004 0.257483189636 y[1] (closed_form) = -0.450484921932 0.2575748398 absolute error = 9.493e-05 relative error = 0.01829 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.628 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = -0.454521811576 0.258179318984 y[1] (closed_form) = -0.454544273974 0.258268878048 absolute error = 9.233e-05 relative error = 0.01766 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.631 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3255 1.056 h = 0.001 0.001 y[1] (numeric) = -0.456957932575 0.258625612368 y[1] (closed_form) = -0.456979329147 0.258715731709 absolute error = 9.262e-05 relative error = 0.01764 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.633 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3265 1.057 h = 0.001 0.003 y[1] (numeric) = -0.457653541829 0.259563620907 y[1] (closed_form) = -0.457674325443 0.259653836533 absolute error = 9.258e-05 relative error = 0.01759 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.633 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1522.4MB, alloc=52.3MB, time=18.57 x[1] = 0.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = -0.459983129225 0.260745827232 y[1] (closed_form) = -0.460005151463 0.260835793104 absolute error = 9.262e-05 relative error = 0.01752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.634 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3276 1.064 h = 0.003 0.006 y[1] (numeric) = -0.463245718129 0.261312711501 y[1] (closed_form) = -0.463268096883 0.261401669962 absolute error = 9.173e-05 relative error = 0.01724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = -0.467805906613 0.264494633721 y[1] (closed_form) = -0.467831158497 0.26458725317 absolute error = 9.600e-05 relative error = 0.01786 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.638 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = -0.471910902747 0.26517881444 y[1] (closed_form) = -0.471933919079 0.265269445384 absolute error = 9.351e-05 relative error = 0.01727 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.641 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3308 1.078 h = 0.001 0.001 y[1] (numeric) = -0.474372948547 0.265618364902 y[1] (closed_form) = -0.4743949432 0.265709551293 absolute error = 9.380e-05 relative error = 0.01725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.643 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = -0.475079615628 0.266562370989 y[1] (closed_form) = -0.475101019679 0.266653658637 absolute error = 9.376e-05 relative error = 0.01721 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.643 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3319 1.083 h = 0.003 0.006 y[1] (numeric) = -0.478370186253 0.26712154044 y[1] (closed_form) = -0.478393272515 0.267211093344 absolute error = 9.248e-05 relative error = 0.01688 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.646 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = -0.482980547588 0.270311408758 y[1] (closed_form) = -0.483006462298 0.270404480751 absolute error = 9.661e-05 relative error = 0.01745 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.647 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1567.8MB, alloc=52.3MB, time=19.12 x[1] = 0.335 1.094 h = 0.0001 0.003 y[1] (numeric) = -0.487121393357 0.270984672844 y[1] (closed_form) = -0.487145117179 0.271075841243 absolute error = 9.420e-05 relative error = 0.0169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.65 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3351 1.097 h = 0.001 0.001 y[1] (numeric) = -0.489604882062 0.271418031699 y[1] (closed_form) = -0.489627621174 0.271509750341 absolute error = 9.450e-05 relative error = 0.01688 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.652 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3361 1.098 h = 0.001 0.003 y[1] (numeric) = -0.490320891927 0.272366787566 y[1] (closed_form) = -0.490343059349 0.272458611063 absolute error = 9.446e-05 relative error = 0.01684 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.652 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = -0.492702048099 0.273549964958 y[1] (closed_form) = -0.492725369373 0.273641524867 absolute error = 9.448e-05 relative error = 0.01676 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.654 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3372 1.105 h = 0.003 0.006 y[1] (numeric) = -0.496026949711 0.274098895151 y[1] (closed_form) = -0.496050580632 0.274189503297 absolute error = 9.364e-05 relative error = 0.01652 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = -0.500693704073 0.277297756586 y[1] (closed_form) = -0.500720112275 0.27739172308 absolute error = 9.761e-05 relative error = 0.01705 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.658 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = -0.504874858321 0.277958791936 y[1] (closed_form) = -0.504899126567 0.278050950935 absolute error = 9.530e-05 relative error = 0.01653 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.661 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3404 1.119 h = 0.001 0.001 y[1] (numeric) = -0.507382455342 0.278385217737 y[1] (closed_form) = -0.507405780765 0.278477920953 absolute error = 9.559e-05 relative error = 0.01652 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.663 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1613.1MB, alloc=52.3MB, time=19.68 x[1] = 0.3414 1.12 h = 0.001 0.003 y[1] (numeric) = -0.508108959924 0.279339323388 y[1] (closed_form) = -0.508131735103 0.279432135473 absolute error = 9.557e-05 relative error = 0.01648 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.663 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = -0.510516464521 0.280522641778 y[1] (closed_form) = -0.51054034954 0.280615183985 absolute error = 9.557e-05 relative error = 0.01641 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.664 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3425 1.127 h = 0.003 0.006 y[1] (numeric) = -0.513873069213 0.281061973063 y[1] (closed_form) = -0.513897240195 0.28115359278 absolute error = 9.475e-05 relative error = 0.01618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.667 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = -0.518594363443 0.284268754534 y[1] (closed_form) = -0.518621259039 0.284363577024 absolute error = 9.856e-05 relative error = 0.01666 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.669 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = -0.522814245116 0.284917447566 y[1] (closed_form) = -0.522839052036 0.285010555186 absolute error = 9.636e-05 relative error = 0.01618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3457 1.141 h = 0.001 0.001 y[1] (numeric) = -0.525345008808 0.285336860469 y[1] (closed_form) = -0.525368913559 0.285430505702 absolute error = 9.665e-05 relative error = 0.01616 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.674 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3467 1.142 h = 0.001 0.003 y[1] (numeric) = -0.526081710236 0.286295986566 y[1] (closed_form) = -0.526105085683 0.286389744193 absolute error = 9.663e-05 relative error = 0.01613 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.674 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = -0.5285146368 0.287479086701 y[1] (closed_form) = -0.528539079147 0.28757256911 absolute error = 9.662e-05 relative error = 0.01606 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.675 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1658.4MB, alloc=52.3MB, time=20.23 x[1] = 0.3478 1.149 h = 0.003 0.006 y[1] (numeric) = -0.531901696492 0.288008731812 y[1] (closed_form) = -0.53192640228 0.28810132063 absolute error = 9.583e-05 relative error = 0.01584 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.678 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = -0.536675708123 0.291222421785 y[1] (closed_form) = -0.536703084549 0.291318062967 absolute error = 9.948e-05 relative error = 0.01629 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.68 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = -0.54093277698 0.291858690023 y[1] (closed_form) = -0.540958116233 0.291952705511 absolute error = 9.737e-05 relative error = 0.01584 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.683 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.351 1.163 h = 0.001 0.001 y[1] (numeric) = -0.543485789911 0.292271028952 y[1] (closed_form) = -0.543510266413 0.292365574917 absolute error = 9.766e-05 relative error = 0.01582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.685 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.352 1.164 h = 0.001 0.003 y[1] (numeric) = -0.544232392642 0.293234860379 y[1] (closed_form) = -0.544256360264 0.2933295218 absolute error = 9.765e-05 relative error = 0.01579 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.685 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.353 1.167 h = 0.0001 0.004 y[1] (numeric) = -0.54668983366 0.294417409158 y[1] (closed_form) = -0.546714826338 0.294511790921 absolute error = 9.763e-05 relative error = 0.01572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.687 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3531 1.171 h = 0.003 0.006 y[1] (numeric) = -0.550106132972 0.29493730521 y[1] (closed_form) = -0.550131367701 0.295030821873 absolute error = 9.686e-05 relative error = 0.01552 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.689 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = -0.554931072022 0.298156952 y[1] (closed_form) = -0.554958922295 0.298253375771 absolute error = 0.0001004 relative error = 0.01593 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.691 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1703.8MB, alloc=52.3MB, time=20.78 x[1] = 0.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = -0.559223829247 0.29878074234 y[1] (closed_form) = -0.559249693956 0.298875626175 absolute error = 9.835e-05 relative error = 0.01551 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.695 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3563 1.185 h = 0.001 0.001 y[1] (numeric) = -0.561798198561 0.299185963959 y[1] (closed_form) = -0.561823238695 0.299281370652 absolute error = 9.864e-05 relative error = 0.0155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.697 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = -0.562554409832 0.300154199585 y[1] (closed_form) = -0.562578960983 0.300249724353 absolute error = 9.863e-05 relative error = 0.01547 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.697 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3574 1.19 h = 0.003 0.006 y[1] (numeric) = -0.565993726721 0.300666048917 y[1] (closed_form) = -0.566019588963 0.30076002607 absolute error = 9.747e-05 relative error = 0.01521 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.7 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = -0.570861151624 0.303889527164 y[1] (closed_form) = -0.570889579584 0.303986291168 absolute error = 0.0001009 relative error = 0.01559 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.702 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = -0.575183310969 0.304502153961 y[1] (closed_form) = -0.575209798755 0.304597448531 absolute error = 9.891e-05 relative error = 0.0152 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.705 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3606 1.204 h = 0.001 0.001 y[1] (numeric) = -0.577775281958 0.304900986933 y[1] (closed_form) = -0.57780097694 0.304996797016 absolute error = 9.920e-05 relative error = 0.01518 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.707 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3616 1.205 h = 0.001 0.003 y[1] (numeric) = -0.57853957977 0.305872673115 y[1] (closed_form) = -0.578564802494 0.305968602963 absolute error = 9.919e-05 relative error = 0.01516 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.707 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1749.3MB, alloc=52.3MB, time=21.34 x[1] = 0.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = -0.581040273904 0.307053127603 y[1] (closed_form) = -0.581066446762 0.307148772239 absolute error = 9.916e-05 relative error = 0.01509 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.709 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3627 1.212 h = 0.003 0.006 y[1] (numeric) = -0.58450774339 0.307554477643 y[1] (closed_form) = -0.584534121743 0.30764930922 absolute error = 9.843e-05 relative error = 0.0149 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.711 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = -0.589422847022 0.310782315273 y[1] (closed_form) = -0.589451734456 0.31087979795 absolute error = 0.0001017 relative error = 0.01526 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.713 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = -0.593778017555 0.311382454257 y[1] (closed_form) = -0.593805016288 0.311478547022 absolute error = 9.981e-05 relative error = 0.01489 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.717 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3659 1.226 h = 0.001 0.001 y[1] (numeric) = -0.596389749707 0.311774142911 y[1] (closed_form) = -0.596415991507 0.311870742807 absolute error = 0.0001001 relative error = 0.01487 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3669 1.227 h = 0.001 0.003 y[1] (numeric) = -0.597163116893 0.312749712617 y[1] (closed_form) = -0.597188905332 0.312846434142 absolute error = 0.0001001 relative error = 0.01485 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = -0.599685836466 0.313928808726 y[1] (closed_form) = -0.599712536413 0.314025242907 absolute error = 0.0001001 relative error = 0.01478 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.72 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.368 1.234 h = 0.003 0.006 y[1] (numeric) = -0.603179252662 0.31442036525 y[1] (closed_form) = -0.603206139791 0.314516013512 absolute error = 9.936e-05 relative error = 0.01461 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.723 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1794.8MB, alloc=52.3MB, time=21.89 x[1] = 0.371 1.24 h = 0.0001 0.005 y[1] (numeric) = -0.608140346763 0.317651771178 y[1] (closed_form) = -0.60816968572 0.317749939818 absolute error = 0.0001025 relative error = 0.01493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.725 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = -0.612527150375 0.318239443218 y[1] (closed_form) = -0.612554651908 0.318336298196 absolute error = 0.0001007 relative error = 0.01458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3712 1.248 h = 0.001 0.001 y[1] (numeric) = -0.615157822452 0.318623989013 y[1] (closed_form) = -0.615184601696 0.318721342385 absolute error = 0.000101 relative error = 0.01457 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.731 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3722 1.249 h = 0.001 0.003 y[1] (numeric) = -0.615939976549 0.319603179482 y[1] (closed_form) = -0.615966320788 0.319700655969 absolute error = 0.000101 relative error = 0.01455 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.731 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = -0.618483892827 0.320780675796 y[1] (closed_form) = -0.618511111084 0.320877863527 absolute error = 0.0001009 relative error = 0.01448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.733 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3733 1.256 h = 0.003 0.006 y[1] (numeric) = -0.622002169749 0.321262456753 y[1] (closed_form) = -0.622029557891 0.321358885189 absolute error = 0.0001002 relative error = 0.01432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.735 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = -0.627007603625 0.324496692411 y[1] (closed_form) = -0.627037385882 0.324595515464 absolute error = 0.0001032 relative error = 0.01462 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.738 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = -0.631424704499 0.325071941137 y[1] (closed_form) = -0.63145270032 0.325169523569 absolute error = 0.0001015 relative error = 0.01429 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.741 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1840.3MB, alloc=52.3MB, time=22.44 x[1] = 0.3765 1.27 h = 0.001 0.001 y[1] (numeric) = -0.634073520356 0.325449359356 y[1] (closed_form) = -0.634100827318 0.32554743113 absolute error = 0.0001018 relative error = 0.01428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.743 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3775 1.271 h = 0.001 0.003 y[1] (numeric) = -0.634864183107 0.326431920623 y[1] (closed_form) = -0.634891072878 0.326530116646 absolute error = 0.0001018 relative error = 0.01426 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.743 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = -0.637428488632 0.327607597116 