|\^/| 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(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0)); > end; exact_soln_y := proc(x) return c(5.0)*ln(c(0.1)*c(x) + c(0.2))*(c(0.1)*c(x) + c(0.2)) - c(0.5)*c(x) - c(1.0) 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 + 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0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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, > array_const_0D1, > array_const_0D2, #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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 mult CONST - LINEAR $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D1[1] * array_x[1]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; > #emit pre sqrt 1 $eq_no = 1 > array_tmp3[1] := sqrt(array_tmp2[1]); > #emit pre ln 1 FULL $eq_no = 1 > array_tmp4[1] := ln(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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 mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre ln 2 FULL $eq_no = 1 > array_tmp4[2] := array_tmp3[2] / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre ln ID_FULL iii = 3 $eq_no = 1 > #emit pre ln 3 $eq_no = 1 > array_tmp4[3] := ( array_tmp3[3] - att(2,array_tmp3,array_tmp4,2) ) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre ln ID_FULL iii = 4 $eq_no = 1 > #emit pre ln 4 $eq_no = 1 > array_tmp4[4] := ( array_tmp3[4] - att(3,array_tmp3,array_tmp4,2) ) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre ln ID_FULL iii = 5 $eq_no = 1 > #emit pre ln 5 $eq_no = 1 > array_tmp4[5] := ( array_tmp3[5] - att(4,array_tmp3,array_tmp4,2) ) / array_tmp3[1]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[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_tmp5[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 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > #emit ln FULL $eq_no = 1 > array_tmp4[kkk] := (array_tmp3[kkk] - att(kkk-1,array_tmp3,array_tmp4,2))/array_tmp3[1]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[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_tmp5[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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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[1] := array_const_0D1[1]*array_x[1]; array_tmp2[1] := array_tmp1[1] + array_const_0D2[1]; array_tmp3[1] := sqrt(array_tmp2[1]); array_tmp4[1] := ln(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_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[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4[2] := array_tmp3[2]/array_tmp3[1]; array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_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_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[3] := (array_tmp3[3] - att(2, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_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_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[4] := (array_tmp3[4] - att(3, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_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_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[5] := (array_tmp3[5] - att(4, array_tmp3, array_tmp4, 2))/array_tmp3[1]; array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_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_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4[kkk] := ( array_tmp3[kkk] - att(kkk - 1, array_tmp3, array_tmp4, 2))/ array_tmp3[1]; array_tmp5[kkk] := array_tmp4[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_tmp5[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, > array_const_0D1, > array_const_0D2, > #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, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > 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:= Array(0..(40),[]); > array_tmp2:= Array(0..(40),[]); > array_tmp3:= Array(0..(40),[]); > array_tmp4:= Array(0..(40),[]); > array_tmp5:= Array(0..(40),[]); > array_m1:= Array(0..(40),[]); > array_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[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp2[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp3[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp5[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_m1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= 40) do # do number 2 > array_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); > zero_ats_ar(array_tmp2); > zero_ats_ar(array_tmp3); > zero_ats_ar(array_tmp4); > zero_ats_ar(array_tmp5); > zero_ats_ar(array_m1); > zero_ats_ar(array_const_1); > array_const_1[1] := c(1); > zero_ats_ar(array_const_0D0); > array_const_0D0[1] := c(0.0); > zero_ats_ar(array_const_0D1); > array_const_0D1[1] := c(0.1); > zero_ats_ar(array_const_0D2); > array_const_0D2[1] := c(0.2); > 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/ln_sqrtpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > 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 := 10.1 + 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,"glob_min_h := 0.001;"); > 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(-2.0);"); > 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(0.5);"); > 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,""); > omniout_str(ALWAYS,"return(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0));"); > 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 := 10.1 + 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_min_h := 0.001; > glob_type_given_pole := 1; > array_given_rad_poles[1,1] := c(-2.0); > array_given_rad_poles[1,2] := c(0.0); > array_given_ord_poles[1,1] := c(0.5); > 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 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; "); > 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,"2017-11-26T15:05:08-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"ln_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ") > ; > 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,"ln_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"ln_sqrt 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_const_0D1, array_const_0D2, 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, array_tmp2, array_tmp3, array_tmp4, array_tmp5, 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 := Array(0 .. 40, []); array_tmp2 := Array(0 .. 40, []); array_tmp3 := Array(0 .. 40, []); array_tmp4 := Array(0 .. 40, []); array_tmp5 := Array(0 .. 40, []); array_m1 := Array(0 .. 40, []); array_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[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 40 do array_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); zero_ats_ar(array_tmp2); zero_ats_ar(array_tmp3); zero_ats_ar(array_tmp4); zero_ats_ar(array_tmp5); zero_ats_ar(array_m1); zero_ats_ar(array_const_1); array_const_1[1] := c(1); zero_ats_ar(array_const_0D0); array_const_0D0[1] := c(0.); zero_ats_ar(array_const_0D1); array_const_0D1[1] := c(0.1); zero_ats_ar(array_const_0D2); array_const_0D2[1] := c(0.2); 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/ln_sqrtpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln ( sqrt ( 0.1 \ * x + 0.2 ) ) ; "); 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 := 10.1 + 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, "glob_min_h := 0.001;"); 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(-2.0);"); 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(0.5);"); 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, ""); omniout_str(ALWAYS, "return(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c\ (0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0));"); 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 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* I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 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 := 10.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_min_h := 0.001; glob_type_given_pole := 1; array_given_rad_poles[1, 1] := c(-2.0); array_given_rad_poles[1, 2] := c(0.); array_given_ord_poles[1, 1] := c(0.5); 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 ) = ln ( sqrt ( 0.1\ * x + 0.2 ) ) ; "); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2017-11-26T15:05:08-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "ln_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ln\ ( sqrt ( 0.1 * x + 0.2 ) ) ; "); 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, "ln_sqrt diffeq.mxt") ; logitem_str(html_log_file, "ln_sqrt 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/ln_sqrtpostcpx.cpx################# diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=40; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 10.1 + 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_min_h := 0.001; glob_type_given_pole := 1; array_given_rad_poles[1,1] := c(-2.0); array_given_rad_poles[1,2] := c(0.0); array_given_ord_poles[1,1] := c(0.5); 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(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0)); 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] = 10.1 0.1 h = 0.0001 0.005 y[1] (numeric) = -4.89695343359 0.00953158714665 y[1] (closed_form) = -4.89695343359 0.00953158714665 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 0 NO 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=29.0MB, alloc=40.3MB, time=0.38 x[1] = 10.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = -4.89696497438 0.0100086586628 y[1] (closed_form) = -4.89696507766 0.0100086616307 absolute error = 1.033e-07 relative error = 2.110e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1002 0.108 h = 0.001 0.001 y[1] (numeric) = -4.8969687667 0.0102951111784 y[1] (closed_form) = -4.89696874606 0.0102951089328 absolute error = 2.076e-08 relative error = 4.240e-07 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1012 0.109 h = 0.001 0.003 y[1] (numeric) = -4.8968779503 0.010394976736 y[1] (closed_form) = -4.89687786995 0.0103949512271 absolute error = 8.430e-08 relative error = 1.722e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = -4.89679612151 0.0106857034405 y[1] (closed_form) = -4.89679616472 0.0106857203735 absolute error = 4.641e-08 relative error = 9.477e-07 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1023 0.116 h = 0.003 0.006 y[1] (numeric) = -4.89680533274 0.0110679472208 y[1] (closed_form) = -4.8968054611 0.0110678926684 absolute error = 1.395e-07 relative error = 2.848e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.1 Order of pole (given) = 0.5 0 NO 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=74.5MB, alloc=52.3MB, time=0.96 x[1] = 10.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = -4.89654828921 0.0116551582618 y[1] (closed_form) = -4.89654848095 0.0116555876986 absolute error = 4.703e-07 relative error = 9.605e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = -4.89656453848 0.0121337631714 y[1] (closed_form) = -4.89656463604 0.0121338901724 absolute error = 1.601e-07 relative error = 3.271e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1055 0.13 h = 0.001 0.001 y[1] (numeric) = -4.89657102797 0.0124209898556 y[1] (closed_form) = -4.89657100168 0.0124211114208 absolute error = 1.244e-07 relative error = 2.540e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1065 0.131 h = 0.001 0.003 y[1] (numeric) = -4.89648089018 0.0125219899982 y[1] (closed_form) = -4.89648080425 0.0125220882025 absolute error = 1.305e-07 relative error = 2.665e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO 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=120.0MB, alloc=52.3MB, time=1.51 x[1] = 10.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = -4.89640155293 0.0128143070583 y[1] (closed_form) = -4.89640159042 0.0128144479089 absolute error = 1.458e-07 relative error = 2.977e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1076 0.138 h = 0.003 0.006 y[1] (numeric) = -4.8964143667 0.0131975544037 y[1] (closed_form) = -4.89641448944 0.013197623956 absolute error = 1.411e-07 relative error = 2.881e-06 % Correct digits = 8 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = -4.89616207512 0.0137888557365 y[1] (closed_form) = -4.89616226033 0.0137894091708 absolute error = 5.836e-07 relative error = 1.192e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = -4.89618283054 0.0142686962782 y[1] (closed_form) = -4.89618292216 0.014268947245 absolute error = 2.672e-07 relative error = 5.457e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1108 0.152 h = 0.001 0.001 y[1] (numeric) = -4.89619201455 0.0145567016621 y[1] (closed_form) = -4.89619198239 0.0145569469714 absolute error = 2.474e-07 relative error = 5.053e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO 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=165.5MB, alloc=52.3MB, time=2.06 x[1] = 10.1118 0.153 h = 0.001 0.003 y[1] (numeric) = -4.89610255302 0.0146588370983 y[1] (closed_form) = -4.89610246129 0.0146590589495 absolute error = 2.401e-07 relative error = 4.903e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = -4.89602570327 0.014952748297 y[1] (closed_form) = -4.89602573483 0.0149530129983 absolute error = 2.666e-07 relative error = 5.445e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1129 0.16 h = 0.003 0.006 y[1] (numeric) = -4.89604211611 0.0153370052708 y[1] (closed_form) = -4.89604223301 0.0153371988609 absolute error = 2.261e-07 relative error = 4.619e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = -4.89579456688 0.0159324036181 y[1] (closed_form) = -4.89579474535 0.0159330809796 absolute error = 7.005e-07 relative error = 1.431e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO 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=211.0MB, alloc=52.3MB, time=2.61 x[1] = 10.116 0.171 h = 0.0001 0.003 y[1] (numeric) = -4.89581982413 0.0164134873781 y[1] (closed_form) = -4.8958199096 0.0164138622428 absolute error = 3.845e-07 relative error = 7.853e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1161 0.174 h = 0.001 0.001 y[1] (numeric) = -4.89583170002 0.0167022759792 y[1] (closed_form) = -4.89583166177 0.016702644965 absolute error = 3.710e-07 relative error = 7.577e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1171 0.175 h = 0.001 0.003 y[1] (numeric) = -4.89574291238 0.0168055474083 y[1] (closed_form) = -4.89574281463 0.016805892839 absolute error = 3.590e-07 relative error = 7.333e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = -4.8956685461 0.0171010565106 y[1] (closed_form) = -4.89566857151 0.0171014449946 absolute error = 3.893e-07 relative error = 7.952e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO 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=256.4MB, alloc=52.3MB, time=3.16 x[1] = 10.1182 0.182 h = 0.003 0.006 y[1] (numeric) = -4.89568855452 0.0174863291576 y[1] (closed_form) = -4.89568866535 0.0174866467177 absolute error = 3.363e-07 relative error = 6.870e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = -4.89544573804 0.0180858312014 y[1] (closed_form) = -4.89544590953 0.0180866324193 absolute error = 8.194e-07 relative error = 1.674e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = -4.89547549278 0.0185681657433 y[1] (closed_form) = -4.89547557187 0.018568664437 absolute error = 5.049e-07 relative error = 1.031e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1214 0.196 h = 0.001 0.001 y[1] (numeric) = -4.89549005787 0.0188577420651 y[1] (closed_form) = -4.89549001331 0.0188582346591 absolute error = 4.946e-07 relative error = 1.010e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = -4.89540194175 0.0189621501772 y[1] (closed_form) = -4.89540183775 0.0189626191196 absolute error = 4.803e-07 relative error = 9.812e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO 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=301.8MB, alloc=52.3MB, time=3.71 x[1] = 10.1225 0.201 h = 0.003 0.006 y[1] (numeric) = -4.89542488964 0.0193482523223 y[1] (closed_form) = -4.89542503602 0.0193486573139 absolute error = 4.306e-07 relative error = 8.797e-06 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.12 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = -4.89518618823 0.0199512357904 y[1] (closed_form) = -4.89518639449 0.0199521243501 absolute error = 9.122e-07 relative error = 1.863e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = -4.8952198258 0.0204345994997 y[1] (closed_form) = -4.89521994016 0.0204351855064 absolute error = 5.971e-07 relative error = 1.220e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1257 0.215 h = 0.001 0.001 y[1] (numeric) = -4.89523671297 0.0207248254708 y[1] (closed_form) = -4.89523670374 0.0207254051872 absolute error = 5.798e-07 relative error = 1.184e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO 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=347.4MB, alloc=52.3MB, time=4.27 x[1] = 10.1267 0.216 h = 0.001 0.003 y[1] (numeric) = -4.89514918653 0.0208302045866 y[1] (closed_form) = -4.89514911793 0.0208307605677 absolute error = 5.602e-07 relative error = 1.144e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = -4.89507944978 0.0211286675041 y[1] (closed_form) = -4.89507950409 0.0211292669163 absolute error = 6.019e-07 relative error = 1.230e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1278 0.223 h = 0.003 0.006 y[1] (numeric) = -4.89510615164 0.0215158033769 y[1] (closed_form) = -4.89510629154 0.0215163322131 absolute error = 5.470e-07 relative error = 1.117e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = -4.89487216514 0.0221229029807 y[1] (closed_form) = -4.89487236402 0.0221239152655 absolute error = 1.032e-06 relative error = 2.108e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = -4.89491029215 0.0226075315375 y[1] (closed_form) = -4.89491039973 0.0226082412461 absolute error = 7.178e-07 relative error = 1.466e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO 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=392.9MB, alloc=52.3MB, time=4.82 x[1] = 10.131 0.237 h = 0.001 0.001 y[1] (numeric) = -4.89492986359 0.0228985536049 y[1] (closed_form) = -4.89492984763 0.022899256803 absolute error = 7.034e-07 relative error = 1.437e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.132 0.238 h = 0.001 0.003 y[1] (numeric) = -4.89484300426 0.0230050706914 y[1] (closed_form) = -4.89484292901 0.0230057500585 absolute error = 6.835e-07 relative error = 1.396e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.133 0.241 h = 0.0001 0.004 y[1] (numeric) = -4.89477573943 0.0233051422318 y[1] (closed_form) = -4.89477578696 0.0233058652311 absolute error = 7.246e-07 relative error = 1.480e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1331 0.245 h = 0.003 0.006 y[1] (numeric) = -4.89480602686 0.0236933110122 y[1] (closed_form) = -4.89480616005 0.0236939636233 absolute error = 6.661e-07 relative error = 1.361e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO 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=438.4MB, alloc=52.3MB, time=5.37 x[1] = 10.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = -4.8945767456 0.0243045333165 y[1] (closed_form) = -4.89457693688 0.0243056692536 absolute error = 1.152e-06 relative error = 2.353e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = -4.89461935767 0.0247904342195 y[1] (closed_form) = -4.89461945823 0.0247912675591 absolute error = 8.394e-07 relative error = 1.715e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1363 0.259 h = 0.001 0.001 y[1] (numeric) = -4.89464161065 0.025082256847 y[1] (closed_form) = -4.89464158775 0.0250830834566 absolute error = 8.269e-07 relative error = 1.689e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1373 0.26 h = 0.001 0.003 y[1] (numeric) = -4.89455541607 0.0251899125682 y[1] (closed_form) = -4.89455533395 0.0251907152511 absolute error = 8.069e-07 relative error = 1.648e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = -4.8944906191 0.0254915964264 y[1] (closed_form) = -4.89449065961 0.0254924429421 absolute error = 8.475e-07 relative error = 1.731e-05 % Correct digits = 7 memory used=484.0MB, alloc=52.3MB, time=5.92 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1384 0.267 h = 0.003 0.006 y[1] (numeric) = -4.89452448851 0.0258808040888 y[1] (closed_form) = -4.89452461479 0.0258815804041 absolute error = 7.865e-07 relative error = 1.607e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = -4.89429990284 0.0264961556174 y[1] (closed_form) = -4.8943000863 0.0264974151329 absolute error = 1.273e-06 relative error = 2.601e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = -4.89434699553 0.026983336342 y[1] (closed_form) = -4.89434708885 0.026984293241 absolute error = 9.614e-07 relative error = 1.964e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1416 0.281 h = 0.001 0.001 y[1] (numeric) = -4.89437192734 0.0272759639796 y[1] (closed_form) = -4.89437189728 0.0272769139295 absolute error = 9.504e-07 relative error = 1.942e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.14 Order of pole (given) = 0.5 0 NO 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=529.6MB, alloc=52.3MB, time=6.48 x[1] = 10.1426 0.282 h = 0.001 0.003 y[1] (numeric) = -4.89428639515 0.0273847589901 y[1] (closed_form) = -4.89428630594 0.0273856849182 absolute error = 9.302e-07 relative error = 1.901e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = -4.89422406194 0.0276880588431 y[1] (closed_form) = -4.89422409523 0.0276890288038 absolute error = 9.705e-07 relative error = 1.983e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1437 0.289 h = 0.003 0.006 y[1] (numeric) = -4.89426150977 0.0280783113431 y[1] (closed_form) = -4.8942616289 0.0280792112915 absolute error = 9.078e-07 relative error = 1.855e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = -4.89404161 0.0286977985788 y[1] (closed_form) = -4.89404178542 0.0286991815983 absolute error = 1.394e-06 relative error = 2.849e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO 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=575.1MB, alloc=52.3MB, time=7.03 x[1] = 10.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = -4.89409317885 0.0291862665773 y[1] (closed_form) = -4.89409326473 0.0291873469636 absolute error = 1.084e-06 relative error = 2.214e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1469 0.303 h = 0.001 0.001 y[1] (numeric) = -4.89412078676 0.029479703661 y[1] (closed_form) = -4.89412074932 0.0294807768795 absolute error = 1.074e-06 relative error = 2.194e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = -4.89403591459 0.0295896386063 y[1] (closed_form) = -4.89403581807 0.029590687708 absolute error = 1.054e-06 relative error = 2.153e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.148 0.308 h = 0.003 0.006 y[1] (numeric) = -4.89407628783 0.0299807444157 y[1] (closed_form) = -4.89407644166 0.0299817319055 absolute error = 9.994e-07 relative error = 2.042e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.15 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.151 0.314 h = 0.0001 0.005 y[1] (numeric) = -4.89386046313 0.0306037410287 y[1] (closed_form) = -4.89386067248 0.0306052114869 absolute error = 1.485e-06 relative error = 3.035e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO 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=620.7MB, alloc=52.3MB, time=7.58 x[1] = 10.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = -4.8939158968 0.0310932697723 y[1] (closed_form) = -4.89391601711 0.0310944375774 absolute error = 1.174e-06 relative error = 2.399e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1512 0.322 h = 0.001 0.001 y[1] (numeric) = -4.89394581571 0.0313873753086 y[1] (closed_form) = -4.89394581277 0.0313885357572 absolute error = 1.160e-06 relative error = 2.371e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1522 0.323 h = 0.001 0.003 y[1] (numeric) = -4.89386152335 0.031498284158 y[1] (closed_form) = -4.89386146139 0.0314994204076 absolute error = 1.138e-06 relative error = 2.325e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = -4.8938037831 0.0318045714909 y[1] (closed_form) = -4.89380384337 0.0318057521448 absolute error = 1.182e-06 relative error = 2.416e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO 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=666.3MB, alloc=52.3MB, time=8.13 x[1] = 10.1533 0.33 h = 0.003 0.006 y[1] (numeric) = -4.89384789254 0.0321967414532 y[1] (closed_form) = -4.89384803882 0.0321978524439 absolute error = 1.121e-06 relative error = 2.290e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = -4.89363673577 0.0328238858423 y[1] (closed_form) = -4.89363693667 0.0328254796668 absolute error = 1.606e-06 relative error = 3.283e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = -4.89369663735 0.033314715719 y[1] (closed_form) = -4.8936967498 0.0333160068775 absolute error = 1.296e-06 relative error = 2.648e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1565 0.344 h = 0.001 0.001 y[1] (numeric) = -4.89372922729 0.0336096389509 y[1] (closed_form) = -4.89372921656 0.0336109225351 absolute error = 1.284e-06 relative error = 2.623e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1575 0.345 h = 0.001 0.003 y[1] (numeric) = -4.89364559055 0.0337216889401 y[1] (closed_form) = -4.89364552087 0.0337229482311 absolute error = 1.261e-06 relative error = 2.577e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO 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=711.9MB, alloc=52.3MB, time=8.69 x[1] = 10.