y[1] (closed_form) = -0.637456216066 0.327705503644 absolute error = 0.0001018 relative error = 0.0142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3786 1.278 h = 0.003 0.006 y[1] (numeric) = -0.640970573942 0.328079638225 y[1] (closed_form) = -0.640998454947 0.328176811547 absolute error = 0.0001011 relative error = 0.01404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.748 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = -0.646018735345 0.331316015541 y[1] (closed_form) = -0.646048952446 0.331415462603 absolute error = 0.0001039 relative error = 0.01431 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.75 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = -0.650464839853 0.3318789057 y[1] (closed_form) = -0.65049332113 0.33197718204 absolute error = 0.0001023 relative error = 0.01401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.754 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3818 1.292 h = 0.001 0.001 y[1] (numeric) = -0.65313102838 0.332249224472 y[1] (closed_form) = -0.653158853026 0.332347980831 absolute error = 0.0001026 relative error = 0.014 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.756 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = -0.653929926025 0.333234919016 y[1] (closed_form) = -0.653957350752 0.333333800424 absolute error = 0.0001026 relative error = 0.01398 % Correct digits = 4 memory used=1885.9MB, alloc=52.3MB, time=23.00 Radius of convergence (given) for eq 1 = 1.756 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3829 1.297 h = 0.003 0.006 y[1] (numeric) = -0.65749070879 0.333698997759 y[1] (closed_form) = -0.65751913791 0.33379652083 absolute error = 0.0001016 relative error = 0.01378 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.759 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = -0.662574402723 0.336936221037 y[1] (closed_form) = -0.662605116499 0.337035918339 absolute error = 0.0001043 relative error = 0.01403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.761 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.386 1.308 h = 0.0001 0.003 y[1] (numeric) = -0.667044322943 0.337488214844 y[1] (closed_form) = -0.667073344879 0.337586798534 absolute error = 0.0001028 relative error = 0.01375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.765 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3861 1.311 h = 0.001 0.001 y[1] (numeric) = -0.669724782932 0.337852259374 y[1] (closed_form) = -0.669753174915 0.337951314505 absolute error = 0.000103 relative error = 0.01374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.767 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3871 1.312 h = 0.001 0.003 y[1] (numeric) = -0.670530587002 0.338840376219 y[1] (closed_form) = -0.670558593506 0.338939556642 absolute error = 0.0001031 relative error = 0.01372 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.767 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = -0.673130729895 0.34001192874 y[1] (closed_form) = -0.673159509433 0.340110820336 absolute error = 0.000103 relative error = 0.01366 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.769 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3882 1.319 h = 0.003 0.006 y[1] (numeric) = -0.676714316648 0.34046574126 y[1] (closed_form) = -0.676743222198 0.34056394688 absolute error = 0.0001024 relative error = 0.01351 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.772 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1931.5MB, alloc=52.3MB, time=23.55 x[1] = 0.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = -0.68183783587 0.343703971339 y[1] (closed_form) = -0.681868967915 0.343804239163 absolute error = 0.000105 relative error = 0.01375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.774 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = -0.686334465343 0.344243792051 y[1] (closed_form) = -0.686363955216 0.344343010518 absolute error = 0.0001035 relative error = 0.01348 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.778 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3914 1.333 h = 0.001 0.001 y[1] (numeric) = -0.689030929947 0.344600828919 y[1] (closed_form) = -0.689059819903 0.344700509113 absolute error = 0.0001038 relative error = 0.01347 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3924 1.334 h = 0.001 0.003 y[1] (numeric) = -0.689844469843 0.345591672032 y[1] (closed_form) = -0.689872990589 0.345691477765 absolute error = 0.0001038 relative error = 0.01345 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.78 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = -0.692462809371 0.34676089318 y[1] (closed_form) = -0.692492070025 0.346860411017 absolute error = 0.0001037 relative error = 0.01339 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.782 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3935 1.341 h = 0.003 0.006 y[1] (numeric) = -0.696067379451 0.347205165933 y[1] (closed_form) = -0.69609675242 0.347304022253 absolute error = 0.0001031 relative error = 0.01326 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.784 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = -0.701229225623 0.350443847412 y[1] (closed_form) = -0.701260767003 0.350544658522 absolute error = 0.0001056 relative error = 0.01347 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.787 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = -0.705751390047 0.350971611017 y[1] (closed_form) = -0.705781338337 0.351071434105 absolute error = 0.0001042 relative error = 0.01322 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.791 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1976.8MB, alloc=52.3MB, time=24.10 x[1] = 0.3967 1.355 h = 0.001 0.001 y[1] (numeric) = -0.708463158977 0.351321699653 y[1] (closed_form) = -0.70849253624 0.351421974586 absolute error = 0.0001045 relative error = 0.01321 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.793 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3977 1.356 h = 0.001 0.003 y[1] (numeric) = -0.70928417527 0.352315064971 y[1] (closed_form) = -0.709313199056 0.352415465417 absolute error = 0.0001045 relative error = 0.0132 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.793 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = -0.711919987767 0.353481807658 y[1] (closed_form) = -0.711949719446 0.353581921646 absolute error = 0.0001044 relative error = 0.01314 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.795 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.3988 1.363 h = 0.003 0.006 y[1] (numeric) = -0.715544617029 0.353916632752 y[1] (closed_form) = -0.715574448176 0.354016109094 absolute error = 0.0001039 relative error = 0.01301 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.798 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = -0.720743332149 0.357155252819 y[1] (closed_form) = -0.720775273819 0.357256581044 absolute error = 0.0001062 relative error = 0.01321 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.8 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = -0.725289898002 0.357671090516 y[1] (closed_form) = -0.725320295014 0.357771489214 absolute error = 0.0001049 relative error = 0.01297 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.804 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.402 1.377 h = 0.001 0.001 y[1] (numeric) = -0.728016295178 0.358014299684 y[1] (closed_form) = -0.728046148927 0.358115140212 absolute error = 0.0001052 relative error = 0.01296 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.806 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.403 1.378 h = 0.001 0.003 y[1] (numeric) = -0.728844533766 0.359009994108 y[1] (closed_form) = -0.728874049247 0.359110959872 absolute error = 0.0001052 relative error = 0.01295 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.806 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2022.3MB, alloc=52.3MB, time=24.66 x[1] = 0.404 1.381 h = 0.0001 0.004 y[1] (numeric) = -0.731497117258 0.360174127828 y[1] (closed_form) = -0.731527309711 0.360274809038 absolute error = 0.0001051 relative error = 0.01289 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.808 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4041 1.385 h = 0.003 0.006 y[1] (numeric) = -0.735140913856 0.360599609202 y[1] (closed_form) = -0.735171193745 0.36069967604 absolute error = 0.0001045 relative error = 0.01277 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.811 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = -0.740375080417 0.363837695613 y[1] (closed_form) = -0.740407413245 0.363939515821 absolute error = 0.0001068 relative error = 0.01295 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.814 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = -0.744944954382 0.364341752409 y[1] (closed_form) = -0.744975790279 0.364442698832 absolute error = 0.0001056 relative error = 0.01273 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.817 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4073 1.399 h = 0.001 0.001 y[1] (numeric) = -0.747685327589 0.364678159371 y[1] (closed_form) = -0.747715646888 0.364779537506 absolute error = 0.0001058 relative error = 0.01272 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4083 1.4 h = 0.003 0.006 y[1] (numeric) = -0.748520539857 0.365676000374 y[1] (closed_form) = -0.748550535573 0.365777503235 absolute error = 0.0001058 relative error = 0.0127 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.82 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = -0.753776332504 0.368915563354 y[1] (closed_form) = -0.753810329575 0.369017507243 absolute error = 0.0001075 relative error = 0.0128 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.822 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = -0.75836191807 0.369412162577 y[1] (closed_form) = -0.758394449283 0.369513270653 absolute error = 0.0001062 relative error = 0.01259 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.826 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2067.9MB, alloc=52.3MB, time=25.21 x[1] = 0.4115 1.414 h = 0.001 0.001 y[1] (numeric) = -0.761111707799 0.369744272549 y[1] (closed_form) = -0.761143740386 0.369845805972 absolute error = 0.0001065 relative error = 0.01258 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4125 1.415 h = 0.001 0.003 y[1] (numeric) = -0.761951526891 0.370743657962 y[1] (closed_form) = -0.761983245719 0.37084531599 absolute error = 0.0001065 relative error = 0.01257 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.829 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = -0.764630957474 0.371903520837 y[1] (closed_form) = -0.764663303458 0.372004897756 absolute error = 0.0001064 relative error = 0.01251 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.83 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4136 1.422 h = 0.003 0.006 y[1] (numeric) = -0.768305400769 0.372313932663 y[1] (closed_form) = -0.768337815077 0.372414732868 absolute error = 0.0001059 relative error = 0.0124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.833 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = -0.773596339432 0.375550972259 y[1] (closed_form) = -0.773630712702 0.375653367768 absolute error = 0.000108 relative error = 0.01256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.836 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = -0.778203472774 0.376036037562 y[1] (closed_form) = -0.778236426678 0.376137648526 absolute error = 0.0001068 relative error = 0.01236 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.84 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4168 1.436 h = 0.001 0.001 y[1] (numeric) = -0.780966188388 0.376361477654 y[1] (closed_form) = -0.780998668529 0.376463503714 absolute error = 0.0001071 relative error = 0.01235 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4178 1.437 h = 0.001 0.003 y[1] (numeric) = -0.781812578342 0.377362718477 y[1] (closed_form) = -0.781844758554 0.377464868268 absolute error = 0.0001071 relative error = 0.01234 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2113.3MB, alloc=52.3MB, time=25.77 x[1] = 0.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = -0.784507001762 0.378519680564 y[1] (closed_form) = -0.784539781069 0.378621552243 absolute error = 0.000107 relative error = 0.01228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.844 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4189 1.444 h = 0.003 0.006 y[1] (numeric) = -0.788198368018 0.378921058375 y[1] (closed_form) = -0.788231205649 0.379022375008 absolute error = 0.0001065 relative error = 0.01218 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.847 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = -0.79352115759 0.382156448237 y[1] (closed_form) = -0.793555897795 0.382259272901 absolute error = 0.0001085 relative error = 0.01232 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.85 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.422 1.455 h = 0.0001 0.003 y[1] (numeric) = -0.798148849848 0.38263015622 y[1] (closed_form) = -0.79818221635 0.382732245088 absolute error = 0.0001074 relative error = 0.01213 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.854 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4221 1.458 h = 0.001 0.001 y[1] (numeric) = -0.800923901155 0.382949023242 y[1] (closed_form) = -0.800956817727 0.383051516928 absolute error = 0.0001076 relative error = 0.01212 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4231 1.459 h = 0.001 0.003 y[1] (numeric) = -0.801776628408 0.383951963535 y[1] (closed_form) = -0.801809258381 0.384054579896 absolute error = 0.0001077 relative error = 0.01211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = -0.804485421118 0.385105948023 y[1] (closed_form) = -0.804518623157 0.385208289598 absolute error = 0.0001076 relative error = 0.01206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.858 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4242 1.466 h = 0.003 0.006 y[1] (numeric) = -0.808192932888 0.385498431022 y[1] (closed_form) = -0.808226183939 0.385600238612 absolute error = 0.0001071 relative error = 0.01196 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.861 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2158.8MB, alloc=52.3MB, time=26.32 x[1] = 0.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = -0.813546303848 0.388731832566 y[1] (closed_form) = -0.813581401726 0.388835064866 absolute error = 0.000109 relative error = 0.01209 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.864 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = -0.81819360373 0.38919436897 y[1] (closed_form) = -0.818227372703 0.389296911789 absolute error = 0.000108 relative error = 0.01191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.868 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4274 1.48 h = 0.001 0.001 y[1] (numeric) = -0.820980422856 0.389506765444 y[1] (closed_form) = -0.821013764728 0.389609702802 absolute error = 0.0001082 relative error = 0.01191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = -0.82183925968 0.390511258386 y[1] (closed_form) = -0.821872327796 0.390614317193 absolute error = 0.0001082 relative error = 0.01189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.87 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4285 1.485 h = 0.003 0.006 y[1] (numeric) = -0.825559405125 0.390896551795 y[1] (closed_form) = -0.825593075393 0.390998564217 absolute error = 0.0001074 relative error = 0.01176 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.874 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = -0.830938084742 0.39412765042 y[1] (closed_form) = -0.830973553488 0.394231019556 absolute error = 0.0001093 relative error = 0.01188 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.876 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = -0.8356013986 0.394580506766 y[1] (closed_form) = -0.835635576801 0.394683223888 absolute error = 0.0001083 relative error = 0.01171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.88 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4317 1.499 h = 0.001 0.001 y[1] (numeric) = -0.838397833689 0.394887288197 y[1] (closed_form) = -0.838431603534 0.394990390769 absolute error = 0.0001085 relative error = 0.01171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.883 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2204.2MB, alloc=52.3MB, time=26.87 x[1] = 0.4327 1.5 h = 0.001 0.003 y[1] (numeric) = -0.83926176784 0.395892937513 y[1] (closed_form) = -0.839295274581 0.395996160212 absolute error = 0.0001085 relative error = 0.01169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.883 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = -0.841995672933 0.397041064071 y[1] (closed_form) = -0.842029704167 0.397144019238 absolute error = 0.0001084 relative error = 0.01165 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.885 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4338 1.507 h = 0.003 0.006 y[1] (numeric) = -0.845731157916 0.397417218166 y[1] (closed_form) = -0.845765222788 0.397519677017 absolute error = 0.000108 relative error = 0.01155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.888 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = -0.851138159084 0.400645795059 y[1] (closed_form) = -0.851173968109 0.400749534314 absolute error = 0.0001097 relative error = 0.01167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.891 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = -0.855819409958 0.401087856316 y[1] (closed_form) = -0.855853971523 0.401190985594 absolute error = 0.0001088 relative error = 0.01151 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.895 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.437 1.521 h = 0.001 0.001 y[1] (numeric) = -0.858626615227 0.401388377078 y[1] (closed_form) = -0.858660789474 0.401491881591 absolute error = 0.000109 relative error = 0.0115 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.897 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.438 1.522 h = 0.001 0.003 y[1] (numeric) = -0.859496249368 0.402395331319 y[1] (closed_form) = -0.859530172466 0.40249895447 absolute error = 0.000109 relative error = 0.01149 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.897 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.439 1.525 h = 0.0001 0.004 y[1] (numeric) = -0.862242853481 0.403540332608 y[1] (closed_form) = -0.86227727688 0.403643692313 absolute error = 0.0001089 relative error = 0.01144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.899 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2249.6MB, alloc=52.3MB, time=27.42 x[1] = 0.4391 1.529 h = 0.003 0.006 y[1] (numeric) = -0.865992423278 0.403908034375 y[1] (closed_form) = -0.866026872786 0.404010917088 absolute error = 0.0001085 relative error = 0.01135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.902 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = -0.871426589512 0.407133836022 y[1] (closed_form) = -0.871462729673 0.407237926424 absolute error = 0.0001102 relative error = 0.01145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.905 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = -0.876124928923 0.407565307719 y[1] (closed_form) = -0.87615986377 0.407668827998 absolute error = 0.0001093 relative error = 0.01131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.909 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4423 1.543 h = 0.001 0.001 y[1] (numeric) = -0.87894239759 0.407859682872 y[1] (closed_form) = -0.878976965235 0.40796356823 absolute error = 0.0001095 relative error = 0.0113 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4433 1.544 h = 0.001 0.003 y[1] (numeric) = -0.879817520966 0.408867819096 y[1] (closed_form) = -0.879851848959 0.408971821479 absolute error = 0.0001095 relative error = 0.01129 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.912 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = -0.882576279335 0.410009661363 y[1] (closed_form) = -0.882611084383 0.410113404598 absolute error = 0.0001094 relative error = 0.01124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.914 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4444 1.551 h = 0.003 0.006 y[1] (numeric) = -0.886339267273 0.410369072366 y[1] (closed_form) = -0.886374091464 0.410472357341 absolute error = 0.000109 relative error = 0.01116 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.917 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = -0.891799480496 0.413591871842 y[1] (closed_form) = -0.891835942717 0.413696295255 absolute error = 0.0001106 relative error = 0.01125 % Correct digits = 4 memory used=2295.0MB, alloc=52.3MB, time=27.97 Radius of convergence (given) for eq 1 = 1.92 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = -0.896514094123 0.41401296469 y[1] (closed_form) = -0.89654939222 0.41411685574 absolute error = 0.0001097 relative error = 0.01111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.924 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4476 1.565 h = 0.001 0.001 y[1] (numeric) = -0.89934133971 0.414301312636 y[1] (closed_form) = -0.89937628983 0.414405558684 absolute error = 0.0001099 relative error = 0.0111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.926 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4486 1.566 h = 0.001 0.003 y[1] (numeric) = -0.900221747467 0.415310515557 y[1] (closed_form) = -0.900256468984 0.415414876903 absolute error = 0.00011 relative error = 0.01109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.927 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = -0.902992134828 0.416449174414 y[1] (closed_form) = -0.903027311075 0.416553281098 absolute error = 0.0001099 relative error = 0.01105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.928 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4497 1.573 h = 0.003 0.006 y[1] (numeric) = -0.906767901156 0.41680046021 y[1] (closed_form) = -0.906803090115 0.416904126776 absolute error = 0.0001095 relative error = 0.01097 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.932 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = -0.912253081095 0.420020055552 y[1] (closed_form) = -0.912289856387 0.420124794647 absolute error = 0.000111 relative error = 0.01105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.935 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = -0.916983187841 0.420430984561 y[1] (closed_form) = -0.917018839226 0.420535227045 absolute error = 0.0001102 relative error = 0.01092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.939 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2340.5MB, alloc=52.3MB, time=28.54 x[1] = 0.4529 1.587 h = 0.001 0.001 y[1] (numeric) = -0.919819743618 0.420713426515 y[1] (closed_form) = -0.919855065387 0.420818014007 absolute error = 0.0001104 relative error = 0.01091 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.941 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = -0.920705236787 0.421723588138 y[1] (closed_form) = -0.920740340566 0.421828289105 absolute error = 0.0001104 relative error = 0.0109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.941 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.454 1.592 h = 0.003 0.006 y[1] (numeric) = -0.924490984205 0.422068335646 y[1] (closed_form) = -0.924526527564 0.422172148874 absolute error = 0.0001097 relative error = 0.0108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.945 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.457 1.598 h = 0.0001 0.005 y[1] (numeric) = -0.929996776989 0.425284748576 y[1] (closed_form) = -0.930033862218 0.425389580781 absolute error = 0.0001112 relative error = 0.01087 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.948 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = -0.934739501356 0.425686931249 y[1] (closed_form) = -0.934775496905 0.425791295608 absolute error = 0.0001104 relative error = 0.01075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.952 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4572 1.606 h = 0.001 0.001 y[1] (numeric) = -0.937583643612 0.425964284675 y[1] (closed_form) = -0.937619324564 0.426068985323 absolute error = 0.0001106 relative error = 0.01074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4582 1.607 h = 0.001 0.003 y[1] (numeric) = -0.938473369066 0.426975132888 y[1] (closed_form) = -0.938508840801 0.427079945251 absolute error = 0.0001107 relative error = 0.01073 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.955 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = -0.941264024124 0.428107707824 y[1] (closed_form) = -0.941299911471 0.428212274525 absolute error = 0.0001106 relative error = 0.01069 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.956 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2385.8MB, alloc=52.3MB, time=29.09 x[1] = 0.4593 1.614 h = 0.003 0.006 y[1] (numeric) = -0.945061862433 0.428444190547 y[1] (closed_form) = -0.945097752054 0.42854834941 absolute error = 0.0001102 relative error = 0.01062 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.96 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = -0.950590708379 0.43165709651 y[1] (closed_form) = -0.950628090028 0.431762214318 absolute error = 0.0001116 relative error = 0.01069 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.963 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = -0.955347560224 0.432049532509 y[1] (closed_form) = -0.955383890556 0.432154214714 absolute error = 0.0001108 relative error = 0.01057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.967 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4625 1.628 h = 0.001 0.001 y[1] (numeric) = -0.958200196334 0.432321216338 y[1] (closed_form) = -0.958236228905 0.43242622506 absolute error = 0.000111 relative error = 0.01056 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.969 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4635 1.629 h = 0.001 0.003 y[1] (numeric) = -0.95909465139 0.433332842729 y[1] (closed_form) = -0.959130484575 0.433437961196 absolute error = 0.0001111 relative error = 0.01055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.97 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = -0.961895536787 0.434462215625 y[1] (closed_form) = -0.961931765759 0.434567093307 absolute error = 0.000111 relative error = 0.01051 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.972 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4646 1.636 h = 0.003 0.006 y[1] (numeric) = -0.965704467328 0.434791069442 y[1] (closed_form) = -0.965740693511 0.434895555782 absolute error = 0.0001106 relative error = 0.01044 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.975 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = -0.971255390802 0.438000329056 y[1] (closed_form) = -0.971293060194 0.4381057173 absolute error = 0.0001119 relative error = 0.0105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.978 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2431.2MB, alloc=52.3MB, time=29.64 x[1] = 0.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = -0.97602567881 0.438383240975 y[1] (closed_form) = -0.976062334257 0.438488224083 absolute error = 0.0001112 relative error = 0.01039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.982 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4678 1.65 h = 0.001 0.001 y[1] (numeric) = -0.978886395443 0.43864938163 y[1] (closed_form) = -0.978922769184 0.438754681614 absolute error = 0.0001114 relative error = 0.01039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4688 1.651 h = 0.001 0.003 y[1] (numeric) = -0.979785397797 0.439661697103 y[1] (closed_form) = -0.979821581583 0.439767104795 absolute error = 0.0001114 relative error = 0.01038 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = -0.982596059684 0.440787873266 y[1] (closed_form) = -0.982632620255 0.440893045148 absolute error = 0.0001113 relative error = 0.01034 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.987 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4699 1.658 h = 0.003 0.006 y[1] (numeric) = -0.986415539574 0.441109272811 y[1] (closed_form) = -0.98645209272 0.441214069291 absolute error = 0.000111 relative error = 0.01027 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.99 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = -0.991987599984 0.444314765979 y[1] (closed_form) = -0.992025548568 0.444420410193 absolute error = 0.0001123 relative error = 0.01033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.994 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.473 1.669 h = 0.0001 0.003 y[1] (numeric) = -0.996770662356 0.444688377843 y[1] (closed_form) = -0.996807633372 0.444793645693 absolute error = 0.0001116 relative error = 0.01022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.998 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4731 1.672 h = 0.001 0.001 y[1] (numeric) = -0.999639063737 0.444949102834 y[1] (closed_form) = -0.999675768352 0.445054678058 absolute error = 0.0001118 relative error = 0.01021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2476.7MB, alloc=52.3MB, time=30.20 x[1] = 0.4741 1.673 h = 0.001 0.003 y[1] (numeric) = -1.00054243676 0.44596202429 y[1] (closed_form) = -1.00057896046 0.44606770513 absolute error = 0.0001118 relative error = 0.01021 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = -1.00336243868 0.447085015306 y[1] (closed_form) = -1.00339932096 0.447190465392 absolute error = 0.0001117 relative error = 0.01017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.002 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4752 1.68 h = 0.003 0.006 y[1] (numeric) = -1.00719194826 0.447399136282 y[1] (closed_form) = -1.00722881888 0.447504226361 absolute error = 0.0001114 relative error = 0.0101 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.006 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = -1.01278423927 0.450600760874 y[1] (closed_form) = -1.01282245862 0.450706647271 absolute error = 0.0001126 relative error = 0.01015 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.009 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = -1.01757944275 0.450965297524 y[1] (closed_form) = -1.01761671992 0.451070834709 absolute error = 0.0001119 relative error = 0.01006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.013 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4784 1.694 h = 0.001 0.001 y[1] (numeric) = -1.02045515009 0.45122073507 y[1] (closed_form) = -1.02049217545 0.451326570277 absolute error = 0.0001121 relative error = 0.01005 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = -1.02136272278 0.452234185099 y[1] (closed_form) = -1.02139957588 0.452340123783 absolute error = 0.0001122 relative error = 0.01004 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4795 1.699 h = 0.003 0.006 y[1] (numeric) = -1.02520005346 0.452542469869 y[1] (closed_form) = -1.02523722105 0.452647662167 absolute error = 0.0001116 relative error = 0.009955 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.019 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2522.2MB, alloc=52.3MB, time=30.75 x[1] = 0.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = -1.03080901065 0.455740468605 y[1] (closed_form) = -1.03084748707 0.455846415624 absolute error = 0.0001127 relative error = 0.01 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.023 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = -1.03561407435 0.456097238988 y[1] (closed_form) = -1.03565163855 0.456202858517 absolute error = 0.0001121 relative error = 0.009906 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.027 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4827 1.713 h = 0.001 0.001 y[1] (numeric) = -1.03849571876 0.456348147046 y[1] (closed_form) = -1.03853304303 0.456454056513 absolute error = 0.0001123 relative error = 0.009899 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.029 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4837 1.714 h = 0.001 0.003 y[1] (numeric) = -1.03940677878 0.45736194683 y[1] (closed_form) = -1.03944393793 0.457467957805 absolute error = 0.0001123 relative error = 0.009892 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.03 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = -1.0422430189 0.458478961361 y[1] (closed_form) = -1.04228050486 0.458584751334 absolute error = 0.0001122 relative error = 0.009856 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.032 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4848 1.721 h = 0.003 0.006 y[1] (numeric) = -1.04608980291 0.458779902065 y[1] (closed_form) = -1.0461272705 0.458885359305 absolute error = 0.0001119 relative error = 0.009797 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.035 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = -1.0517173918 0.461973895601 y[1] (closed_form) = -1.05175612357 0.462080060959 absolute error = 0.000113 relative error = 0.009837 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.038 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = -1.05653349369 0.462322016178 y[1] (closed_form) = -1.05657134677 0.462427878388 absolute error = 0.0001124 relative error = 0.009748 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.043 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2567.7MB, alloc=52.3MB, time=31.30 x[1] = 0.488 1.735 h = 0.001 0.001 y[1] (numeric) = -1.05942178405 0.462567880171 y[1] (closed_form) = -1.05945941051 0.462674023276 absolute error = 0.0001126 relative error = 0.009741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.045 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.489 1.736 h = 0.001 0.003 y[1] (numeric) = -1.06033673934 0.463582080489 y[1] (closed_form) = -1.06037420868 0.463688322902 absolute error = 0.0001127 relative error = 0.009734 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.045 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.49 1.739 h = 0.0001 0.004 y[1] (numeric) = -1.06318116306 0.464695977483 y[1] (closed_form) = -1.06321894314 0.464802004075 absolute error = 0.0001126 relative error = 0.0097 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.047 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4901 1.743 h = 0.003 0.006 y[1] (numeric) = -1.06703661367 0.464990149366 y[1] (closed_form) = -1.06707437217 0.465095857118 absolute error = 0.0001122 relative error = 0.009643 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.051 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = -1.07268202152 0.468180079843 y[1] (closed_form) = -1.07272100065 0.468286451547 absolute error = 0.0001133 relative error = 0.009679 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.054 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = -1.07750860477 0.468519774489 y[1] (closed_form) = -1.07754673776 0.468625865972 absolute error = 0.0001127 relative error = 0.009594 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.059 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4933 1.757 h = 0.001 0.001 y[1] (numeric) = -1.08040320779 0.468760722678 y[1] (closed_form) = -1.08044112683 0.468867086185 absolute error = 0.0001129 relative error = 0.009587 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.061 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4943 1.758 h = 0.001 0.003 y[1] (numeric) = -1.08132190294 0.469775260713 y[1] (closed_form) = -1.0813596725 0.469881721304 absolute error = 0.000113 relative error = 0.009581 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.061 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2613.2MB, alloc=52.3MB, time=31.85 x[1] = 0.