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = -4.89359030238 0.0340296027348 y[1] (closed_form) = -4.8935903548 0.034030906628 absolute error = 1.305e-06 relative error = 2.667e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1586 0.352 h = 0.003 0.006 y[1] (numeric) = -4.89363797996 0.0344228345131 y[1] (closed_form) = -4.89363811848 0.0344240689314 absolute error = 1.242e-06 relative error = 2.538e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.16 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = -4.89343148139 0.0350541330437 y[1] (closed_form) = -4.89343167363 0.035055850158 absolute error = 1.728e-06 relative error = 3.531e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = -4.89349584638 0.0355462714395 y[1] (closed_form) = -4.89349595076 0.035547685877 absolute error = 1.418e-06 relative error = 2.898e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO 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=757.5MB, alloc=52.3MB, time=9.24 x[1] = 10.1618 0.366 h = 0.001 0.001 y[1] (numeric) = -4.89353110458 0.0358420167626 y[1] (closed_form) = -4.89353108584 0.0358434234085 absolute error = 1.407e-06 relative error = 2.875e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1628 0.367 h = 0.001 0.003 y[1] (numeric) = -4.89344812108 0.035955208511 y[1] (closed_form) = -4.89344804347 0.0359565907698 absolute error = 1.384e-06 relative error = 2.829e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = -4.89339528088 0.0362647523741 y[1] (closed_form) = -4.89339532523 0.0362661794323 absolute error = 1.428e-06 relative error = 2.918e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1639 0.374 h = 0.003 0.006 y[1] (numeric) = -4.89344652295 0.0366590518521 y[1] (closed_form) = -4.89344665348 0.0366604096239 absolute error = 1.364e-06 relative error = 2.787e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = -4.89324467285 0.0372945108484 y[1] (closed_form) = -4.89324485621 0.0372963511753 absolute error = 1.849e-06 relative error = 3.779e-05 % Correct digits = 6 memory used=803.1MB, alloc=52.3MB, time=9.79 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.167 0.385 h = 0.0001 0.003 y[1] (numeric) = -4.89331349671 0.0377879651259 y[1] (closed_form) = -4.89331359279 0.0377895027674 absolute error = 1.541e-06 relative error = 3.148e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1671 0.388 h = 0.001 0.001 y[1] (numeric) = -4.89335142037 0.0380845369215 y[1] (closed_form) = -4.89335139342 0.0380860665546 absolute error = 1.530e-06 relative error = 3.126e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1681 0.389 h = 0.001 0.003 y[1] (numeric) = -4.89326908775 0.0381988710393 y[1] (closed_form) = -4.893269002 0.0382003761918 absolute error = 1.508e-06 relative error = 3.081e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = -4.89321869139 0.0385100485591 y[1] (closed_form) = -4.89321872746 0.0385115987074 absolute error = 1.551e-06 relative error = 3.169e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO 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=848.7MB, alloc=52.3MB, time=10.34 x[1] = 10.1692 0.396 h = 0.003 0.006 y[1] (numeric) = -4.89327349429 0.0389054216015 y[1] (closed_form) = -4.89327361661 0.0389069026521 absolute error = 1.486e-06 relative error = 3.037e-05 % Correct digits = 7 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = -4.89307628291 0.0395450473465 y[1] (closed_form) = -4.89307645717 0.0395470108083 absolute error = 1.971e-06 relative error = 4.028e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = -4.89314956108 0.040039824845 y[1] (closed_form) = -4.89314964865 0.0400414856148 absolute error = 1.663e-06 relative error = 3.399e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1724 0.41 h = 0.001 0.001 y[1] (numeric) = -4.89319014741 0.0403372274801 y[1] (closed_form) = -4.89319011202 0.0403388800251 absolute error = 1.653e-06 relative error = 3.378e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO 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=894.3MB, alloc=52.3MB, time=10.90 x[1] = 10.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = -4.8931084633 0.0404527045685 y[1] (closed_form) = -4.89310836918 0.0404543325397 absolute error = 1.631e-06 relative error = 3.333e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1735 0.415 h = 0.003 0.006 y[1] (numeric) = -4.89316617721 0.0408489543731 y[1] (closed_form) = -4.89316633338 0.0408505230597 absolute error = 1.576e-06 relative error = 3.222e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = -4.8929730006 0.0414921166183 y[1] (closed_form) = -4.89297320795 0.0414941676004 absolute error = 2.061e-06 relative error = 4.213e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = -4.89305012511 0.0419879859749 y[1] (closed_form) = -4.89305024626 0.041989734254 absolute error = 1.752e-06 relative error = 3.581e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1767 0.429 h = 0.001 0.001 y[1] (numeric) = -4.89309301109 0.0422860755829 y[1] (closed_form) = -4.89309300936 0.0422878154505 absolute error = 1.740e-06 relative error = 3.556e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.18 Order of pole (given) = 0.5 0 NO 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=939.9MB, alloc=52.3MB, time=11.45 x[1] = 10.1777 0.43 h = 0.001 0.003 y[1] (numeric) = -4.89301189693 0.0424025292901 y[1] (closed_form) = -4.89301183652 0.0424042445032 absolute error = 1.716e-06 relative error = 3.507e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = -4.89296605654 0.0427167271566 y[1] (closed_form) = -4.89296611769 0.042718487731 absolute error = 1.762e-06 relative error = 3.600e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1788 0.437 h = 0.003 0.006 y[1] (numeric) = -4.89302748843 0.0431140710842 y[1] (closed_form) = -4.89302763599 0.043115762911 absolute error = 1.698e-06 relative error = 3.471e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = -4.89283893245 0.0437614117764 y[1] (closed_form) = -4.89283913029 0.0437635857491 absolute error = 2.183e-06 relative error = 4.461e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO 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=985.7MB, alloc=52.3MB, time=12.01 x[1] = 10.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = -4.89292050281 0.0442586180023 y[1] (closed_form) = -4.89292061505 0.0442604892695 absolute error = 1.875e-06 relative error = 3.831e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.182 0.451 h = 0.001 0.001 y[1] (numeric) = -4.89296604628 0.0445575465712 y[1] (closed_form) = -4.89296603571 0.0445594092114 absolute error = 1.863e-06 relative error = 3.807e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.183 0.452 h = 0.001 0.003 y[1] (numeric) = -4.89288557623 0.0446751443718 y[1] (closed_form) = -4.89288550706 0.0446769822649 absolute error = 1.839e-06 relative error = 3.759e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.184 0.455 h = 0.0001 0.004 y[1] (numeric) = -4.89284216787 0.0449909861083 y[1] (closed_form) = -4.89284222012 0.0449928695571 absolute error = 1.884e-06 relative error = 3.851e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1841 0.459 h = 0.003 0.006 y[1] (numeric) = -4.89290715006 0.0453894203178 y[1] (closed_form) = -4.89290728879 0.045391235208 absolute error = 1.820e-06 relative error = 3.720e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.19 Order of pole (given) = 0.5 0 NO 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=1031.2MB, alloc=52.3MB, time=12.56 x[1] = 10.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = -4.89272320492 0.0460409456224 y[1] (closed_form) = -4.89272339305 0.0460432425059 absolute error = 2.305e-06 relative error = 4.710e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = -4.89280921652 0.0465394959895 y[1] (closed_form) = -4.89280931963 0.0465414901669 absolute error = 1.997e-06 relative error = 4.081e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1873 0.473 h = 0.001 0.001 y[1] (numeric) = -4.89285741464 0.0468392678452 y[1] (closed_form) = -4.89285739501 0.0468412531806 absolute error = 1.985e-06 relative error = 4.058e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1883 0.474 h = 0.001 0.003 y[1] (numeric) = -4.89277758633 0.0469580103144 y[1] (closed_form) = -4.89277750818 0.0469599708106 absolute error = 1.962e-06 relative error = 4.010e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO 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=1076.9MB, alloc=52.3MB, time=13.11 x[1] = 10.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = -4.89273660584 0.0472754994383 y[1] (closed_form) = -4.89273664897 0.047277505684 absolute error = 2.007e-06 relative error = 4.101e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1894 0.481 h = 0.003 0.006 y[1] (numeric) = -4.8928051346 0.0476750297213 y[1] (closed_form) = -4.89280526429 0.0476769675974 absolute error = 1.942e-06 relative error = 3.969e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = -4.8926257905 0.0483307457627 y[1] (closed_form) = -4.89262596871 0.0483331654765 absolute error = 2.426e-06 relative error = 4.959e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = -4.8927162387 0.0488306475187 y[1] (closed_form) = -4.89271633247 0.0488327645279 absolute error = 2.119e-06 relative error = 4.331e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1926 0.495 h = 0.001 0.001 y[1] (numeric) = -4.89276708862 0.0491312669727 y[1] (closed_form) = -4.89276705972 0.0491333749254 absolute error = 2.108e-06 relative error = 4.308e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO 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=1122.5MB, alloc=52.3MB, time=13.66 x[1] = 10.1936 0.496 h = 0.001 0.003 y[1] (numeric) = -4.89268789968 0.0492511546767 y[1] (closed_form) = -4.89268781234 0.0492532376984 absolute error = 2.085e-06 relative error = 4.261e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = -4.8926493429 0.0495702946871 y[1] (closed_form) = -4.8926493767 0.0495724236514 absolute error = 2.129e-06 relative error = 4.352e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.2 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1947 0.503 h = 0.003 0.006 y[1] (numeric) = -4.89272141449 0.049970926816 y[1] (closed_form) = -4.89272153492 0.0499729875997 absolute error = 2.064e-06 relative error = 4.219e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = -4.89254666162 0.0506308396774 y[1] (closed_form) = -4.89254682968 0.0506333821401 absolute error = 2.548e-06 relative error = 5.208e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO 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=1168.0MB, alloc=52.3MB, time=14.21 x[1] = 10.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = -4.89264154175 0.0511321000462 y[1] (closed_form) = -4.89264162596 0.0511343398079 absolute error = 2.241e-06 relative error = 4.581e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1979 0.517 h = 0.001 0.001 y[1] (numeric) = -4.89269504061 0.0514335713954 y[1] (closed_form) = -4.89269500224 0.0514358018868 absolute error = 2.231e-06 relative error = 4.559e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = -4.89261648868 0.0515546048914 y[1] (closed_form) = -4.89261639193 0.0515568103603 absolute error = 2.208e-06 relative error = 4.512e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.199 0.522 h = 0.003 0.006 y[1] (numeric) = -4.89269145653 0.0519561368703 y[1] (closed_form) = -4.89269160997 0.0519582853695 absolute error = 2.154e-06 relative error = 4.402e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO 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=1213.6MB, alloc=52.3MB, time=14.78 x[1] = 10.202 0.528 h = 0.0001 0.005 y[1] (numeric) = -4.89252069787 0.0526196125228 y[1] (closed_form) = -4.89252089818 0.0526222425727 absolute error = 2.638e-06 relative error = 5.391e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = -4.89261940542 0.0531219953895 y[1] (closed_form) = -4.89261952237 0.0531243227362 absolute error = 2.330e-06 relative error = 4.763e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2022 0.536 h = 0.001 0.001 y[1] (numeric) = -4.89267519231 0.053424171944 y[1] (closed_form) = -4.89267518675 0.0534264898355 absolute error = 2.318e-06 relative error = 4.737e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2032 0.537 h = 0.001 0.003 y[1] (numeric) = -4.89259720046 0.0535461845892 y[1] (closed_form) = -4.89259713659 0.053548477379 absolute error = 2.294e-06 relative error = 4.688e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = -4.89256316228 0.0538683770104 y[1] (closed_form) = -4.89256321927 0.0538707161019 absolute error = 2.340e-06 relative error = 4.782e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO 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=1259.2MB, alloc=52.3MB, time=15.32 x[1] = 10.2043 0.544 h = 0.003 0.006 y[1] (numeric) = -4.89264182946 0.0542710326189 y[1] (closed_form) = -4.89264197324 0.054273303881 absolute error = 2.276e-06 relative error = 4.651e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = -4.89247564382 0.0549387164184 y[1] (closed_form) = -4.89247583359 0.0549414690669 absolute error = 2.759e-06 relative error = 5.639e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = -4.89257877466 0.0554424713322 y[1] (closed_form) = -4.89257888165 0.055444921285 absolute error = 2.452e-06 relative error = 5.012e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2075 0.558 h = 0.001 0.001 y[1] (numeric) = -4.89263720519 0.055745507773 y[1] (closed_form) = -4.89263718975 0.0557479480576 absolute error = 2.440e-06 relative error = 4.987e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO 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=1304.9MB, alloc=52.3MB, time=15.88 x[1] = 10.2085 0.559 h = 0.001 0.003 y[1] (numeric) = -4.89255984596 0.0558686672513 y[1] (closed_form) = -4.89255977228 0.0558710823433 absolute error = 2.416e-06 relative error = 4.938e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = -4.89252821955 0.0561925205172 y[1] (closed_form) = -4.89252826659 0.056194982102 absolute error = 2.462e-06 relative error = 5.032e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2096 0.566 h = 0.003 0.006 y[1] (numeric) = -4.8926104188 0.0565962944238 y[1] (closed_form) = -4.89261055271 0.0565986883684 absolute error = 2.398e-06 relative error = 4.900e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = -4.89244879634 0.0572681923357 y[1] (closed_form) = -4.89244897535 0.0572710674997 absolute error = 2.881e-06 relative error = 5.888e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = -4.89255634574 0.0577733264519 y[1] (closed_form) = -4.89255644257 0.0577758989297 absolute error = 2.574e-06 relative error = 5.261e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO 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=1350.4MB, alloc=52.3MB, time=16.43 x[1] = 10.2128 0.58 h = 0.001 0.001 y[1] (numeric) = -4.89261741702 0.0580772270343 y[1] (closed_form) = -4.89261739149 0.0580797896313 absolute error = 2.563e-06 relative error = 5.238e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2138 0.581 h = 0.001 0.003 y[1] (numeric) = -4.89254068803 0.0582015338772 y[1] (closed_form) = -4.89254060433 0.0582040711913 absolute error = 2.539e-06 relative error = 5.189e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = -4.8925114692 0.0585270514157 y[1] (closed_form) = -4.89251150609 0.0585296354129 absolute error = 2.584e-06 relative error = 5.282e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2149 0.588 h = 0.003 0.006 y[1] (numeric) = -4.8925971967 0.0589319493183 y[1] (closed_form) = -4.89259732052 0.0589344658647 absolute error = 2.520e-06 relative error = 5.149e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO 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=1396.1MB, alloc=52.3MB, time=16.98 x[1] = 10.