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = -1.08417413658 0.470886070966 y[1] (closed_form) = -1.08421220153 0.470992320933 absolute error = 0.0001129 relative error = 0.009548 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.063 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4954 1.765 h = 0.003 0.006 y[1] (numeric) = -1.08803781668 0.471173649452 y[1] (closed_form) = -1.08807585715 0.471279593972 absolute error = 0.0001126 relative error = 0.009493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.067 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = -1.09370026176 0.474359472456 y[1] (closed_form) = -1.0937394804 0.474466039093 absolute error = 0.0001136 relative error = 0.009525 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.07 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = -1.09853679444 0.474690963918 y[1] (closed_form) = -1.09857519855 0.474797271915 absolute error = 0.000113 relative error = 0.009445 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.075 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4986 1.779 h = 0.001 0.001 y[1] (numeric) = -1.10143739168 0.474927124098 y[1] (closed_form) = -1.10147559388 0.475033695423 absolute error = 0.0001132 relative error = 0.009438 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.4996 1.78 h = 0.001 0.003 y[1] (numeric) = -1.10235967652 0.475941941624 y[1] (closed_form) = -1.10239773656 0.476048607793 absolute error = 0.0001133 relative error = 0.009432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.077 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = -1.10521936149 0.477049699841 y[1] (closed_form) = -1.10525770223 0.477156160589 absolute error = 0.0001132 relative error = 0.009399 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.08 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5007 1.787 h = 0.003 0.006 y[1] (numeric) = -1.10909085355 0.477330859437 y[1] (closed_form) = -1.10912916722 0.477437027642 absolute error = 0.0001129 relative error = 0.009347 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.083 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2658.7MB, alloc=52.3MB, time=32.41 x[1] = 0.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = -1.11476958426 0.480512542969 y[1] (closed_form) = -1.11480903477 0.480619293682 absolute error = 0.0001138 relative error = 0.009375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.087 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = -1.11961555849 0.480836052462 y[1] (closed_form) = -1.11965422509 0.480942564834 absolute error = 0.0001133 relative error = 0.009299 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.091 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5039 1.801 h = 0.001 0.001 y[1] (numeric) = -1.12252184579 0.481067551714 y[1] (closed_form) = -1.12256032193 0.481174318899 absolute error = 0.0001135 relative error = 0.009292 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.093 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = -1.12344757527 0.482082594842 y[1] (closed_form) = -1.12348591625 0.482189454621 absolute error = 0.0001135 relative error = 0.009286 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.094 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.505 1.806 h = 0.003 0.006 y[1] (numeric) = -1.12732514944 0.482358622382 y[1] (closed_form) = -1.12736371007 0.482464859431 absolute error = 0.000113 relative error = 0.009217 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.097 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.508 1.812 h = 0.0001 0.005 y[1] (numeric) = -1.1330172692 0.485536543572 y[1] (closed_form) = -1.13305693152 0.485643331216 absolute error = 0.0001139 relative error = 0.009241 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.101 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = -1.13787088982 0.485853253492 y[1] (closed_form) = -1.13790979407 0.485959818941 absolute error = 0.0001134 relative error = 0.009168 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.105 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5082 1.82 h = 0.001 0.001 y[1] (numeric) = -1.14078178841 0.48608077872 y[1] (closed_form) = -1.14082051151 0.486187591673 absolute error = 0.0001136 relative error = 0.009162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.107 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2704.2MB, alloc=52.3MB, time=32.96 x[1] = 0.5092 1.821 h = 0.001 0.003 y[1] (numeric) = -1.14171037252 0.48709593724 y[1] (closed_form) = -1.14174896621 0.487202840768 absolute error = 0.0001137 relative error = 0.009156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.108 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = -1.14458298284 0.488198041062 y[1] (closed_form) = -1.14462183167 0.48830474898 absolute error = 0.0001136 relative error = 0.009125 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.11 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5103 1.828 h = 0.003 0.006 y[1] (numeric) = -1.14846789233 0.488467634457 y[1] (closed_form) = -1.14850671013 0.488574072609 absolute error = 0.0001133 relative error = 0.009077 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.113 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = -1.15417497639 0.491641394509 y[1] (closed_form) = -1.15421485662 0.491748347516 absolute error = 0.0001141 relative error = 0.009098 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.117 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = -1.15903715688 0.491950534204 y[1] (closed_form) = -1.15907630791 0.492057283108 absolute error = 0.0001137 relative error = 0.00903 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.121 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5135 1.842 h = 0.001 0.001 y[1] (numeric) = -1.1619532173 0.492173635568 y[1] (closed_form) = -1.16199219759 0.492280623814 absolute error = 0.0001139 relative error = 0.009023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5145 1.843 h = 0.001 0.003 y[1] (numeric) = -1.16288498893 0.49318893171 y[1] (closed_form) = -1.16292384625 0.49329600828 absolute error = 0.0001139 relative error = 0.009017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = -1.16576410446 0.494288104537 y[1] (closed_form) = -1.16580320404 0.494394990643 absolute error = 0.0001138 relative error = 0.008988 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.126 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2749.7MB, alloc=52.3MB, time=33.51 x[1] = 0.5156 1.85 h = 0.003 0.006 y[1] (numeric) = -1.16965573524 0.494551774777 y[1] (closed_form) = -1.16969480193 0.494658402689 absolute error = 0.0001136 relative error = 0.008942 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.13 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = -1.1753771136 0.497721371669 y[1] (closed_form) = -1.17541720454 0.497828480648 absolute error = 0.0001144 relative error = 0.008959 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = -1.18024740981 0.498023155824 y[1] (closed_form) = -1.18028679952 0.498130077684 absolute error = 0.0001139 relative error = 0.008894 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5188 1.864 h = 0.001 0.001 y[1] (numeric) = -1.18316836591 0.49824195705 y[1] (closed_form) = -1.18320759477 0.498349110279 absolute error = 0.0001141 relative error = 0.008888 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.14 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5198 1.865 h = 0.001 0.003 y[1] (numeric) = -1.18410319414 0.499257347951 y[1] (closed_form) = -1.18414230617 0.499364587257 absolute error = 0.0001141 relative error = 0.008882 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.141 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = -1.18698851023 0.500353635827 y[1] (closed_form) = -1.18702785222 0.50046068978 absolute error = 0.0001141 relative error = 0.008854 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.143 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5209 1.872 h = 0.003 0.006 y[1] (numeric) = -1.19088651372 0.500611551002 y[1] (closed_form) = -1.19092582119 0.500718357895 absolute error = 0.0001138 relative error = 0.008809 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.146 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = -1.19662154316 0.50377699166 y[1] (closed_form) = -1.19666183781 0.503884247689 absolute error = 0.0001146 relative error = 0.008824 % Correct digits = 4 memory used=2795.2MB, alloc=52.3MB, time=34.08 Radius of convergence (given) for eq 1 = 2.15 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.524 1.883 h = 0.0001 0.003 y[1] (numeric) = -1.20149953162 0.504071632215 y[1] (closed_form) = -1.20153915209 0.50417871706 absolute error = 0.0001142 relative error = 0.008763 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5241 1.886 h = 0.001 0.001 y[1] (numeric) = -1.20442512957 0.504286255571 y[1] (closed_form) = -1.20446459857 0.504393564002 absolute error = 0.0001143 relative error = 0.008756 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5251 1.887 h = 0.001 0.003 y[1] (numeric) = -1.20536288816 0.505301701812 y[1] (closed_form) = -1.2054022462 0.505409094084 absolute error = 0.0001144 relative error = 0.008751 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.157 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = -1.20825411299 0.506395152948 y[1] (closed_form) = -1.20829368926 0.506502364933 absolute error = 0.0001143 relative error = 0.008723 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.16 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5262 1.894 h = 0.003 0.006 y[1] (numeric) = -1.21215815683 0.506647478981 y[1] (closed_form) = -1.21219769716 0.506754454613 absolute error = 0.000114 relative error = 0.00868 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.163 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = -1.21790622012 0.509808778497 y[1] (closed_form) = -1.21794671161 0.509916173105 absolute error = 0.0001148 relative error = 0.008693 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.167 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = -1.22279149718 0.510096484409 y[1] (closed_form) = -1.22283134067 0.510203722771 absolute error = 0.0001144 relative error = 0.008634 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.171 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2840.6MB, alloc=52.3MB, time=34.63 x[1] = 0.5294 1.908 h = 0.001 0.001 y[1] (numeric) = -1.22572149495 0.510307050558 y[1] (closed_form) = -1.22576119589 0.510414504915 absolute error = 0.0001146 relative error = 0.008627 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = -1.22666206225 0.511322515957 y[1] (closed_form) = -1.22670165783 0.511430051934 absolute error = 0.0001146 relative error = 0.008622 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.174 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5305 1.913 h = 0.003 0.006 y[1] (numeric) = -1.23057080162 0.511570383946 y[1] (closed_form) = -1.23061054596 0.511677403784 absolute error = 0.0001142 relative error = 0.008566 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.178 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = -1.23632955997 0.514727990964 y[1] (closed_form) = -1.23637022502 0.514835405586 absolute error = 0.0001149 relative error = 0.008576 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.181 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = -1.24122072287 0.51500981203 y[1] (closed_form) = -1.24126076192 0.515117082207 absolute error = 0.0001145 relative error = 0.00852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.186 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5337 1.927 h = 0.001 0.001 y[1] (numeric) = -1.24415427635 0.51521693247 y[1] (closed_form) = -1.24419418005 0.515324412163 absolute error = 0.0001146 relative error = 0.008513 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.188 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5347 1.928 h = 0.001 0.003 y[1] (numeric) = -1.24509716697 0.516232356148 y[1] (closed_form) = -1.2451369699 0.5163399155 absolute error = 0.0001147 relative error = 0.008508 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.189 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = -1.24799861967 0.517320600551 y[1] (closed_form) = -1.24803862046 0.517427989024 absolute error = 0.0001146 relative error = 0.008482 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.191 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2886.1MB, alloc=52.3MB, time=35.18 x[1] = 0.5358 1.935 h = 0.003 0.006 y[1] (numeric) = -1.25191300949 0.517562896604 y[1] (closed_form) = -1.25195297233 0.517670067564 absolute error = 0.0001144 relative error = 0.008443 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.194 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = -1.25768371971 0.520716416485 y[1] (closed_form) = -1.25772456924 0.520823955133 absolute error = 0.000115 relative error = 0.00845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.198 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = -1.2625814726 0.520991687376 y[1] (closed_form) = -1.26262172069 0.52109909481 absolute error = 0.0001147 relative error = 0.008397 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.203 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.539 1.949 h = 0.001 0.001 y[1] (numeric) = -1.26551900684 0.521194972989 y[1] (closed_form) = -1.26555912765 0.521302582712 absolute error = 0.0001148 relative error = 0.008391 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.205 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.54 1.95 h = 0.001 0.003 y[1] (numeric) = -1.2664644912 0.522210357784 y[1] (closed_form) = -1.26650451638 0.522318044982 absolute error = 0.0001149 relative error = 0.008386 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.206 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.541 1.953 h = 0.0001 0.004 y[1] (numeric) = -1.2693710854 0.523295915789 y[1] (closed_form) = -1.26941129819 0.523403437003 absolute error = 0.0001148 relative error = 0.00836 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.208 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5411 1.957 h = 0.003 0.006 y[1] (numeric) = -1.27329065054 0.523533087192 y[1] (closed_form) = -1.27333082449 0.523640400446 absolute error = 0.0001146 relative error = 0.008323 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.211 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = -1.27907276509 0.526682554227 y[1] (closed_form) = -1.27911379274 0.526790209611 absolute error = 0.0001152 relative error = 0.008328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.215 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2931.4MB, alloc=52.3MB, time=35.73 x[1] = 0.