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = -4.89244012756 0.059608067267 y[1] (closed_form) = -4.89244029562 0.0596110648627 absolute error = 3.002e-06 relative error = 6.136e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.218 0.599 h = 0.0001 0.003 y[1] (numeric) = -4.89255209079 0.0601145877169 y[1] (closed_form) = -4.89255217723 0.0601172826379 absolute error = 2.696e-06 relative error = 5.511e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2181 0.602 h = 0.001 0.001 y[1] (numeric) = -4.89261579991 0.0604193566814 y[1] (closed_form) = -4.89261576407 0.0604220415096 absolute error = 2.685e-06 relative error = 5.488e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2191 0.603 h = 0.001 0.003 y[1] (numeric) = -4.89253969879 0.0605448114113 y[1] (closed_form) = -4.89253960487 0.0605474708666 absolute error = 2.661e-06 relative error = 5.439e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.23 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = -4.89251288334 0.0608719966321 y[1] (closed_form) = -4.89251290985 0.06087470296 absolute error = 2.706e-06 relative error = 5.531e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO 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=1441.8MB, alloc=52.3MB, time=17.54 x[1] = 10.2202 0.61 h = 0.003 0.006 y[1] (numeric) = -4.89260213526 0.061278024209 y[1] (closed_form) = -4.89260224878 0.0612806632756 absolute error = 2.642e-06 relative error = 5.399e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = -4.89244960958 0.0619583680778 y[1] (closed_form) = -4.89244976646 0.0619614880207 absolute error = 3.124e-06 relative error = 6.385e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = -4.89256598188 0.0624662819682 y[1] (closed_form) = -4.89256605772 0.06246909925 absolute error = 2.818e-06 relative error = 5.760e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2234 0.624 h = 0.001 0.001 y[1] (numeric) = -4.8926323259 0.0627719235405 y[1] (closed_form) = -4.89263227955 0.062774730518 absolute error = 2.807e-06 relative error = 5.737e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO 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=1487.5MB, alloc=52.3MB, time=18.09 x[1] = 10.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = -4.89255685031 0.0628985266712 y[1] (closed_form) = -4.89255674595 0.062901308186 absolute error = 2.783e-06 relative error = 5.689e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2245 0.629 h = 0.003 0.006 y[1] (numeric) = -4.89264898342 0.0633054768153 y[1] (closed_form) = -4.89264912911 0.0633082036618 absolute error = 2.731e-06 relative error = 5.581e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = -4.89250041114 0.0639894089334 y[1] (closed_form) = -4.89250059942 0.0639926165153 absolute error = 3.213e-06 relative error = 6.567e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = -4.89262059149 0.0644984754802 y[1] (closed_form) = -4.89262069924 0.0645013804076 absolute error = 2.907e-06 relative error = 5.941e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO 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=1533.1MB, alloc=52.3MB, time=18.64 x[1] = 10.2277 0.643 h = 0.001 0.001 y[1] (numeric) = -4.89268921168 0.0648048401975 y[1] (closed_form) = -4.89268919731 0.0648077346378 absolute error = 2.894e-06 relative error = 5.915e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2287 0.644 h = 0.001 0.003 y[1] (numeric) = -4.89261428631 0.0649324248248 y[1] (closed_form) = -4.89261421398 0.0649352937247 absolute error = 2.870e-06 relative error = 5.865e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = -4.89259195171 0.0652626937138 y[1] (closed_form) = -4.89259199955 0.0652656098391 absolute error = 2.917e-06 relative error = 5.961e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2298 0.651 h = 0.003 0.006 y[1] (numeric) = -4.8926877651 0.0656707965233 y[1] (closed_form) = -4.89268790009 0.0656736457391 absolute error = 2.852e-06 relative error = 5.829e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = -4.89254371797 0.0663589655172 y[1] (closed_form) = -4.89254389468 0.0663622952898 absolute error = 3.334e-06 relative error = 6.815e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO 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=1578.7MB, alloc=52.3MB, time=19.20 x[1] = 10.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = -4.89266829855 0.0668694387212 y[1] (closed_form) = -4.89266839531 0.0668724658567 absolute error = 3.029e-06 relative error = 6.190e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.233 0.665 h = 0.001 0.001 y[1] (numeric) = -4.89273954824 0.0671766839052 y[1] (closed_form) = -4.89273952296 0.0671797003431 absolute error = 3.017e-06 relative error = 6.165e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.234 0.666 h = 0.001 0.003 y[1] (numeric) = -4.89266524399 0.0673054178934 y[1] (closed_form) = -4.89266516084 0.0673084087018 absolute error = 2.992e-06 relative error = 6.115e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.235 0.669 h = 0.0001 0.004 y[1] (numeric) = -4.89264530073 0.0676373641666 y[1] (closed_form) = -4.89264533759 0.067640402388 absolute error = 3.038e-06 relative error = 6.210e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO 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=1624.4MB, alloc=52.3MB, time=19.75 x[1] = 10.2351 0.673 h = 0.003 0.006 y[1] (numeric) = -4.89274462755 0.0680466128333 y[1] (closed_form) = -4.89274475164 0.0680495843348 absolute error = 2.974e-06 relative error = 6.078e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.25 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = -4.89260509568 0.0687390244685 y[1] (closed_form) = -4.89260526062 0.0687424763456 absolute error = 3.456e-06 relative error = 7.063e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = -4.89273407167 0.069250911367 y[1] (closed_form) = -4.89273415723 0.0692540606263 absolute error = 3.150e-06 relative error = 6.438e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2383 0.687 h = 0.001 0.001 y[1] (numeric) = -4.89280794791 0.0695590412014 y[1] (closed_form) = -4.89280791151 0.069562179553 absolute error = 3.139e-06 relative error = 6.414e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2393 0.688 h = 0.001 0.003 y[1] (numeric) = -4.89273426242 0.0696889250384 y[1] (closed_form) = -4.89273416823 0.0696920376719 absolute error = 3.114e-06 relative error = 6.364e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO 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=1670.0MB, alloc=52.3MB, time=20.30 x[1] = 10.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = -4.89271670626 0.070022552034 y[1] (closed_form) = -4.89271673193 0.0700257122673 absolute error = 3.160e-06 relative error = 6.459e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2404 0.695 h = 0.003 0.006 y[1] (numeric) = -4.89281954263 0.0704329521608 y[1] (closed_form) = -4.89281965559 0.0704360458639 absolute error = 3.096e-06 relative error = 6.327e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = -4.8926845161 0.0711296121619 y[1] (closed_form) = -4.89268466905 0.0711331860564 absolute error = 3.577e-06 relative error = 7.310e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = -4.89281788266 0.0716429197677 y[1] (closed_form) = -4.89281795681 0.0716461910658 absolute error = 3.272e-06 relative error = 6.687e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO 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=1715.6MB, alloc=52.3MB, time=20.86 x[1] = 10.2436 0.709 h = 0.001 0.001 y[1] (numeric) = -4.89289438249 0.071951938421 y[1] (closed_form) = -4.89289433476 0.0719551986019 absolute error = 3.261e-06 relative error = 6.663e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.26 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2446 0.71 h = 0.001 0.003 y[1] (numeric) = -4.8928213134 0.0720829725862 y[1] (closed_form) = -4.89282120795 0.0720862069607 absolute error = 3.236e-06 relative error = 6.613e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = -4.8928061401 0.0724182836237 y[1] (closed_form) = -4.89280615437 0.0724215657842 absolute error = 3.282e-06 relative error = 6.707e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2457 0.717 h = 0.003 0.006 y[1] (numeric) = -4.89291248209 0.0728298407938 y[1] (closed_form) = -4.89291258373 0.0728330566138 absolute error = 3.217e-06 relative error = 6.575e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = -4.89278195101 0.0735307548443 y[1] (closed_form) = -4.89278209176 0.0735344506684 absolute error = 3.699e-06 relative error = 7.558e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO 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=1761.1MB, alloc=52.3MB, time=21.41 x[1] = 10.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = -4.89291970327 0.0740454901455 y[1] (closed_form) = -4.8929197658 0.0740488833968 absolute error = 3.394e-06 relative error = 6.935e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2489 0.731 h = 0.001 0.001 y[1] (numeric) = -4.89299882371 0.0743554017714 y[1] (closed_form) = -4.89299876445 0.0743587836964 absolute error = 3.382e-06 relative error = 6.912e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = -4.89292636866 0.0744875867351 y[1] (closed_form) = -4.89292625176 0.0744909427658 absolute error = 3.358e-06 relative error = 6.862e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.25 0.736 h = 0.003 0.006 y[1] (numeric) = -4.89303557648 0.0749000888133 y[1] (closed_form) = -4.89303570944 0.0749033924627 absolute error = 3.306e-06 relative error = 6.756e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.27 Order of pole (given) = 0.5 0 NO 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=1806.6MB, alloc=52.3MB, time=21.96 x[1] = 10.253 0.742 h = 0.0001 0.005 y[1] (numeric) = -4.89290895774 0.0756046157387 y[1] (closed_form) = -4.89290912907 0.0756083992392 absolute error = 3.787e-06 relative error = 7.740e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = -4.89305049829 0.0761205333664 y[1] (closed_form) = -4.89305059189 0.076124014309 absolute error = 3.482e-06 relative error = 7.116e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2532 0.75 h = 0.001 0.001 y[1] (numeric) = -4.89313188278 0.0764311857798 y[1] (closed_form) = -4.89313185466 0.0764346552157 absolute error = 3.470e-06 relative error = 7.090e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2542 0.751 h = 0.001 0.003 y[1] (numeric) = -4.89305996809 0.0765643544064 y[1] (closed_form) = -4.8930598824 0.0765677978716 absolute error = 3.445e-06 relative error = 7.039e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO 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=1852.4MB, alloc=52.3MB, time=22.51 x[1] = 10.