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = -1.28397675669 0.526951474085 y[1] (closed_form) = -1.28401720664 0.527059010631 absolute error = 0.0001149 relative error = 0.008278 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.22 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5443 1.971 h = 0.001 0.001 y[1] (numeric) = -1.28691806092 0.527151040142 y[1] (closed_form) = -1.28695839125 0.527258771942 absolute error = 0.000115 relative error = 0.008271 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.222 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5453 1.972 h = 0.001 0.003 y[1] (numeric) = -1.28786602981 0.528166358035 y[1] (closed_form) = -1.28790626939 0.528274165149 absolute error = 0.0001151 relative error = 0.008266 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.223 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = -1.29077751917 0.529249283516 y[1] (closed_form) = -1.2908179366 0.529356929473 absolute error = 0.000115 relative error = 0.008242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.225 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5464 1.979 h = 0.003 0.006 y[1] (numeric) = -1.29470198397 0.529481486113 y[1] (closed_form) = -1.29474236181 0.529588933283 absolute error = 0.0001148 relative error = 0.008205 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = -1.30049497805 0.532626940183 y[1] (closed_form) = -1.30053617765 0.532734705389 absolute error = 0.0001154 relative error = 0.008209 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.232 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = -1.30540487399 0.532889704498 y[1] (closed_form) = -1.3054455188 0.532997362437 absolute error = 0.0001151 relative error = 0.008161 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.237 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5496 1.993 h = 0.001 0.001 y[1] (numeric) = -1.30834974752 0.533085664243 y[1] (closed_form) = -1.30839027996 0.53319351059 absolute error = 0.0001152 relative error = 0.008154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2976.7MB, alloc=52.3MB, time=36.28 x[1] = 0.5506 1.994 h = 0.001 0.003 y[1] (numeric) = -1.30930009582 0.534100889749 y[1] (closed_form) = -1.30934054219 0.534208809277 absolute error = 0.0001152 relative error = 0.00815 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.24 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = -1.31221624475 0.535181237512 y[1] (closed_form) = -1.31225685966 0.535289000634 absolute error = 0.0001152 relative error = 0.008126 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.242 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5517 2.001 h = 0.003 0.006 y[1] (numeric) = -1.31614534679 0.535408624278 y[1] (closed_form) = -1.31618592152 0.535516197421 absolute error = 0.000115 relative error = 0.008091 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.246 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = -1.3219487176 0.538550110285 y[1] (closed_form) = -1.32199008313 0.538657978761 absolute error = 0.0001155 relative error = 0.008093 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.25 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = -1.32686419964 0.538806910779 y[1] (closed_form) = -1.32690503251 0.538914682793 absolute error = 0.0001152 relative error = 0.008047 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.254 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5549 2.015 h = 0.001 0.001 y[1] (numeric) = -1.32981245143 0.538999375353 y[1] (closed_form) = -1.32985317879 0.53910732912 absolute error = 0.0001154 relative error = 0.008041 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.257 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = -1.33076507803 0.540014485357 y[1] (closed_form) = -1.33080572377 0.5401225102 absolute error = 0.0001154 relative error = 0.008036 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.257 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.556 2.02 h = 0.003 0.006 y[1] (numeric) = -1.33469777922 0.540238038509 y[1] (closed_form) = -1.33473852154 0.540345638 absolute error = 0.0001151 relative error = 0.00799 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.261 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3022.2MB, alloc=52.3MB, time=36.84 x[1] = 0.559 2.026 h = 0.0001 0.005 y[1] (numeric) = -1.34050964907 0.543376032488 y[1] (closed_form) = -1.34055115609 0.543483909183 absolute error = 0.0001156 relative error = 0.007991 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.265 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = -1.34542962845 0.543627788422 y[1] (closed_form) = -1.34547062136 0.543735577126 absolute error = 0.0001153 relative error = 0.007947 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.269 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5592 2.034 h = 0.001 0.001 y[1] (numeric) = -1.34838060235 0.543817294498 y[1] (closed_form) = -1.34842149528 0.543925259301 absolute error = 0.0001154 relative error = 0.00794 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.272 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5602 2.035 h = 0.001 0.003 y[1] (numeric) = -1.3493351103 0.544832262699 y[1] (closed_form) = -1.34937592525 0.54494029674 absolute error = 0.0001155 relative error = 0.007936 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.272 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = -1.35225930856 0.545907912804 y[1] (closed_form) = -1.35230027595 0.546015799171 absolute error = 0.0001154 relative error = 0.007913 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.274 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5613 2.042 h = 0.003 0.006 y[1] (numeric) = -1.35619633086 0.546126686937 y[1] (closed_form) = -1.3562372574 0.546234398785 absolute error = 0.0001152 relative error = 0.007881 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.278 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = -1.36201769827 0.549260813384 y[1] (closed_form) = -1.36205936041 0.549368782125 absolute error = 0.0001157 relative error = 0.00788 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.282 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = -1.36694271448 0.549506955244 y[1] (closed_form) = -1.3669838832 0.549614845499 absolute error = 0.0001155 relative error = 0.007838 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.286 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3067.7MB, alloc=52.3MB, time=37.39 x[1] = 0.5645 2.056 h = 0.001 0.001 y[1] (numeric) = -1.36989673671 0.549693169168 y[1] (closed_form) = -1.36993781165 0.549801229218 absolute error = 0.0001156 relative error = 0.007831 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.289 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5655 2.057 h = 0.001 0.003 y[1] (numeric) = -1.37085334477 0.550707985746 y[1] (closed_form) = -1.3708943458 0.550816112991 absolute error = 0.0001156 relative error = 0.007827 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.29 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = -1.37378158509 0.551781220733 y[1] (closed_form) = -1.37382273046 0.551889204819 absolute error = 0.0001156 relative error = 0.007805 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.292 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5666 2.064 h = 0.003 0.006 y[1] (numeric) = -1.37772256385 0.551995602695 y[1] (closed_form) = -1.37776366814 0.552103420087 absolute error = 0.0001154 relative error = 0.007774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.295 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = -1.38355298466 0.555125917829 y[1] (closed_form) = -1.38359479637 0.555233973003 absolute error = 0.0001159 relative error = 0.007772 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.299 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = -1.38848276195 0.555366625889 y[1] (closed_form) = -1.38852410021 0.555474611432 absolute error = 0.0001156 relative error = 0.007732 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.304 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5698 2.078 h = 0.001 0.001 y[1] (numeric) = -1.39143966685 0.555549652364 y[1] (closed_form) = -1.39148091719 0.555657801583 absolute error = 0.0001157 relative error = 0.007725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5708 2.079 h = 0.001 0.003 y[1] (numeric) = -1.39239828466 0.556564300126 y[1] (closed_form) = -1.39243946496 0.55667251453 absolute error = 0.0001158 relative error = 0.007721 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.307 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3113.2MB, alloc=52.3MB, time=37.94 x[1] = 0.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = -1.39533036924 0.557635176533 y[1] (closed_form) = -1.39537168619 0.557743252208 absolute error = 0.0001157 relative error = 0.0077 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5719 2.086 h = 0.003 0.006 y[1] (numeric) = -1.39927508808 0.557845307358 y[1] (closed_form) = -1.39931636381 0.557953223842 absolute error = 0.0001155 relative error = 0.00767 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.313 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = -1.40511413715 0.560971870563 y[1] (closed_form) = -1.40515609307 0.561080006856 absolute error = 0.000116 relative error = 0.007666 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.317 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.575 2.097 h = 0.0001 0.003 y[1] (numeric) = -1.41004841342 0.561207321042 y[1] (closed_form) = -1.41008991512 0.561315395947 absolute error = 0.0001158 relative error = 0.007628 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.321 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5751 2.1 h = 0.001 0.001 y[1] (numeric) = -1.41300804345 0.561387262481 y[1] (closed_form) = -1.41304946279 0.561495495124 absolute error = 0.0001159 relative error = 0.007622 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.324 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5761 2.101 h = 0.001 0.003 y[1] (numeric) = -1.41396858418 0.562401726056 y[1] (closed_form) = -1.41400993718 0.562510021912 absolute error = 0.0001159 relative error = 0.007618 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.325 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = -1.41690432414 0.563470300517 y[1] (closed_form) = -1.41694580645 0.563578461982 absolute error = 0.0001158 relative error = 0.007597 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5772 2.108 h = 0.003 0.006 y[1] (numeric) = -1.42085257735 0.56367631806 y[1] (closed_form) = -1.4208940184 0.563784327529 absolute error = 0.0001157 relative error = 0.007568 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.33 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3158.6MB, alloc=52.3MB, time=38.50 x[1] = 0.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = -1.42669984791 0.566799191481 y[1] (closed_form) = -1.42674194282 0.566907403865 absolute error = 0.0001161 relative error = 0.007563 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.335 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = -1.43163837407 0.567029556505 y[1] (closed_form) = -1.4316800333 0.567137715168 absolute error = 0.0001159 relative error = 0.007527 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.339 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5804 2.122 h = 0.001 0.001 y[1] (numeric) = -1.4346005795 0.567206513 y[1] (closed_form) = -1.43464216161 0.567314823641 absolute error = 0.000116 relative error = 0.00752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.342 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = -1.43556295974 0.56822077872 y[1] (closed_form) = -1.43560447902 0.568329150637 absolute error = 0.0001161 relative error = 0.007516 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.342 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5815 2.127 h = 0.003 0.006 y[1] (numeric) = -1.43951395161 0.568423527409 y[1] (closed_form) = -1.43955552964 0.568531550544 absolute error = 0.0001157 relative error = 0.007478 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.346 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = -1.44536794381 0.571543184713 y[1] (closed_form) = -1.44541015357 0.571651397343 absolute error = 0.0001162 relative error = 0.007473 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.35 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = -1.45030988034 0.571769260222 y[1] (closed_form) = -1.45035166992 0.571877425081 absolute error = 0.000116 relative error = 0.007438 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.354 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5847 2.141 h = 0.001 0.001 y[1] (numeric) = -1.45327415439 0.571943697353 y[1] (closed_form) = -1.45331587107 0.572052009317 absolute error = 0.0001161 relative error = 0.007431 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.357 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3204.1MB, alloc=52.3MB, time=39.05 x[1] = 0.5857 2.142 h = 0.001 0.003 y[1] (numeric) = -1.45423805119 0.57295776241 y[1] (closed_form) = -1.4542797079 0.573066133974 absolute error = 0.0001161 relative error = 0.007428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.358 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = -1.45718009331 0.574022165378 y[1] (closed_form) = -1.45722186669 0.574130410461 absolute error = 0.000116 relative error = 0.007408 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.36 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5868 2.149 h = 0.003 0.006 y[1] (numeric) = -1.46113436509 0.574220848184 y[1] (closed_form) = -1.46117609745 0.574328953869 absolute error = 0.0001159 relative error = 0.007381 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.364 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = -1.4669958691 0.577336941785 y[1] (closed_form) = -1.46703820852 0.57744522192 absolute error = 0.0001163 relative error = 0.007374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.368 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = -1.47194162669 0.577558243788 y[1] (closed_form) = -1.47198356322 0.577666482838 absolute error = 0.0001161 relative error = 0.007341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.372 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.59 2.163 h = 0.001 0.001 y[1] (numeric) = -1.4749082182 0.57772987757 y[1] (closed_form) = -1.47495008654 0.577838258295 absolute error = 0.0001162 relative error = 0.007335 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.375 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.591 2.164 h = 0.001 0.003 y[1] (numeric) = -1.47587380787 0.578743724368 y[1] (closed_form) = -1.47591561945 0.578852162829 absolute error = 0.0001162 relative error = 0.007331 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.375 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.592 2.167 h = 0.0001 0.004 y[1] (numeric) = -1.47881901157 0.579805988715 y[1] (closed_form) = -1.47886093347 0.579914304767 absolute error = 0.0001161 relative error = 0.007312 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.378 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3249.5MB, alloc=52.3MB, time=39.60 x[1] = 0.5921 2.171 h = 0.003 0.006 y[1] (numeric) = -1.48277628569 0.580000936904 y[1] (closed_form) = -1.48281816677 0.580109119926 absolute error = 0.000116 relative error = 0.007286 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.381 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = -1.48864494347 0.583113534672 y[1] (closed_form) = -1.48868740778 0.583221878024 absolute error = 0.0001164 relative error = 0.007278 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.386 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = -1.49359430713 0.583330223361 y[1] (closed_form) = -1.49363638519 0.583438531828 absolute error = 0.0001162 relative error = 0.007246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.39 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5953 2.185 h = 0.001 0.001 y[1] (numeric) = -1.49656308674 0.583499147091 y[1] (closed_form) = -1.49660510108 0.583607591972 absolute error = 0.0001163 relative error = 0.00724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.393 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5963 2.186 h = 0.001 0.003 y[1] (numeric) = -1.49753029504 0.584512766161 y[1] (closed_form) = -1.49757225567 0.584621266954 absolute error = 0.0001163 relative error = 0.007236 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.393 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = -1.5004785025 0.585572947655 y[1] (closed_form) = -1.5005205674 0.585681330017 absolute error = 0.0001163 relative error = 0.007218 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.396 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.5974 2.193 h = 0.003 0.006 y[1] (numeric) = -1.50443861024 0.585764286527 y[1] (closed_form) = -1.50448063459 0.585872541959 absolute error = 0.0001161 relative error = 0.007193 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.399 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = -1.51031407949 0.588873457795 y[1] (closed_form) = -1.51035666407 0.588981860313 absolute error = 0.0001165 relative error = 0.007184 % Correct digits = 4 memory used=3295.1MB, alloc=52.3MB, time=40.16 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = -1.51526684515 0.589085689244 y[1] (closed_form) = -1.51530905951 0.589194062618 absolute error = 0.0001163 relative error = 0.007154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.408 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6006 2.207 h = 0.001 0.001 y[1] (numeric) = -1.51823769003 0.589251993867 y[1] (closed_form) = -1.51827984488 0.589360498561 absolute error = 0.0001164 relative error = 0.007147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.411 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6016 2.208 h = 0.001 0.003 y[1] (numeric) = -1.5192064457 0.590265377026 y[1] (closed_form) = -1.51924854973 0.590373935849 absolute error = 0.0001164 relative error = 0.007144 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.411 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = -1.52215750637 0.591323530991 y[1] (closed_form) = -1.52219970894 0.591431975267 absolute error = 0.0001164 relative error = 0.007126 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.414 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6027 2.215 h = 0.003 0.006 y[1] (numeric) = -1.52612028755 0.591511382622 y[1] (closed_form) = -1.52616244989 0.591619705808 absolute error = 0.0001162 relative error = 0.007102 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.417 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = -1.53200224114 0.594617197909 y[1] (closed_form) = -1.53204494152 0.594725655766 absolute error = 0.0001166 relative error = 0.007093 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.422 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = -1.53695821513 0.594825124091 y[1] (closed_form) = -1.5370005607 0.594933558113 absolute error = 0.0001164 relative error = 0.007063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.426 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3340.5MB, alloc=52.3MB, time=40.72 x[1] = 0.6059 2.229 h = 0.001 0.001 y[1] (numeric) = -1.53993100868 0.594988898204 y[1] (closed_form) = -1.53997329872 0.595097458616 absolute error = 0.0001165 relative error = 0.007057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.429 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = -1.54090124336 0.59600203846 y[1] (closed_form) = -1.54094348534 0.596110651257 absolute error = 0.0001165 relative error = 0.007053 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.429 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.607 2.234 h = 0.003 0.006 y[1] (numeric) = -1.54486609245 0.596187122752 y[1] (closed_form) = -1.54490836626 0.596295450821 absolute error = 0.0001163 relative error = 0.007022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.433 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.61 2.24 h = 0.0001 0.005 y[1] (numeric) = -1.55075333789 0.5992900343 y[1] (closed_form) = -1.55079613112 0.599398487233 absolute error = 0.0001166 relative error = 0.007013 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.437 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = -1.55571187712 0.599494337969 y[1] (closed_form) = -1.5557543284 0.599602771139 absolute error = 0.0001164 relative error = 0.006984 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.442 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6102 2.248 h = 0.001 0.001 y[1] (numeric) = -1.55868623045 0.599655981635 y[1] (closed_form) = -1.55872862938 0.599764537035 absolute error = 0.0001165 relative error = 0.006978 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.445 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6112 2.249 h = 0.001 0.003 y[1] (numeric) = -1.5596576826 0.600668891491 y[1] (closed_form) = -1.55970003571 0.600777497777 absolute error = 0.0001166 relative error = 0.006975 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.445 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = -1.56261365271 0.601723388018 y[1] (closed_form) = -1.56265609449 0.601831886793 absolute error = 0.0001165 relative error = 0.006957 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.448 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3386.0MB, alloc=52.3MB, time=41.27 x[1] = 0.6123 2.256 h = 0.003 0.006 y[1] (numeric) = -1.56658097167 0.601905036916 y[1] (closed_form) = -1.56662337404 0.602013424809 absolute error = 0.0001164 relative error = 0.006935 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.451 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = -1.57247413187 0.605004729493 y[1] (closed_form) = -1.57251703292 0.60511323125 absolute error = 0.0001167 relative error = 0.006925 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.456 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = -1.57743554681 0.605205001889 y[1] (closed_form) = -1.57747812025 0.605313488464 absolute error = 0.0001165 relative error = 0.006897 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.46 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6155 2.27 h = 0.001 0.001 y[1] (numeric) = -1.58041164844 0.605364274927 y[1] (closed_form) = -1.5804541731 0.6054728791 absolute error = 0.0001166 relative error = 0.006891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6165 2.271 h = 0.001 0.003 y[1] (numeric) = -1.58138445966 0.606376932477 y[1] (closed_form) = -1.58142694101 0.60648558587 absolute error = 0.0001167 relative error = 0.006888 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.463 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = -1.58434289038 0.607429558125 y[1] (closed_form) = -1.58438545544 0.607538107616 absolute error = 0.0001166 relative error = 0.006871 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.466 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6176 2.278 h = 0.003 0.006 y[1] (numeric) = -1.5883124697 0.60760805295 y[1] (closed_form) = -1.58835499582 0.607716496712 absolute error = 0.0001165 relative error = 0.006849 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.469 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = -1.5942112576 0.610704598962 y[1] (closed_form) = -1.5942542624 0.610813146294 absolute error = 0.0001168 relative error = 0.006839 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.474 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3431.4MB, alloc=52.3MB, time=41.82 x[1] = 0.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = -1.59917538172 0.610900980378 y[1] (closed_form) = -1.59921807271 0.611009516748 absolute error = 0.0001166 relative error = 0.006813 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.478 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6208 2.292 h = 0.001 0.001 y[1] (numeric) = -1.6021531313 0.611057964684 y[1] (closed_form) = -1.60219577686 0.611166614173 absolute error = 0.0001167 relative error = 0.006807 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.481 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6218 2.293 h = 0.001 0.003 y[1] (numeric) = -1.60312724094 0.612070365843 y[1] (closed_form) = -1.60316984557 0.612179062926 absolute error = 0.0001167 relative error = 0.006803 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.482 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = -1.60608800701 0.613121173455 y[1] (closed_form) = -1.60613069066 0.613229770152 absolute error = 0.0001167 relative error = 0.006787 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.484 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6229 2.3 h = 0.003 0.006 y[1] (numeric) = -1.61005971597 0.613296623932 y[1] (closed_form) = -1.61010236118 0.613405119831 absolute error = 0.0001166 relative error = 0.006766 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.488 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = -1.61596385747 0.616390096095 y[1] (closed_form) = -1.61600696208 0.616498685937 absolute error = 0.0001168 relative error = 0.006755 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.492 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.626 2.311 h = 0.0001 0.003 y[1] (numeric) = -1.62093053288 0.616582722859 y[1] (closed_form) = -1.62097333695 0.616691305622 absolute error = 0.0001167 relative error = 0.00673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.497 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6261 2.314 h = 0.001 0.001 y[1] (numeric) = -1.62390983523 0.616737498051 y[1] (closed_form) = -1.62395259704 0.616846189603 absolute error = 0.0001168 relative error = 0.006724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.499 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3477.0MB, alloc=52.3MB, time=42.38 x[1] = 0.6271 2.315 h = 0.001 0.003 y[1] (numeric) = -1.62488518515 0.617749639612 y[1] (closed_form) = -1.6249279083 0.617858377175 absolute error = 0.0001168 relative error = 0.00672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.5 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = -1.62784816722 0.618798681267 y[1] (closed_form) = -1.62789096492 0.618907321864 absolute error = 0.0001168 relative error = 0.006705 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.502 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6282 2.322 h = 0.003 0.006 y[1] (numeric) = -1.63182188189 0.618971194019 y[1] (closed_form) = -1.63186464169 0.619079738535 absolute error = 0.0001167 relative error = 0.006684 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.506 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = -1.63773111527 0.622061665176 y[1] (closed_form) = -1.6377743159 0.622170294638 absolute error = 0.0001169 relative error = 0.006673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.51 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = -1.64270019234 0.622250669704 y[1] (closed_form) = -1.64274310517 0.622359295652 absolute error = 0.0001168 relative error = 0.006649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.515 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6314 2.336 h = 0.001 0.001 y[1] (numeric) = -1.64568095724 0.622403313144 y[1] (closed_form) = -1.64572383079 0.622512043698 absolute error = 0.0001169 relative error = 0.006643 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.518 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = -1.64665749171 0.623415192713 y[1] (closed_form) = -1.64670032875 0.623523967733 absolute error = 0.0001169 relative error = 0.006639 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.518 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6325 2.341 h = 0.003 0.006 y[1] (numeric) = -1.65063275476 0.623585377125 y[1] (closed_form) = -1.65067560489 0.623693920635 absolute error = 0.0001167 relative error = 0.006613 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.522 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3522.3MB, alloc=52.3MB, time=42.93 x[1] = 0.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = -1.65654613602 0.626673266787 y[1] (closed_form) = -1.65658941143 0.626781888185 absolute error = 0.0001169 relative error = 0.006601 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.526 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = -1.66151712546 0.62685923017 y[1] (closed_form) = -1.66156012369 0.62696785074 absolute error = 0.0001168 relative error = 0.006578 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.531 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6357 2.355 h = 0.001 0.001 y[1] (numeric) = -1.66449905644 0.627010082874 y[1] (closed_form) = -1.66454201777 0.62711880453 absolute error = 0.0001169 relative error = 0.006572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.534 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6367 2.356 h = 0.001 0.003 y[1] (numeric) = -1.66547656454 0.62802172233 y[1] (closed_form) = -1.6655194911 0.628130487132 absolute error = 0.0001169 relative error = 0.006569 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.534 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = -1.66844335194 0.629067590448 y[1] (closed_form) = -1.66848634539 0.629176264453 absolute error = 0.0001169 relative error = 0.006554 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.537 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6378 2.363 h = 0.003 0.006 y[1] (numeric) = -1.67242045869 0.629234889402 y[1] (closed_form) = -1.67246341539 0.629343475556 absolute error = 0.0001168 relative error = 0.006535 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.541 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = -1.67833847698 0.632319916165 y[1] (closed_form) = -1.67838184164 0.632428572282 absolute error = 0.000117 relative error = 0.006523 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.545 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = -1.68331161173 0.632502495042 y[1] (closed_form) = -1.68335471104 0.632611153361 absolute error = 0.0001169 relative error = 0.0065 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.55 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3567.8MB, alloc=52.3MB, time=43.48 x[1] = 0.641 2.377 h = 0.001 0.001 y[1] (numeric) = -1.68629485057 0.632651354999 y[1] (closed_form) = -1.68633791565 0.632760110485 absolute error = 0.000117 relative error = 0.006494 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.552 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.642 2.378 h = 0.001 0.003 y[1] (numeric) = -1.68727344565 0.633662730542 y[1] (closed_form) = -1.68731647791 0.633771527706 absolute error = 0.000117 relative error = 0.006491 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.553 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.643 2.381 h = 0.0001 0.004 y[1] (numeric) = -1.69024213851 0.634706978277 y[1] (closed_form) = -1.69028523381 0.634815687801 absolute error = 0.0001169 relative error = 0.006477 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.555 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6431 2.385 h = 0.003 0.006 y[1] (numeric) = -1.69422093224 0.634871629001 y[1] (closed_form) = -1.69426399142 0.634980254823 absolute error = 0.0001168 relative error = 0.006458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.559 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = -1.70014335857 0.637953865062 y[1] (closed_form) = -1.70018680904 0.638062553457 absolute error = 0.0001171 relative error = 0.006446 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.564 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = -1.70511851044 0.638133180877 y[1] (closed_form) = -1.70516170691 0.638241874241 absolute error = 0.000117 relative error = 0.006424 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.568 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6463 2.399 h = 0.001 0.001 y[1] (numeric) = -1.70810297975 0.638280119121 y[1] (closed_form) = -1.70814614451 0.638388905868 absolute error = 0.000117 relative error = 0.006418 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.571 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6473 2.4 h = 0.001 0.003 y[1] (numeric) = -1.70908261251 0.639291230302 y[1] (closed_form) = -1.7091257463 0.639400057299 absolute error = 0.0001171 relative error = 0.006415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.572 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3613.3MB, alloc=52.3MB, time=44.03 x[1] = 0.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = -1.71205311193 0.640333906337 y[1] (closed_form) = -1.71209630513 0.640442648762 absolute error = 0.000117 relative error = 0.006401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.574 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6484 2.407 h = 0.003 0.006 y[1] (numeric) = -1.716033492 0.640496003811 y[1] (closed_form) = -1.71607664971 0.640604666501 absolute error = 0.0001169 relative error = 0.006383 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.578 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = -1.7219601079 0.643575520931 y[1] (closed_form) = -1.72200364085 0.643684239306 absolute error = 0.0001171 relative error = 0.00637 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.582 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = -1.72693715549 0.643751691447 y[1] (closed_form) = -1.72698044536 0.643860417311 absolute error = 0.000117 relative error = 0.006349 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.587 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6516 2.421 h = 0.001 0.001 y[1] (numeric) = -1.72992278199 0.643896776884 y[1] (closed_form) = -1.7299660425 0.64400559248 absolute error = 0.0001171 relative error = 0.006344 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6526 2.422 h = 0.001 0.003 y[1] (numeric) = -1.73090340523 0.644907623836 y[1] (closed_form) = -1.73094663653 0.645016478293 absolute error = 0.0001171 relative error = 0.006341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.59 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = -1.73387561705 0.645948775922 y[1] (closed_form) = -1.73391890431 0.646057548784 absolute error = 0.0001171 relative error = 0.006327 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.593 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6537 2.429 h = 0.003 0.006 y[1] (numeric) = -1.73785748815 0.646108412247 y[1] (closed_form) = -1.73790074059 0.646217109166 absolute error = 0.000117 relative error = 0.006309 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.596 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3658.7MB, alloc=52.3MB, time=44.59 x[1] = 0.