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = -4.89304923757 0.0769027795599 y[1] (closed_form) = -4.89304927131 0.0769062711573 absolute error = 3.492e-06 relative error = 7.135e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = -4.8931621062 0.0773164628612 y[1] (closed_form) = -4.89316222745 0.0773198884705 absolute error = 3.428e-06 relative error = 7.004e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2554 0.762 h = 0.003 0.006 y[1] (numeric) = -4.89327571021 0.0777301528675 y[1] (closed_form) = -4.89327583145 0.0777335784941 absolute error = 3.428e-06 relative error = 7.004e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = -4.89315449987 0.0784395163947 y[1] (closed_form) = -4.89315465845 0.0784434216785 absolute error = 3.909e-06 relative error = 7.987e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = -4.89330122689 0.0789569622122 y[1] (closed_form) = -4.89330130842 0.0789605649489 absolute error = 3.604e-06 relative error = 7.364e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO 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=1898.1MB, alloc=52.3MB, time=23.07 x[1] = 10.2586 0.776 h = 0.001 0.001 y[1] (numeric) = -4.89338571178 0.0792685744977 y[1] (closed_form) = -4.89338567168 0.0792721654804 absolute error = 3.591e-06 relative error = 7.338e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2596 0.777 h = 0.001 0.003 y[1] (numeric) = -4.89331455465 0.0794030713887 y[1] (closed_form) = -4.89331445706 0.0794066362956 absolute error = 3.566e-06 relative error = 7.287e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.28 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = -4.89330666717 0.0797433952726 y[1] (closed_form) = -4.89330668886 0.0797470085331 absolute error = 3.613e-06 relative error = 7.383e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2607 0.784 h = 0.003 0.006 y[1] (numeric) = -4.89342367761 0.0801583253077 y[1] (closed_form) = -4.89342378688 0.0801618728002 absolute error = 3.549e-06 relative error = 7.252e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO 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=1943.8MB, alloc=52.3MB, time=23.62 x[1] = 10.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = -4.89330693285 0.080871960362 y[1] (closed_form) = -4.8933070786 0.0808759873158 absolute error = 4.030e-06 relative error = 8.234e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = -4.89345803106 0.081390855165 y[1] (closed_form) = -4.89345810033 0.0813945796012 absolute error = 3.725e-06 relative error = 7.611e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2639 0.798 h = 0.001 0.001 y[1] (numeric) = -4.89354512766 0.0817033730799 y[1] (closed_form) = -4.89354507539 0.0817070855548 absolute error = 3.713e-06 relative error = 7.586e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2649 0.799 h = 0.001 0.003 y[1] (numeric) = -4.89347457743 0.0818390222581 y[1] (closed_form) = -4.89347446775 0.0818427085703 absolute error = 3.688e-06 relative error = 7.535e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = -4.89346905578 0.0821810435954 y[1] (closed_form) = -4.89346906523 0.0821847784444 absolute error = 3.735e-06 relative error = 7.631e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO 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=1989.5MB, alloc=52.3MB, time=24.18 x[1] = 10.266 0.806 h = 0.003 0.006 y[1] (numeric) = -4.8935895562 0.0825971531878 y[1] (closed_form) = -4.8935896533 0.0826008224588 absolute error = 3.671e-06 relative error = 7.500e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.269 0.812 h = 0.0001 0.005 y[1] (numeric) = -4.89347726707 0.0833150652875 y[1] (closed_form) = -4.89347739978 0.0833192138211 absolute error = 4.151e-06 relative error = 8.481e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = -4.89363273153 0.0838354159651 y[1] (closed_form) = -4.89363278833 0.0838392620127 absolute error = 3.846e-06 relative error = 7.859e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2692 0.82 h = 0.001 0.001 y[1] (numeric) = -4.89372243681 0.0841488436031 y[1] (closed_form) = -4.89372237217 0.0841526774824 absolute error = 3.834e-06 relative error = 7.834e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO 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=2035.2MB, alloc=52.3MB, time=24.73 x[1] = 10.2702 0.821 h = 0.001 0.003 y[1] (numeric) = -4.89365249113 0.0842856455033 y[1] (closed_form) = -4.89365236916 0.0842894531335 absolute error = 3.810e-06 relative error = 7.784e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = -4.89364933103 0.0846293675204 y[1] (closed_form) = -4.89364932803 0.08463322387 absolute error = 3.856e-06 relative error = 7.879e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2713 0.828 h = 0.003 0.006 y[1] (numeric) = -4.89377331744 0.085046662154 y[1] (closed_form) = -4.89377340215 0.0850504531154 absolute error = 3.792e-06 relative error = 7.747e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = -4.89366547398 0.0857688567762 y[1] (closed_form) = -4.89366559345 0.0857731267988 absolute error = 4.272e-06 relative error = 8.728e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = -4.89382529972 0.0862906701928 y[1] (closed_form) = -4.89382534386 0.0862946377629 absolute error = 3.968e-06 relative error = 8.107e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO 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=2080.9MB, alloc=52.3MB, time=25.28 x[1] = 10.2745 0.842 h = 0.001 0.001 y[1] (numeric) = -4.89391761067 0.0866050116324 y[1] (closed_form) = -4.89391753344 0.0866089668278 absolute error = 3.956e-06 relative error = 8.082e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2755 0.843 h = 0.001 0.003 y[1] (numeric) = -4.89384826718 0.0867429666806 y[1] (closed_form) = -4.89384813269 0.0867468955408 absolute error = 3.931e-06 relative error = 8.032e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = -4.89384746434 0.0870883925856 y[1] (closed_form) = -4.89384744868 0.0870923703469 absolute error = 3.978e-06 relative error = 8.127e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2766 0.85 h = 0.003 0.006 y[1] (numeric) = -4.89397493273 0.087506877724 y[1] (closed_form) = -4.89397500486 0.0875107902872 absolute error = 3.913e-06 relative error = 7.995e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO 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=2126.5MB, alloc=52.3MB, time=25.84 x[1] = 10.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = -4.89387152498 0.088233360305 y[1] (closed_form) = -4.893871631 0.0882377517251 absolute error = 4.393e-06 relative error = 8.974e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = -4.89403570704 0.0887566433 y[1] (closed_form) = -4.89403573829 0.088760732303 absolute error = 4.089e-06 relative error = 8.354e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2798 0.864 h = 0.001 0.001 y[1] (numeric) = -4.89413062059 0.0890719026044 y[1] (closed_form) = -4.89413053058 0.0890759790268 absolute error = 4.077e-06 relative error = 8.330e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = -4.89406187693 0.089211011218 y[1] (closed_form) = -4.89406172974 0.0892150612196 absolute error = 4.053e-06 relative error = 8.279e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2809 0.869 h = 0.003 0.006 y[1] (numeric) = -4.8941921918 0.0896304685776 y[1] (closed_form) = -4.89419229421 0.0896344690172 absolute error = 4.002e-06 relative error = 8.175e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.31 Order of pole (given) = 0.5 0 NO 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=2172.2MB, alloc=52.3MB, time=26.39 x[1] = 10.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = -4.89409264532 0.0903605937363 y[1] (closed_form) = -4.89409278089 0.0903650728649 absolute error = 4.481e-06 relative error = 9.155e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.284 0.88 h = 0.0001 0.003 y[1] (numeric) = -4.89426059077 0.0908850953416 y[1] (closed_form) = -4.89426065207 0.0908892720784 absolute error = 4.177e-06 relative error = 8.533e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2841 0.883 h = 0.001 0.001 y[1] (numeric) = -4.89435775312 0.0912011170029 y[1] (closed_form) = -4.89435769322 0.0912052809815 absolute error = 4.164e-06 relative error = 8.507e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2851 0.884 h = 0.001 0.003 y[1] (numeric) = -4.89428953764 0.0913412117878 y[1] (closed_form) = -4.89428942063 0.091345349271 absolute error = 4.139e-06 relative error = 8.456e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO 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=2217.7MB, alloc=52.3MB, time=26.94 x[1] = 10.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = -4.89429313008 0.0916897887462 y[1] (closed_form) = -4.8942931316 0.0916939754686 absolute error = 4.187e-06 relative error = 8.553e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2862 0.891 h = 0.003 0.006 y[1] (numeric) = -4.89442708127 0.0921104622453 y[1] (closed_form) = -4.8944271707 0.0921145841223 absolute error = 4.123e-06 relative error = 8.422e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = -4.89433195199 0.0928448854882 y[1] (closed_form) = -4.89433207373 0.0928494858448 absolute error = 4.602e-06 relative error = 9.401e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = -4.89450424453 0.0933708693913 y[1] (closed_form) = -4.89450429256 0.0933751673953 absolute error = 4.298e-06 relative error = 8.780e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO 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=2263.4MB, alloc=52.3MB, time=27.50 x[1] = 10.2894 0.905 h = 0.001 0.001 y[1] (numeric) = -4.89460400384 0.0936878164746 y[1] (closed_form) = -4.89460393077 0.0936921015155 absolute error = 4.286e-06 relative error = 8.754e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2904 0.906 h = 0.001 0.003 y[1] (numeric) = -4.89453638382 0.0938290656063 y[1] (closed_form) = -4.89453625371 0.0938333240668 absolute error = 4.260e-06 relative error = 8.703e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = -4.89454232126 0.0941793555784 y[1] (closed_form) = -4.89454230954 0.0941836634578 absolute error = 4.308e-06 relative error = 8.800e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2915 0.913 h = 0.003 0.006 y[1] (numeric) = -4.89467974298 0.0946012351501 y[1] (closed_form) = -4.89467981923 0.0946054783741 absolute error = 4.244e-06 relative error = 8.669e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = -4.89458902091 0.0953399617964 y[1] (closed_form) = -4.89458912861 0.0953446832877 absolute error = 4.723e-06 relative error = 9.647e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO 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=2309.0MB, alloc=52.3MB, time=28.05 x[1] = 10.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = -4.8947656555 0.0958674347651 y[1] (closed_form) = -4.89476569007 0.095871853945 absolute error = 4.419e-06 relative error = 9.027e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2947 0.927 h = 0.001 0.001 y[1] (numeric) = -4.8948680087 0.0961853112902 y[1] (closed_form) = -4.89486792226 0.0961897173026 absolute error = 4.407e-06 relative error = 9.001e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2957 0.928 h = 0.001 0.003 y[1] (numeric) = -4.89480098179 0.0963277151612 y[1] (closed_form) = -4.89480083839 0.0963320945086 absolute error = 4.382e-06 relative error = 8.950e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = -4.89480925992 0.0966797212834 y[1] (closed_form) = -4.89480923476 0.0966841502287 absolute error = 4.429e-06 relative error = 9.047e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO 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=2354.7MB, alloc=52.3MB, time=28.60 x[1] = 10.2968 0.935 h = 0.003 0.006 y[1] (numeric) = -4.8949501481 0.0971028123137 y[1] (closed_form) = -4.89495021097 0.0971071767936 absolute error = 4.365e-06 relative error = 8.915e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = -4.89486382324 0.0978458476417 y[1] (closed_form) = -4.8948639167 0.0978506901739 absolute error = 4.843e-06 relative error = 9.893e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = -4.89504479485 0.0983748164187 y[1] (closed_form) = -4.89504481575 0.0983793566825 absolute error = 4.540e-06 relative error = 9.273e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3 0.949 h = 0.001 0.001 y[1] (numeric) = -4.89514973886 0.0986936263902 y[1] (closed_form) = -4.89514963883 0.0986981532828 absolute error = 4.528e-06 relative error = 9.248e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.301 0.95 h = 0.001 0.003 y[1] (numeric) = -4.8950833027 0.0988371853843 y[1] (closed_form) = -4.89508314579 0.0988416855276 absolute error = 4.503e-06 relative error = 9.197e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO 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=2400.4MB, alloc=52.3MB, time=29.16 x[1] = 10.302 0.953 h = 0.0001 0.004 y[1] (numeric) = -4.89509391721 0.0991909107743 y[1] (closed_form) = -4.89509387839 0.0991954606936 absolute error = 4.550e-06 relative error = 9.293e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3021 0.957 h = 0.003 0.006 y[1] (numeric) = -4.89523826778 0.099615218629 y[1] (closed_form) = -4.89523831706 0.0996197042731 absolute error = 4.486e-06 relative error = 9.162e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = -4.89515633012 0.100362567876 y[1] (closed_form) = -4.89515640914 0.100367531355 absolute error = 4.964e-06 relative error = 0.0001014 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = -4.89534163368 0.100893039179 y[1] (closed_form) = -4.8953416407 0.100897700434 absolute error = 4.661e-06 relative error = 9.520e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO 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=2446.1MB, alloc=52.3MB, time=29.71 x[1] = 10.3053 0.971 h = 0.001 0.001 y[1] (numeric) = -4.89544916539 0.101212786586 y[1] (closed_form) = -4.89544905158 0.101217434267 absolute error = 4.649e-06 relative error = 9.495e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = -4.89538331764 0.101357501078 y[1] (closed_form) = -4.89538314703 0.101362121926 absolute error = 4.624e-06 relative error = 9.444e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.34 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3064 0.976 h = 0.003 0.006 y[1] (numeric) = -4.89553049865 0.101782802636 y[1] (closed_form) = -4.89553057738 0.101787376174 absolute error = 4.574e-06 relative error = 9.342e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = -4.89545238081 0.102533817226 y[1] (closed_form) = -4.89545248855 0.102538868419 absolute error = 5.052e-06 relative error = 0.0001032 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = -4.8956414271 0.103065535693 y[1] (closed_form) = -4.89564146333 0.103070284696 absolute error = 4.749e-06 relative error = 9.699e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO 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=2491.8MB, alloc=52.3MB, time=30.26 x[1] = 10.3096 0.99 h = 0.001 0.001 y[1] (numeric) = -4.89575119497 0.103386062422 y[1] (closed_form) = -4.89575111044 0.103390797675 absolute error = 4.736e-06 relative error = 9.672e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3106 0.991 h = 0.001 0.003 y[1] (numeric) = -4.89568586559 0.103531764852 y[1] (closed_form) = -4.89568572433 0.103536473198 absolute error = 4.710e-06 relative error = 9.620e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = -4.8957008366 0.103888669923 y[1] (closed_form) = -4.89570081315 0.103893428377 absolute error = 4.759e-06 relative error = 9.718e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3117 0.998 h = 0.003 0.006 y[1] (numeric) = -4.89585163364 0.104315215087 y[1] (closed_form) = -4.8958516984 0.104319909619 absolute error = 4.695e-06 relative error = 9.588e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.35 Order of pole (given) = 0.5 0 NO 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=2537.4MB, alloc=52.3MB, time=30.82 x[1] = 10.