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = -1.74378808523 0.649185281632 y[1] (closed_form) = -1.74383169745 0.649294027823 absolute error = 0.0001172 relative error = 0.006297 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.601 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = -1.74876691367 0.649358420997 y[1] (closed_form) = -1.74881029329 0.649467176967 absolute error = 0.0001171 relative error = 0.006276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.606 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6569 2.443 h = 0.001 0.001 y[1] (numeric) = -1.75175362795 0.649501720444 y[1] (closed_form) = -1.75179698043 0.649610562621 absolute error = 0.0001172 relative error = 0.006271 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.608 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = -1.75273519646 0.65051230383 y[1] (closed_form) = -1.7527785214 0.650621183521 absolute error = 0.0001172 relative error = 0.006268 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.609 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.658 2.448 h = 0.003 0.006 y[1] (numeric) = -1.75671821606 0.65066999169 y[1] (closed_form) = -1.75676154143 0.65077868383 absolute error = 0.000117 relative error = 0.006246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.613 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.661 2.454 h = 0.0001 0.005 y[1] (numeric) = -1.76265205013 0.653744594287 y[1] (closed_form) = -1.76269572238 0.653853330714 absolute error = 0.0001172 relative error = 0.006233 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.617 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = -1.76763228984 0.653915193771 y[1] (closed_form) = -1.7676757382 0.654023941656 absolute error = 0.0001171 relative error = 0.006213 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.622 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6612 2.462 h = 0.001 0.001 y[1] (numeric) = -1.77061986749 0.654056995933 y[1] (closed_form) = -1.77066329047 0.654165827068 absolute error = 0.0001172 relative error = 0.006207 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.625 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3704.2MB, alloc=52.3MB, time=45.14 x[1] = 0.6622 2.463 h = 0.001 0.003 y[1] (numeric) = -1.77160221181 0.65506734279 y[1] (closed_form) = -1.7716456086 0.655176210288 absolute error = 0.0001172 relative error = 0.006205 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.625 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = -1.77457735796 0.656105765003 y[1] (closed_form) = -1.7746208048 0.656214556252 absolute error = 0.0001171 relative error = 0.006191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.628 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6633 2.47 h = 0.003 0.006 y[1] (numeric) = -1.77856174027 0.656261041881 y[1] (closed_form) = -1.77860515359 0.656369763791 absolute error = 0.0001171 relative error = 0.006175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.631 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = -1.78449919397 0.659333129637 y[1] (closed_form) = -1.78454293979 0.659441890226 absolute error = 0.0001172 relative error = 0.006162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.636 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = -1.7894810182 0.659500902194 y[1] (closed_form) = -1.78952454984 0.659609676145 absolute error = 0.0001172 relative error = 0.006143 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.641 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6665 2.484 h = 0.001 0.001 y[1] (numeric) = -1.79246956495 0.659641037991 y[1] (closed_form) = -1.79251307319 0.659749891898 absolute error = 0.0001172 relative error = 0.006137 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.643 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6675 2.485 h = 0.001 0.003 y[1] (numeric) = -1.79345277553 0.660651124256 y[1] (closed_form) = -1.79349625909 0.66076001325 absolute error = 0.0001173 relative error = 0.006134 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.644 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = -1.79642938963 0.661688154733 y[1] (closed_form) = -1.79647292027 0.661796970208 absolute error = 0.0001172 relative error = 0.006122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.647 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3749.7MB, alloc=52.3MB, time=45.69 x[1] = 0.6686 2.492 h = 0.003 0.006 y[1] (numeric) = -1.80041501859 0.661841219466 y[1] (closed_form) = -1.80045851642 0.661949968929 absolute error = 0.0001171 relative error = 0.006106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.65 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = -1.80635591005 0.66491086136 y[1] (closed_form) = -1.80639972655 0.665019644294 absolute error = 0.0001173 relative error = 0.006092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.655 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = -1.81133922073 0.665075911121 y[1] (closed_form) = -1.81138283236 0.665184709132 absolute error = 0.0001172 relative error = 0.006074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.66 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6718 2.506 h = 0.001 0.001 y[1] (numeric) = -1.81432867729 0.665214441568 y[1] (closed_form) = -1.81437226738 0.665323316359 absolute error = 0.0001173 relative error = 0.006069 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.662 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6728 2.507 h = 0.001 0.003 y[1] (numeric) = -1.81531271423 0.666224269152 y[1] (closed_form) = -1.81535628107 0.66633317779 absolute error = 0.0001173 relative error = 0.006066 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.663 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = -1.81829071855 0.667259951823 y[1] (closed_form) = -1.81833432968 0.66736878959 absolute error = 0.0001173 relative error = 0.006053 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.665 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6739 2.514 h = 0.003 0.006 y[1] (numeric) = -1.82227751715 0.667410885854 y[1] (closed_form) = -1.82232109616 0.667519660787 absolute error = 0.0001172 relative error = 0.006038 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.669 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = -1.82822167301 0.670478149971 y[1] (closed_form) = -1.8282655574 0.670586953544 absolute error = 0.0001173 relative error = 0.006025 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.674 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3795.1MB, alloc=52.3MB, time=46.24 x[1] = 0.677 2.525 h = 0.0001 0.003 y[1] (numeric) = -1.83320637742 0.670640577736 y[1] (closed_form) = -1.83325006588 0.670749397923 absolute error = 0.0001173 relative error = 0.006007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.679 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6771 2.528 h = 0.001 0.001 y[1] (numeric) = -1.83619668769 0.670777561913 y[1] (closed_form) = -1.83624035635 0.67088645582 absolute error = 0.0001173 relative error = 0.006001 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.681 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6781 2.529 h = 0.001 0.003 y[1] (numeric) = -1.83718151284 0.671787133092 y[1] (closed_form) = -1.83722515961 0.671896059642 absolute error = 0.0001173 relative error = 0.005999 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.682 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = -1.84016083345 0.672821510888 y[1] (closed_form) = -1.84020452184 0.672930369133 absolute error = 0.0001173 relative error = 0.005986 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.684 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6792 2.536 h = 0.003 0.006 y[1] (numeric) = -1.84414872887 0.672970393054 y[1] (closed_form) = -1.84419238585 0.6730791915 absolute error = 0.0001172 relative error = 0.005971 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.688 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = -1.85009598392 0.676035346517 y[1] (closed_form) = -1.8501399335 0.676144169126 absolute error = 0.0001174 relative error = 0.005958 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.693 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = -1.8550819944 0.676195249827 y[1] (closed_form) = -1.85512575663 0.67630409042 absolute error = 0.0001173 relative error = 0.005941 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.698 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6824 2.55 h = 0.001 0.001 y[1] (numeric) = -1.85807310535 0.676330744923 y[1] (closed_form) = -1.85811684941 0.676439656287 absolute error = 0.0001174 relative error = 0.005935 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.7 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3840.6MB, alloc=52.3MB, time=46.80 x[1] = 0.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = -1.85905868219 0.6773400623 y[1] (closed_form) = -1.85910240564 0.677449005142 absolute error = 0.0001174 relative error = 0.005933 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.701 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6835 2.555 h = 0.003 0.006 y[1] (numeric) = -1.86304742025 0.677487321631 y[1] (closed_form) = -1.86309113592 0.677596113049 absolute error = 0.0001172 relative error = 0.005914 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.705 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = -1.8689971902 0.680550304749 y[1] (closed_form) = -1.86904118781 0.680659116889 absolute error = 0.0001174 relative error = 0.005901 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.709 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = -1.87398422985 0.68070809654 y[1] (closed_form) = -1.87402804723 0.680816927625 absolute error = 0.0001173 relative error = 0.005884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.714 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6867 2.569 h = 0.001 0.001 y[1] (numeric) = -1.87697597289 0.680842345538 y[1] (closed_form) = -1.87701977338 0.680951244922 absolute error = 0.0001174 relative error = 0.005879 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.717 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6877 2.57 h = 0.001 0.003 y[1] (numeric) = -1.87796216577 0.68185143837 y[1] (closed_form) = -1.87800594669 0.681960368243 absolute error = 0.0001174 relative error = 0.005876 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.717 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = -1.88094373682 0.682883485153 y[1] (closed_form) = -1.88098755484 0.68299235131 absolute error = 0.0001174 relative error = 0.005864 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.72 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6888 2.577 h = 0.003 0.006 y[1] (numeric) = -1.88493347049 0.68302873922 y[1] (closed_form) = -1.88497725846 0.683137550856 absolute error = 0.0001173 relative error = 0.00585 % Correct digits = 4 memory used=3886.1MB, alloc=52.3MB, time=47.35 Radius of convergence (given) for eq 1 = 2.724 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = -1.89088605346 0.686089535585 y[1] (closed_form) = -1.89093011149 0.686198364064 absolute error = 0.0001174 relative error = 0.005837 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.728 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = -1.89587424982 0.686244976919 y[1] (closed_form) = -1.89591813555 0.686353825441 absolute error = 0.0001174 relative error = 0.005821 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.733 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.692 2.591 h = 0.001 0.001 y[1] (numeric) = -1.89886670305 0.686377838919 y[1] (closed_form) = -1.89891057335 0.68648675299 absolute error = 0.0001174 relative error = 0.005815 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.736 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.693 2.592 h = 0.001 0.003 y[1] (numeric) = -1.8998535839 0.687386683949 y[1] (closed_form) = -1.89989743579 0.687495627406 absolute error = 0.0001174 relative error = 0.005812 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.737 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.694 2.595 h = 0.0001 0.004 y[1] (numeric) = -1.90283627968 0.688417543863 y[1] (closed_form) = -1.90288016641 0.688526425945 absolute error = 0.0001174 relative error = 0.005801 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.739 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6941 2.599 h = 0.003 0.006 y[1] (numeric) = -1.90682692401 0.688560958448 y[1] (closed_form) = -1.90687078139 0.688669788667 absolute error = 0.0001173 relative error = 0.005787 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.743 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = -1.91278217615 0.69161963205 y[1] (closed_form) = -1.91282629219 0.691728475529 absolute error = 0.0001174 relative error = 0.005774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.748 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3931.5MB, alloc=52.3MB, time=47.91 x[1] = 0.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = -1.9177714547 0.691772811512 y[1] (closed_form) = -1.91781540604 0.691881675998 absolute error = 0.0001174 relative error = 0.005758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.752 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6973 2.613 h = 0.001 0.001 y[1] (numeric) = -1.92076457298 0.691904338499 y[1] (closed_form) = -1.92080851024 0.692013265885 absolute error = 0.0001175 relative error = 0.005753 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.755 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6983 2.614 h = 0.001 0.003 y[1] (numeric) = -1.92175210965 0.692912939074 y[1] (closed_form) = -1.9217960296 0.69302189478 absolute error = 0.0001175 relative error = 0.00575 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.756 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = -1.92473586935 0.693942651134 y[1] (closed_form) = -1.92477982199 0.69405154773 absolute error = 0.0001174 relative error = 0.005739 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.758 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.6994 2.621 h = 0.003 0.006 y[1] (numeric) = -1.92872736578 0.694084295526 y[1] (closed_form) = -1.92877128979 0.694193142794 absolute error = 0.0001174 relative error = 0.005726 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.762 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = -1.93468515011 0.697140909208 y[1] (closed_form) = -1.93472932182 0.697249766435 absolute error = 0.0001175 relative error = 0.005712 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.767 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = -1.93967544048 0.697291912421 y[1] (closed_form) = -1.93971945478 0.697400791493 absolute error = 0.0001174 relative error = 0.005697 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.772 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7026 2.635 h = 0.001 0.001 y[1] (numeric) = -1.94266918115 0.697422154658 y[1] (closed_form) = -1.94271318265 0.697531094078 absolute error = 0.0001175 relative error = 0.005692 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.774 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3977.0MB, alloc=52.3MB, time=48.46 x[1] = 0.7036 2.636 h = 0.001 0.003 y[1] (numeric) = -1.94365734292 0.698430514337 y[1] (closed_form) = -1.94370132815 0.698539481045 absolute error = 0.0001175 relative error = 0.005689 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.775 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = -1.94664210874 0.69945911656 y[1] (closed_form) = -1.94668612463 0.69956802635 absolute error = 0.0001175 relative error = 0.005679 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.778 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7047 2.643 h = 0.003 0.006 y[1] (numeric) = -1.950634402 0.69959905773 y[1] (closed_form) = -1.95067838996 0.699707920612 absolute error = 0.0001174 relative error = 0.005666 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.781 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = -1.95659458808 0.70265367316 y[1] (closed_form) = -1.95663881322 0.702762542957 absolute error = 0.0001175 relative error = 0.005652 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.786 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = -1.96158582386 0.70280258286 y[1] (closed_form) = -1.96162989858 0.702911475226 absolute error = 0.0001175 relative error = 0.005638 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.791 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7079 2.657 h = 0.001 0.001 y[1] (numeric) = -1.96458014664 0.702931588929 y[1] (closed_form) = -1.96462420974 0.703040539187 absolute error = 0.0001175 relative error = 0.005632 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = -1.96556890413 0.703939711457 y[1] (closed_form) = -1.96561295195 0.704048688003 absolute error = 0.0001175 relative error = 0.00563 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.709 2.662 h = 0.003 0.006 y[1] (numeric) = -1.96956180763 0.704078306742 y[1] (closed_form) = -1.96960584266 0.704187161425 absolute error = 0.0001174 relative error = 0.005614 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.798 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4022.4MB, alloc=52.3MB, time=49.02 x[1] = 0.712 2.668 h = 0.0001 0.005 y[1] (numeric) = -1.97552393856 0.707131223991 y[1] (closed_form) = -1.975568202 0.707240083287 absolute error = 0.0001175 relative error = 0.0056 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.803 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = -1.98051591415 0.707278385515 y[1] (closed_form) = -1.98056003296 0.707387267837 absolute error = 0.0001175 relative error = 0.005586 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.808 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7122 2.676 h = 0.001 0.001 y[1] (numeric) = -1.9835106935 0.707406358862 y[1] (closed_form) = -1.98355480162 0.707515297023 absolute error = 0.0001175 relative error = 0.005581 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.81 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7132 2.677 h = 0.001 0.003 y[1] (numeric) = -1.98449993847 0.708414273736 y[1] (closed_form) = -1.98454403211 0.708523237339 absolute error = 0.0001175 relative error = 0.005578 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.811 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = -1.98748642022 0.709440898116 y[1] (closed_form) = -1.98753054106 0.709549808712 absolute error = 0.0001175 relative error = 0.005568 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.814 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7143 2.684 h = 0.003 0.006 y[1] (numeric) = -1.99148004105 0.709577832472 y[1] (closed_form) = -1.9915241353 0.709686700362 absolute error = 0.0001175 relative error = 0.005556 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.817 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = -1.99744434814 0.712628864369 y[1] (closed_form) = -1.99748866103 0.712737734271 absolute error = 0.0001175 relative error = 0.005542 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.822 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = -2.00243715629 0.712774079601 y[1] (closed_form) = -2.00248133101 0.71288297306 absolute error = 0.0001175 relative error = 0.005528 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4067.8MB, alloc=52.3MB, time=49.58 x[1] = 0.7175 2.698 h = 0.001 0.001 y[1] (numeric) = -2.00543244925 0.712900903274 y[1] (closed_form) = -2.00547661433 0.713009850287 absolute error = 0.0001176 relative error = 0.005523 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.83 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7185 2.699 h = 0.001 0.003 y[1] (numeric) = -2.00642223875 0.713908588692 y[1] (closed_form) = -2.00646639023 0.714017560206 absolute error = 0.0001176 relative error = 0.005521 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.83 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = -2.00940957719 0.71493420713 y[1] (closed_form) = -2.00945375415 0.715043127628 absolute error = 0.0001175 relative error = 0.005511 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.833 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7196 2.706 h = 0.003 0.006 y[1] (numeric) = -2.013403854 0.715069618138 y[1] (closed_form) = -2.01344800506 0.715178498044 absolute error = 0.0001175 relative error = 0.005499 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.837 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = -2.01937022393 0.718118822778 y[1] (closed_form) = -2.01941458427 0.718227702311 absolute error = 0.0001176 relative error = 0.005485 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.842 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = -2.02436380842 0.718262166573 y[1] (closed_form) = -2.02440803677 0.718371070103 absolute error = 0.0001175 relative error = 0.005472 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.846 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7228 2.72 h = 0.001 0.001 y[1] (numeric) = -2.02735958085 0.718387884564 y[1] (closed_form) = -2.02740380052 0.718496839448 absolute error = 0.0001176 relative error = 0.005467 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.849 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7238 2.721 h = 0.001 0.003 y[1] (numeric) = -2.02834988905 0.719395344661 y[1] (closed_form) = -2.02839409598 0.719504323136 absolute error = 0.0001176 relative error = 0.005464 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.85 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4113.1MB, alloc=52.3MB, time=50.13 x[1] = 0.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = -2.03133803682 0.72041999137 y[1] (closed_form) = -2.03138226759 0.720528920754 absolute error = 0.0001176 relative error = 0.005455 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.852 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7249 2.728 h = 0.003 0.006 y[1] (numeric) = -2.03533292541 0.720553937584 y[1] (closed_form) = -2.03537713097 0.720662828392 absolute error = 0.0001175 relative error = 0.005443 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.856 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = -2.04130125037 0.723601371805 y[1] (closed_form) = -2.04134565621 0.723710260059 absolute error = 0.0001176 relative error = 0.00543 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.861 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.728 2.739 h = 0.0001 0.003 y[1] (numeric) = -2.04629555819 0.723742916425 y[1] (closed_form) = -2.04633983796 0.72385182903 absolute error = 0.0001176 relative error = 0.005416 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.866 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7281 2.742 h = 0.001 0.001 y[1] (numeric) = -2.04929177787 0.723867571211 y[1] (closed_form) = -2.04933604989 0.723976533054 absolute error = 0.0001176 relative error = 0.005411 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.869 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7291 2.743 h = 0.001 0.003 y[1] (numeric) = -2.05028258014 0.724874810225 y[1] (closed_form) = -2.0503268402 0.724983794779 absolute error = 0.0001176 relative error = 0.005409 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.869 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = -2.05327149225 0.725898518466 y[1] (closed_form) = -2.05331577461 0.726007455789 absolute error = 0.0001176 relative error = 0.005399 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.872 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7302 2.75 h = 0.003 0.006 y[1] (numeric) = -2.05726695097 0.726031056414 y[1] (closed_form) = -2.0573112088 0.726139957082 absolute error = 0.0001176 relative error = 0.005388 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.876 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4158.5MB, alloc=52.3MB, time=50.68 x[1] = 0.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = -2.06323712838 0.729076775787 y[1] (closed_form) = -2.06328157786 0.729185671913 absolute error = 0.0001176 relative error = 0.005375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.88 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = -2.06823210957 0.729216590973 y[1] (closed_form) = -2.06827643865 0.729325511725 absolute error = 0.0001176 relative error = 0.005362 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.885 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7334 2.764 h = 0.001 0.001 y[1] (numeric) = -2.07122874614 0.72934022356 y[1] (closed_form) = -2.07127306832 0.729449191514 absolute error = 0.0001176 relative error = 0.005357 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.888 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = -2.07222001892 0.730347245815 y[1] (closed_form) = -2.07226432989 0.730456235629 absolute error = 0.0001177 relative error = 0.005355 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.889 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7345 2.769 h = 0.003 0.006 y[1] (numeric) = -2.07621591254 0.730478671862 y[1] (closed_form) = -2.07626020801 0.730587563905 absolute error = 0.0001176 relative error = 0.005341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.893 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = -2.0821875866 0.733522938188 y[1] (closed_form) = -2.08223206653 0.733631824216 absolute error = 0.0001176 relative error = 0.005328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.897 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = -2.08718309011 0.733661311444 y[1] (closed_form) = -2.08722745434 0.73377022221 absolute error = 0.0001176 relative error = 0.005315 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.902 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7377 2.783 h = 0.001 0.001 y[1] (numeric) = -2.090180051 0.733784091394 y[1] (closed_form) = -2.09022440899 0.733893047665 absolute error = 0.0001176 relative error = 0.00531 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.905 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4204.0MB, alloc=52.3MB, time=51.24 x[1] = 0.7387 2.784 h = 0.001 0.003 y[1] (numeric) = -2.09117170822 0.734790925342 y[1] (closed_form) = -2.0912160556 0.734899902755 absolute error = 0.0001177 relative error = 0.005308 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.906 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = -2.09416192035 0.735812964694 y[1] (closed_form) = -2.09420628742 0.735921898186 absolute error = 0.0001176 relative error = 0.005299 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.908 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7398 2.791 h = 0.003 0.006 y[1] (numeric) = -2.09815832191 0.735943020192 y[1] (closed_form) = -2.09820266572 0.736051920362 absolute error = 0.0001176 relative error = 0.005288 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.912 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = -2.10413167129 0.73898567278 y[1] (closed_form) = -2.10417619156 0.739094565265 absolute error = 0.0001176 relative error = 0.005275 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.917 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = -2.10912776357 0.739122440423 y[1] (closed_form) = -2.10917217338 0.739231357793 absolute error = 0.0001176 relative error = 0.005263 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.922 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.743 2.805 h = 0.001 0.001 y[1] (numeric) = -2.11212508987 0.739244271019 y[1] (closed_form) = -2.11216949418 0.739353232002 absolute error = 0.0001177 relative error = 0.005258 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.925 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.744 2.806 h = 0.001 0.003 y[1] (numeric) = -2.1131171766 0.740250896676 y[1] (closed_form) = -2.11316157099 0.740359878003 absolute error = 0.0001177 relative error = 0.005256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.925 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.745 2.809 h = 0.0001 0.004 y[1] (numeric) = -2.11610803704 0.741272088032 y[1] (closed_form) = -2.11615244981 0.74138102712 absolute error = 0.0001176 relative error = 0.005247 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.928 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4249.4MB, alloc=52.3MB, time=51.80 x[1] = 0.7451 2.813 h = 0.003 0.006 y[1] (numeric) = -2.12010490296 0.741400886683 y[1] (closed_form) = -2.12014929311 0.741509794126 absolute error = 0.0001176 relative error = 0.005236 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.932 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = -2.12607983875 0.74444197741 y[1] (closed_form) = -2.12612439771 0.744550875654 absolute error = 0.0001177 relative error = 0.005223 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.937 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = -2.13107647771 0.744577202333 y[1] (closed_form) = -2.13112093122 0.744686125546 absolute error = 0.0001176 relative error = 0.005211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.941 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7483 2.827 h = 0.001 0.001 y[1] (numeric) = -2.13407414379 0.74469812058 y[1] (closed_form) = -2.13411859248 0.744807085588 absolute error = 0.0001177 relative error = 0.005206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.944 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7493 2.828 h = 0.001 0.003 y[1] (numeric) = -2.1350666394 0.745704542419 y[1] (closed_form) = -2.13511107881 0.745813527 absolute error = 0.0001177 relative error = 0.005204 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.945 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = -2.1380581114 0.746724915473 y[1] (closed_form) = -2.13810256796 0.746833859439 absolute error = 0.0001177 relative error = 0.005195 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.948 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7504 2.835 h = 0.003 0.006 y[1] (numeric) = -2.1420554086 0.746852506479 y[1] (closed_form) = -2.14209984318 0.746961420397 absolute error = 0.0001176 relative error = 0.005185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.951 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = -2.14803184627 0.74989208595 y[1] (closed_form) = -2.1480764423 0.750000989304 absolute error = 0.0001177 relative error = 0.005172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.956 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4294.9MB, alloc=52.3MB, time=52.36 x[1] = 0.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = -2.1530289923 0.750025828798 y[1] (closed_form) = -2.15307348767 0.750134757147 absolute error = 0.0001177 relative error = 0.005161 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.961 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7536 2.849 h = 0.001 0.001 y[1] (numeric) = -2.15602697402 0.750145870392 y[1] (closed_form) = -2.15607146523 0.750254838788 absolute error = 0.0001177 relative error = 0.005156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.964 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7546 2.85 h = 0.001 0.003 y[1] (numeric) = -2.15701985879 0.751152092912 y[1] (closed_form) = -2.15706434131 0.751261080136 absolute error = 0.0001177 relative error = 0.005154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.965 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = -2.16001190752 0.75217167648 y[1] (closed_form) = -2.16005640603 0.752280624657 absolute error = 0.0001177 relative error = 0.005145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.967 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7557 2.857 h = 0.003 0.006 y[1] (numeric) = -2.16400960484 0.752298107284 y[1] (closed_form) = -2.16405408201 0.752407026936 absolute error = 0.0001177 relative error = 0.005135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.971 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = -2.16998746403 0.755336224841 y[1] (closed_form) = -2.1700320956 0.7554451327 absolute error = 0.0001177 relative error = 0.005122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.976 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = -2.17498507987 0.755468544082 y[1] (closed_form) = -2.17502961537 0.755577476909 absolute error = 0.0001177 relative error = 0.005111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.981 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 0.7589 2.871 h = 0.001 0.001 y[1] (numeric) = -2.17798335453 0.755587743442 y[1] (closed_form) = -2.17802788646 0.755696714637 absolute error = 0.0001177 relative error = 0.005106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.984 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4340.4MB, alloc=52.3MB, time=52.91 x[1] = 0.7599 2.872 h = 0.001 0.003 y[1] (numeric) = -2.17897660964 0.756593771162 y[1] (closed_form) = -2.17902113345 0.756702760466 absolute error = 0.0001177 relative error = 0.005104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.984 Order of pole (given) = 0 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = tan ( x ) ; Iterations = 754 Total Elapsed Time = 52 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 52 Seconds > quit memory used=4351.3MB, alloc=52.3MB, time=53.04