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = -4.89577788442 0.105070553352 y[1] (closed_form) = -4.89577797734 0.105075725317 absolute error = 5.173e-06 relative error = 0.0001056 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = -4.89597125327 0.105603786838 y[1] (closed_form) = -4.89597127525 0.10560865666 absolute error = 4.870e-06 relative error = 9.944e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3149 1.012 h = 0.001 0.001 y[1] (numeric) = -4.89608360311 0.105925258422 y[1] (closed_form) = -4.89608350442 0.105930114293 absolute error = 4.857e-06 relative error = 9.918e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3159 1.013 h = 0.001 0.003 y[1] (numeric) = -4.89601885777 0.106072117053 y[1] (closed_form) = -4.89601870243 0.106076945935 absolute error = 4.831e-06 relative error = 9.866e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = -4.89603615282 0.10643075026 memory used=2583.1MB, alloc=52.3MB, time=31.37 y[1] (closed_form) = -4.89603611513 0.106435629425 absolute error = 4.879e-06 relative error = 9.963e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.317 1.02 h = 0.003 0.006 y[1] (numeric) = -4.89619040058 0.106858527537 y[1] (closed_form) = -4.89619045117 0.106863342969 absolute error = 4.816e-06 relative error = 9.833e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.32 1.026 h = 0.0001 0.005 y[1] (numeric) = -4.89612100997 0.107618194598 y[1] (closed_form) = -4.89612108787 0.107623487237 absolute error = 5.293e-06 relative error = 0.0001081 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = -4.89631869626 0.108152949747 y[1] (closed_form) = -4.89631870378 0.108157940295 absolute error = 4.991e-06 relative error = 0.0001019 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3202 1.034 h = 0.001 0.001 y[1] (numeric) = -4.89643362493 0.108475370133 y[1] (closed_form) = -4.89643351189 0.108480346527 absolute error = 4.978e-06 relative error = 0.0001016 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO 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=2628.8MB, alloc=52.3MB, time=31.92 x[1] = 10.3212 1.035 h = 0.001 0.003 y[1] (numeric) = -4.89636946129 0.108623385315 y[1] (closed_form) = -4.89636929168 0.108628334638 absolute error = 4.952e-06 relative error = 0.0001011 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = -4.89638907603 0.108983749704 y[1] (closed_form) = -4.89638902391 0.108988749486 absolute error = 5.000e-06 relative error = 0.0001021 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3223 1.042 h = 0.003 0.006 y[1] (numeric) = -4.8965467704 0.10941276438 y[1] (closed_form) = -4.89654680661 0.109417700619 absolute error = 4.936e-06 relative error = 0.0001008 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = -4.89648172836 0.110176765317 y[1] (closed_form) = -4.89648179104 0.110182178535 absolute error = 5.414e-06 relative error = 0.0001105 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO 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=2674.4MB, alloc=52.3MB, time=32.48 x[1] = 10.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = -4.89668372696 0.11071304875 y[1] (closed_form) = -4.89668371983 0.110718159929 absolute error = 5.111e-06 relative error = 0.0001044 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3255 1.056 h = 0.001 0.001 y[1] (numeric) = -4.89680123134 0.111036421866 y[1] (closed_form) = -4.89680110373 0.111041518691 absolute error = 5.098e-06 relative error = 0.0001041 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3265 1.057 h = 0.001 0.003 y[1] (numeric) = -4.89673764705 0.111185593943 y[1] (closed_form) = -4.89673746295 0.111190663613 absolute error = 5.073e-06 relative error = 0.0001036 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = -4.89675957714 0.111547692541 y[1] (closed_form) = -4.89675951037 0.111552812845 absolute error = 5.121e-06 relative error = 0.0001045 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3276 1.064 h = 0.003 0.006 y[1] (numeric) = -4.89692071397 0.111977949883 y[1] (closed_form) = -4.8969207356 0.111983006834 absolute error = 5.057e-06 relative error = 0.0001032 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.37 Order of pole (given) = 0.5 0 NO 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=2719.9MB, alloc=52.3MB, time=33.03 x[1] = 10.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = -4.89686001047 0.112746289736 y[1] (closed_form) = -4.89686005772 0.112751823436 absolute error = 5.534e-06 relative error = 0.000113 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = -4.89706631623 0.113284108046 y[1] (closed_form) = -4.89706629424 0.113289339761 absolute error = 5.232e-06 relative error = 0.0001068 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3308 1.078 h = 0.001 0.001 y[1] (numeric) = -4.89718639316 0.113608437808 y[1] (closed_form) = -4.8971862508 0.113613654968 absolute error = 5.219e-06 relative error = 0.0001065 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = -4.89712338589 0.113758767113 y[1] (closed_form) = -4.89712318711 0.113763957036 absolute error = 5.194e-06 relative error = 0.000106 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO 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=2765.6MB, alloc=52.3MB, time=33.58 x[1] = 10.3319 1.083 h = 0.003 0.006 y[1] (numeric) = -4.89728733685 0.114190039249 y[1] (closed_form) = -4.89728738711 0.114195184097 absolute error = 5.145e-06 relative error = 0.000105 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = -4.89723041153 0.114962066383 y[1] (closed_form) = -4.89723048669 0.114967687788 absolute error = 5.622e-06 relative error = 0.0001148 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.335 1.094 h = 0.0001 0.003 y[1] (numeric) = -4.89744043902 0.115501159902 y[1] (closed_form) = -4.89744044541 0.115506479364 absolute error = 5.319e-06 relative error = 0.0001086 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3351 1.097 h = 0.001 0.001 y[1] (numeric) = -4.89756273925 0.115826285643 y[1] (closed_form) = -4.89756262535 0.115831590377 absolute error = 5.306e-06 relative error = 0.0001083 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3361 1.098 h = 0.001 0.003 y[1] (numeric) = -4.89750024056 0.115977604476 y[1] (closed_form) = -4.89750007031 0.115982881901 absolute error = 5.280e-06 relative error = 0.0001078 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.38 Order of pole (given) = 0.5 0 NO 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=2811.2MB, alloc=52.3MB, time=34.14 x[1] = 10.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = -4.89752648813 0.116342910568 y[1] (closed_form) = -4.89752643493 0.116348238952 absolute error = 5.329e-06 relative error = 0.0001088 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3372 1.105 h = 0.003 0.006 y[1] (numeric) = -4.89769403447 0.116775453281 y[1] (closed_form) = -4.89769406977 0.116780718666 absolute error = 5.266e-06 relative error = 0.0001075 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = -4.89764142905 0.117551828719 y[1] (closed_form) = -4.89764148842 0.117557570425 absolute error = 5.742e-06 relative error = 0.0001172 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = -4.89785575415 0.11809246938 y[1] (closed_form) = -4.89785574532 0.118097909201 absolute error = 5.440e-06 relative error = 0.000111 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO 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=2856.9MB, alloc=52.3MB, time=34.70 x[1] = 10.3404 1.119 h = 0.001 0.001 y[1] (numeric) = -4.89798062111 0.118418559048 y[1] (closed_form) = -4.89798049207 0.11842398394 absolute error = 5.426e-06 relative error = 0.0001108 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3414 1.12 h = 0.001 0.003 y[1] (numeric) = -4.89791869508 0.118571035733 y[1] (closed_form) = -4.89791850978 0.118576433236 absolute error = 5.401e-06 relative error = 0.0001102 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = -4.89794724557 0.118938084645 y[1] (closed_form) = -4.89794717715 0.118943533279 absolute error = 5.449e-06 relative error = 0.0001112 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3425 1.127 h = 0.003 0.006 y[1] (numeric) = -4.89811822252 0.119371885029 y[1] (closed_form) = -4.89811824267 0.119377270854 absolute error = 5.386e-06 relative error = 0.0001099 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.39 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = -4.89806992695 0.120152613694 y[1] (closed_form) = -4.89806997032 0.120158475602 absolute error = 5.862e-06 relative error = 0.0001196 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO 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=2902.5MB, alloc=52.3MB, time=35.25 x[1] = 10.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = -4.89828854447 0.120694808018 y[1] (closed_form) = -4.8982885202 0.1207003681 absolute error = 5.560e-06 relative error = 0.0001135 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3457 1.141 h = 0.001 0.001 y[1] (numeric) = -4.89841597497 0.121021865483 y[1] (closed_form) = -4.8984158306 0.121027410438 absolute error = 5.547e-06 relative error = 0.0001132 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3467 1.142 h = 0.001 0.003 y[1] (numeric) = -4.89835461926 0.121175500331 y[1] (closed_form) = -4.89835441871 0.121181017816 absolute error = 5.521e-06 relative error = 0.0001127 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = -4.89838546831 0.121544295018 y[1] (closed_form) = -4.89838538449 0.121549863805 absolute error = 5.569e-06 relative error = 0.0001137 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO 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=2948.1MB, alloc=52.3MB, time=35.80 x[1] = 10.3478 1.149 h = 0.003 0.006 y[1] (numeric) = -4.89855987168 0.121979358261 y[1] (closed_form) = -4.89855987647 0.121984864429 absolute error = 5.506e-06 relative error = 0.0001124 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = -4.8985158759 0.122764445036 y[1] (closed_form) = -4.89851590308 0.122770427046 absolute error = 5.982e-06 relative error = 0.0001221 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.4 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = -4.89873878062 0.123308199518 y[1] (closed_form) = -4.89873874073 0.123313879765 absolute error = 5.680e-06 relative error = 0.0001159 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.351 1.163 h = 0.001 0.001 y[1] (numeric) = -4.89886877149 0.123636228635 y[1] (closed_form) = -4.89886861159 0.123641893556 absolute error = 5.667e-06 relative error = 0.0001156 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO 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=2993.7MB, alloc=52.3MB, time=36.36 x[1] = 10.352 1.164 h = 0.001 0.003 y[1] (numeric) = -4.89880798377 0.123791021947 y[1] (closed_form) = -4.89880776776 0.123796659316 absolute error = 5.642e-06 relative error = 0.0001151 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.353 1.167 h = 0.0001 0.004 y[1] (numeric) = -4.898841127 0.124161565346 y[1] (closed_form) = -4.89884102757 0.124167254189 absolute error = 5.690e-06 relative error = 0.0001161 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3531 1.171 h = 0.003 0.006 y[1] (numeric) = -4.89901895258 0.124597896615 y[1] (closed_form) = -4.89901894182 0.124603523029 absolute error = 5.626e-06 relative error = 0.0001148 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = -4.89897924653 0.125387346342 y[1] (closed_form) = -4.89897925732 0.125393448355 absolute error = 6.102e-06 relative error = 0.0001245 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = -4.89920643323 0.125932667454 y[1] (closed_form) = -4.8992063775 0.125938467766 absolute error = 5.801e-06 relative error = 0.0001184 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO 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=3039.2MB, alloc=52.3MB, time=36.92 x[1] = 10.3563 1.185 h = 0.001 0.001 y[1] (numeric) = -4.89933898126 0.126261672062 y[1] (closed_form) = -4.89933880563 0.126267456851 absolute error = 5.787e-06 relative error = 0.0001181 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = -4.89927875919 0.126417624129 y[1] (closed_form) = -4.89927852754 0.126423381286 absolute error = 5.762e-06 relative error = 0.0001176 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3574 1.19 h = 0.003 0.006 y[1] (numeric) = -4.89945938233 0.126854990889 y[1] (closed_form) = -4.89945939938 0.126860705189 absolute error = 5.714e-06 relative error = 0.0001166 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.41 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = -4.89942341272 0.127648149011 y[1] (closed_form) = -4.8994234506 0.127654338707 absolute error = 6.190e-06 relative error = 0.0001263 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.42 Order of pole (given) = 0.5 0 NO 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=3084.8MB, alloc=52.3MB, time=37.47 x[1] = 10.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = -4.89965429977 0.128194772864 y[1] (closed_form) = -4.89965427161 0.128200660908 absolute error = 5.888e-06 relative error = 0.0001201 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3606 1.204 h = 0.001 0.001 y[1] (numeric) = -4.89978905805 0.128524589796 y[1] (closed_form) = -4.89978891007 0.128530462147 absolute error = 5.874e-06 relative error = 0.0001198 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3616 1.205 h = 0.001 0.003 y[1] (numeric) = -4.89972933481 0.128681532809 y[1] (closed_form) = -4.89972913087 0.128687377458 absolute error = 5.848e-06 relative error = 0.0001193 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = -4.89976675625 0.129055310702 y[1] (closed_form) = -4.8997666686 0.129061207144 absolute error = 5.897e-06 relative error = 0.0001203 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3627 1.212 h = 0.003 0.006 y[1] (numeric) = -4.89995095379 0.129493974509 y[1] (closed_form) = -4.89995095491 0.129499808873 absolute error = 5.834e-06 relative error = 0.000119 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.42 Order of pole (given) = 0.5 0 NO 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=3130.4MB, alloc=52.3MB, time=38.02 x[1] = 10.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = -4.89991925522 0.130291504605 y[1] (closed_form) = -4.89991927634 0.130297814118 absolute error = 6.310e-06 relative error = 0.0001287 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = -4.90015441454 0.13083970712 y[1] (closed_form) = -4.9001543702 0.130845715048 absolute error = 6.008e-06 relative error = 0.0001226 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3659 1.226 h = 0.001 0.001 y[1] (numeric) = -4.90029172407 0.131170506685 y[1] (closed_form) = -4.90029155999 0.131176498723 absolute error = 5.994e-06 relative error = 0.0001223 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3669 1.227 h = 0.001 0.003 y[1] (numeric) = -4.90023256215 0.131328609002 y[1] (closed_form) = -4.9002323422 0.131334573259 absolute error = 5.968e-06 relative error = 0.0001218 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO 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=3176.0MB, alloc=52.3MB, time=38.58 x[1] = 10.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = -4.90027226528 0.131704143961 y[1] (closed_form) = -4.90027216145 0.131710160178 absolute error = 6.017e-06 relative error = 0.0001227 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.368 1.234 h = 0.003 0.006 y[1] (numeric) = -4.900459873 0.132144090513 y[1] (closed_form) = -4.900459858 0.132150044843 absolute error = 5.954e-06 relative error = 0.0001215 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.371 1.24 h = 0.0001 0.005 y[1] (numeric) = -4.90043243539 0.13294599731 y[1] (closed_form) = -4.90043243957 0.132952426538 absolute error = 6.429e-06 relative error = 0.0001311 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = -4.90067186172 0.133495784884 y[1] (closed_form) = -4.90067180098 0.133501912596 absolute error = 6.128e-06 relative error = 0.000125 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3712 1.248 h = 0.001 0.001 y[1] (numeric) = -4.90081171928 0.133827570877 y[1] (closed_form) = -4.90081153891 0.133833682502 absolute error = 6.114e-06 relative error = 0.0001247 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.43 Order of pole (given) = 0.5 0 NO 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=3221.6MB, alloc=52.3MB, time=39.13 x[1] = 10.3722 1.249 h = 0.001 0.003 y[1] (numeric) = -4.90075311634 0.133986832767 y[1] (closed_form) = -4.90075288018 0.133992916533 absolute error = 6.088e-06 relative error = 0.0001242 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = -4.90079509677 0.134364127656 y[1] (closed_form) = -4.90079497657 0.134370263551 absolute error = 6.137e-06 relative error = 0.0001252 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3733 1.256 h = 0.003 0.006 y[1] (numeric) = -4.90098611041 0.134805362042 y[1] (closed_form) = -4.9009860791 0.134811436239 absolute error = 6.074e-06 relative error = 0.0001239 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = -4.90096292369 0.135611650227 y[1] (closed_form) = -4.90096291072 0.135618199068 absolute error = 6.549e-06 relative error = 0.0001336 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO 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=3267.1MB, alloc=52.3MB, time=39.69 x[1] = 10.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = -4.90120661173 0.13616302923 y[1] (closed_form) = -4.9012065344 0.136169276626 absolute error = 6.248e-06 relative error = 0.0001274 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3765 1.27 h = 0.001 0.001 y[1] (numeric) = -4.90134901409 0.136495805429 y[1] (closed_form) = -4.90134881723 0.136502036543 absolute error = 6.234e-06 relative error = 0.0001271 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3775 1.271 h = 0.001 0.003 y[1] (numeric) = -4.90129096781 0.136656227153 y[1] (closed_form) = -4.90129071524 0.136662430328 absolute error = 6.208e-06 relative error = 0.0001266 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = -4.90133522114 0.13703528482 y[1] (closed_form) = -4.90133508438 0.137041540291 absolute error = 6.257e-06 relative error = 0.0001276 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO 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=3312.7MB, alloc=52.3MB, time=40.24 x[1] = 10.3786 1.278 h = 0.003 0.006 y[1] (numeric) = -4.90152963645 0.137477812106 y[1] (closed_form) = -4.90152958862 0.137484006069 absolute error = 6.194e-06 relative error = 0.0001263 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = -4.90151069052 0.138288486325 y[1] (closed_form) = -4.90151066021 0.138295154675 absolute error = 6.668e-06 relative error = 0.000136 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = -4.90175863497 0.138841463102 y[1] (closed_form) = -4.90175854086 0.13884783008 absolute error = 6.368e-06 relative error = 0.0001299 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3818 1.292 h = 0.001 0.001 y[1] (numeric) = -4.90190357888 0.139175233271 y[1] (closed_form) = -4.90190336534 0.139181583772 absolute error = 6.354e-06 relative error = 0.0001296 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = -4.90184608694 0.139336815081 y[1] (closed_form) = -4.90184581776 0.139343137564 absolute error = 6.328e-06 relative error = 0.000129 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO 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=3358.3MB, alloc=52.3MB, time=40.80 x[1] = 10.3829 1.297 h = 0.003 0.006 y[1] (numeric) = -4.90204328298 0.139780398158 y[1] (closed_form) = -4.90204326214 0.139786679981 absolute error = 6.282e-06 relative error = 0.0001281 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = -4.90202803163 0.140594801065 y[1] (closed_form) = -4.90202802761 0.140601557064 absolute error = 6.756e-06 relative error = 0.0001378 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.386 1.308 h = 0.0001 0.003 y[1] (numeric) = -4.90227965473 0.141149107598 y[1] (closed_form) = -4.90227958737 0.141155562281 absolute error = 6.455e-06 relative error = 0.0001316 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3861 1.311 h = 0.001 0.001 y[1] (numeric) = -4.90242679563 0.141483706124 y[1] (closed_form) = -4.90242660893 0.141490144162 absolute error = 6.441e-06 relative error = 0.0001313 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO 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=3403.8MB, alloc=52.3MB, time=41.35 x[1] = 10.3871 1.312 h = 0.001 0.003 y[1] (numeric) = -4.9023697928 0.141646280126 y[1] (closed_form) = -4.90236955054 0.141652690077 absolute error = 6.415e-06 relative error = 0.0001308 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = -4.90241828485 0.142028598474 y[1] (closed_form) = -4.9024181581 0.142035061033 absolute error = 6.464e-06 relative error = 0.0001318 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3882 1.319 h = 0.003 0.006 y[1] (numeric) = -4.902619034 0.14247350456 y[1] (closed_form) = -4.90261899628 0.142479905964 absolute error = 6.402e-06 relative error = 0.0001305 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = -4.90260800473 0.14329230216 y[1] (closed_form) = -4.902607983 0.143299177478 absolute error = 6.875e-06 relative error = 0.0001402 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = -4.90286387439 0.143848218268 y[1] (closed_form) = -4.90286378989 0.143854792347 absolute error = 6.575e-06 relative error = 0.000134 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO 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=3449.3MB, alloc=52.3MB, time=41.90 x[1] = 10.3914 1.333 h = 0.001 0.001 y[1] (numeric) = -4.90301355085 0.144183817765 y[1] (closed_form) = -4.9030133471 0.144190375004 absolute error = 6.560e-06 relative error = 0.0001337 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3924 1.334 h = 0.001 0.003 y[1] (numeric) = -4.90295709803 0.144347552326 y[1] (closed_form) = -4.9029568388 0.144354081401 absolute error = 6.534e-06 relative error = 0.0001332 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.46 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = -4.90300785043 0.144731641547 y[1] (closed_form) = -4.90300770655 0.144738223395 absolute error = 6.583e-06 relative error = 0.0001342 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3935 1.341 h = 0.003 0.006 y[1] (numeric) = -4.90321198902 0.145177854966 y[1] (closed_form) = -4.90321193423 0.145184375849 absolute error = 6.521e-06 relative error = 0.0001329 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO 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=3494.9MB, alloc=52.3MB, time=42.46 x[1] = 10.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = -4.90320517173 0.146001051789 y[1] (closed_form) = -4.90320513211 0.146008046323 absolute error = 6.995e-06 relative error = 0.0001426 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = -4.90346528261 0.146558583744 y[1] (closed_form) = -4.90346518077 0.146565277115 absolute error = 6.694e-06 relative error = 0.0001365 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3967 1.355 h = 0.001 0.001 y[1] (numeric) = -4.90361749136 0.14689518793 y[1] (closed_form) = -4.90361727037 0.146901864269 absolute error = 6.680e-06 relative error = 0.0001362 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3977 1.356 h = 0.001 0.003 y[1] (numeric) = -4.90356158623 0.147060083279 y[1] (closed_form) = -4.90356130985 0.147066731376 absolute error = 6.654e-06 relative error = 0.0001356 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = -4.90361459456 0.147445946148 y[1] (closed_form) = -4.90361443337 0.147452647183 absolute error = 6.703e-06 relative error = 0.0001366 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO 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=3540.5MB, alloc=52.3MB, time=43.00 x[1] = 10.3988 1.363 h = 0.003 0.006 y[1] (numeric) = -4.90382211829 0.147893471887 y[1] (closed_form) = -4.90382204623 0.147900112145 absolute error = 6.641e-06 relative error = 0.0001354 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = -4.90381950289 0.148721072425 y[1] (closed_form) = -4.90381944518 0.148728186069 absolute error = 7.114e-06 relative error = 0.000145 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = -4.90408384962 0.14928022647 y[1] (closed_form) = -4.90408373024 0.149287039031 absolute error = 6.814e-06 relative error = 0.0001389 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.402 1.377 h = 0.001 0.001 y[1] (numeric) = -4.90423858738 0.149617839049 y[1] (closed_form) = -4.90423834896 0.149624634385 absolute error = 6.800e-06 relative error = 0.0001386 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO 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=3586.0MB, alloc=52.3MB, time=43.56 x[1] = 10.403 1.378 h = 0.001 0.003 y[1] (numeric) = -4.90418322763 0.149783895405 y[1] (closed_form) = -4.9041829339 0.149790662423 absolute error = 6.773e-06 relative error = 0.0001381 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.404 1.381 h = 0.0001 0.004 y[1] (numeric) = -4.90423848748 0.150171534681 y[1] (closed_form) = -4.90423830878 0.150178354799 absolute error = 6.822e-06 relative error = 0.000139 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4041 1.385 h = 0.003 0.006 y[1] (numeric) = -4.90444939203 0.150620377705 y[1] (closed_form) = -4.9044493025 0.150627137236 absolute error = 6.760e-06 relative error = 0.0001378 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = -4.9044509684 0.151452386408 y[1] (closed_form) = -4.90445089241 0.151459619058 absolute error = 7.233e-06 relative error = 0.0001474 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.48 Order of pole (given) = 0.5 0 NO 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=3631.7MB, alloc=52.3MB, time=44.12 x[1] = 10.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = -4.90471954561 0.152013168764 y[1] (closed_form) = -4.9047194085 0.152020100411 absolute error = 6.933e-06 relative error = 0.0001413 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4073 1.399 h = 0.001 0.001 y[1] (numeric) = -4.9048768091 0.152351793423 y[1] (closed_form) = -4.90487655306 0.152358707653 absolute error = 6.919e-06 relative error = 0.000141 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4083 1.4 h = 0.003 0.006 y[1] (numeric) = -4.90482199241 0.152519010999 y[1] (closed_form) = -4.90482168114 0.152525896833 absolute error = 6.893e-06 relative error = 0.0001405 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = -4.90482593149 0.153354041768 y[1] (closed_form) = -4.90482603693 0.153361518622 absolute error = 7.478e-06 relative error = 0.0001524 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = -4.90509737445 0.153916054219 y[1] (closed_form) = -4.90509741915 0.153923230142 absolute error = 7.176e-06 relative error = 0.0001462 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO 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=3677.2MB, alloc=52.3MB, time=44.67 x[1] = 10.4115 1.414 h = 0.001 0.001 y[1] (numeric) = -4.90525634786 0.154255440734 y[1] (closed_form) = -4.90525627369 0.15426259911 absolute error = 7.159e-06 relative error = 0.0001459 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4125 1.415 h = 0.001 0.003 y[1] (numeric) = -4.90520187413 0.154423470826 y[1] (closed_form) = -4.90520174479 0.154430600757 absolute error = 7.131e-06 relative error = 0.0001453 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = -4.90526087937 0.154814171151 y[1] (closed_form) = -4.90526086478 0.154821354453 absolute error = 7.183e-06 relative error = 0.0001464 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4136 1.422 h = 0.003 0.006 y[1] (numeric) = -4.90547744705 0.155265333735 y[1] (closed_form) = -4.90547752171 0.155272456771 absolute error = 7.123e-06 relative error = 0.0001451 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.49 Order of pole (given) = 0.5 0 NO 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=3722.8MB, alloc=52.3MB, time=45.23 x[1] = 10.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = -4.90548596446 0.156104897946 y[1] (closed_form) = -4.9054860513 0.156112493622 absolute error = 7.596e-06 relative error = 0.0001548 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = -4.90576162863 0.156668549009 y[1] (closed_form) = -4.90576165527 0.156675843838 absolute error = 7.295e-06 relative error = 0.0001486 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4168 1.436 h = 0.001 0.001 y[1] (numeric) = -4.90592312212 0.157008953709 y[1] (closed_form) = -4.90592303001 0.157016230799 absolute error = 7.278e-06 relative error = 0.0001483 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4178 1.437 h = 0.001 0.003 y[1] (numeric) = -4.90586918754 0.157178145302 y[1] (closed_form) = -4.90586904034 0.15718539387 absolute error = 7.250e-06 relative error = 0.0001477 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = -4.90593043235 0.15757062924 y[1] (closed_form) = -4.90593039973 0.157577931343 absolute error = 7.302e-06 relative error = 0.0001488 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 0 NO 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=3768.3MB, alloc=52.3MB, time=45.78 x[1] = 10.4189 1.444 h = 0.003 0.006 y[1] (numeric) = -4.90615036904 0.158023122244 y[1] (closed_form) = -4.90615042572 0.15803036427 absolute error = 7.242e-06 relative error = 0.0001475 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.5 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = -4.90616305096 0.158867106134 y[1] (closed_form) = -4.90616311901 0.158874820524 absolute error = 7.715e-06 relative error = 0.0001572 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.422 1.455 h = 0.0001 0.003 y[1] (numeric) = -4.90644293091 0.159432401957 y[1] (closed_form) = -4.90644293932 0.159439815586 absolute error = 7.414e-06 relative error = 0.000151 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4221 1.458 h = 0.001 0.001 y[1] (numeric) = -4.90660694118 0.159773828487 y[1] (closed_form) = -4.90660683094 0.159781224187 absolute error = 7.397e-06 relative error = 0.0001507 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO 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=3813.9MB, alloc=52.3MB, time=46.33 x[1] = 10.4231 1.459 h = 0.001 0.003 y[1] (numeric) = -4.90655354344 0.159944181769 y[1] (closed_form) = -4.90655337819 0.159951548872 absolute error = 7.369e-06 relative error = 0.0001501 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = -4.90661702339 0.160338452012 y[1] (closed_form) = -4.90661697256 0.160345872809 absolute error = 7.421e-06 relative error = 0.0001512 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4242 1.466 h = 0.003 0.006 y[1] (numeric) = -4.90684032472 0.160792280325 y[1] (closed_form) = -4.90684036324 0.160799641234 absolute error = 7.361e-06 relative error = 0.0001499 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = -4.90685716104 0.161640688196 y[1] (closed_form) = -4.90685721012 0.161648521193 absolute error = 7.833e-06 relative error = 0.0001596 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = -4.90714125135 0.162207634902 y[1] (closed_form) = -4.90714124133 0.162215167225 absolute error = 7.532e-06 relative error = 0.0001534 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.51 Order of pole (given) = 0.5 0 NO 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=3859.4MB, alloc=52.3MB, time=46.88 x[1] = 10.4274 1.48 h = 0.001 0.001 y[1] (numeric) = -4.9073077751 0.162550086891 y[1] (closed_form) = -4.90730764652 0.162557601096 absolute error = 7.515e-06 relative error = 0.0001531 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = -4.90725491189 0.162721602045 y[1] (closed_form) = -4.90725472839 0.162729087578 absolute error = 7.488e-06 relative error = 0.0001525 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4285 1.485 h = 0.003 0.006 y[1] (numeric) = -4.90748096369 0.163176520756 y[1] (closed_form) = -4.90748102777 0.163183969445 absolute error = 7.449e-06 relative error = 0.0001517 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = -4.90750142064 0.164028690737 y[1] (closed_form) = -4.90750149458 0.164036611282 absolute error = 7.921e-06 relative error = 0.0001613 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO 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=3905.0MB, alloc=52.3MB, time=47.44 x[1] = 10.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = -4.90778915049 0.164597013285 y[1] (closed_form) = -4.90778916581 0.164604633227 absolute error = 7.620e-06 relative error = 0.0001552 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4317 1.499 h = 0.001 0.001 y[1] (numeric) = -4.90795784736 0.164940320963 y[1] (closed_form) = -4.90795774422 0.164947922622 absolute error = 7.602e-06 relative error = 0.0001548 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4327 1.5 h = 0.001 0.003 y[1] (numeric) = -4.90790545626 0.165112830028 y[1] (closed_form) = -4.90790529827 0.165120402949 absolute error = 7.575e-06 relative error = 0.0001542 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = -4.90797310483 0.165510404759 y[1] (closed_form) = -4.90797306096 0.165518031673 absolute error = 7.627e-06 relative error = 0.0001553 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO 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=3950.5MB, alloc=52.3MB, time=47.99 x[1] = 10.4338 1.507 h = 0.003 0.006 y[1] (numeric) = -4.90820267137 0.165966690753 y[1] (closed_form) = -4.90820271693 0.165974258131 absolute error = 7.568e-06 relative error = 0.0001541 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.52 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = -4.90822726396 0.16682329274 y[1] (closed_form) = -4.90822731857 0.166831331693 absolute error = 8.039e-06 relative error = 0.0001637 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = -4.90851919409 0.167393277559 y[1] (closed_form) = -4.90851919063 0.167401016 absolute error = 7.738e-06 relative error = 0.0001576 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.437 1.521 h = 0.001 0.001 y[1] (numeric) = -4.90869039829 0.167737617446 y[1] (closed_form) = -4.90869027647 0.167745337415 absolute error = 7.721e-06 relative error = 0.0001572 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.438 1.522 h = 0.001 0.003 y[1] (numeric) = -4.90863853743 0.167911288727 y[1] (closed_form) = -4.90863836085 0.167918979884 absolute error = 7.693e-06 relative error = 0.0001566 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.53 Order of pole (given) = 0.5 0 NO 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=3995.9MB, alloc=52.3MB, time=48.54 x[1] = 10.439 1.525 h = 0.0001 0.004 y[1] (numeric) = -4.90870840849 0.168310657406 y[1] (closed_form) = -4.90870834586 0.168318402716 absolute error = 7.746e-06 relative error = 0.0001577 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4391 1.529 h = 0.003 0.006 y[1] (numeric) = -4.90894132718 0.168768292631 y[1] (closed_form) = -4.90894135403 0.168775978593 absolute error = 7.686e-06 relative error = 0.0001565 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = -4.90897004528 0.169629330815 y[1] (closed_form) = -4.90897008038 0.169637488068 absolute error = 8.157e-06 relative error = 0.0001661 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = -4.90926617023 0.170200983953 y[1] (closed_form) = -4.90926614779 0.170208840786 absolute error = 7.857e-06 relative error = 0.0001599 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO 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=4041.5MB, alloc=52.3MB, time=49.09 x[1] = 10.4423 1.543 h = 0.001 0.001 y[1] (numeric) = -4.90943987842 0.170546359633 y[1] (closed_form) = -4.90943973774 0.170554197807 absolute error = 7.839e-06 relative error = 0.0001596 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4433 1.544 h = 0.001 0.003 y[1] (numeric) = -4.90938854551 0.17072119329 y[1] (closed_form) = -4.90938835014 0.170729002577 absolute error = 7.812e-06 relative error = 0.000159 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = -4.90946063461 0.171122358536 y[1] (closed_form) = -4.90946055303 0.171130222133 absolute error = 7.864e-06 relative error = 0.0001601 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4444 1.551 h = 0.003 0.006 y[1] (numeric) = -4.90969690105 0.171581347799 y[1] (closed_form) = -4.90969690899 0.171589152238 absolute error = 7.804e-06 relative error = 0.0001589 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = -4.90972973455 0.172446826331 y[1] (closed_form) = -4.90972974994 0.172455101776 absolute error = 8.275e-06 relative error = 0.0001684 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.54 Order of pole (given) = 0.5 0 NO 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=4087.1MB, alloc=52.3MB, time=49.64 x[1] = 10.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = -4.91003004883 0.173020153809 y[1] (closed_form) = -4.91003000723 0.173028128928 absolute error = 7.975e-06 relative error = 0.0001623 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4476 1.565 h = 0.001 0.001 y[1] (numeric) = -4.91020625767 0.173366568852 y[1] (closed_form) = -4.91020609793 0.173374525123 absolute error = 7.958e-06 relative error = 0.000162 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4486 1.566 h = 0.001 0.003 y[1] (numeric) = -4.91015545041 0.173542565035 y[1] (closed_form) = -4.91015523607 0.173550492346 absolute error = 7.930e-06 relative error = 0.0001614 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = -4.91022975309 0.173945529448 y[1] (closed_form) = -4.91022965238 0.173953511226 absolute error = 7.982e-06 relative error = 0.0001625 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO 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=4132.6MB, alloc=52.3MB, time=50.20 x[1] = 10.4497 1.573 h = 0.003 0.006 y[1] (numeric) = -4.91046936286 0.174405877536 y[1] (closed_form) = -4.91046935172 0.174413800344 absolute error = 7.923e-06 relative error = 0.0001612 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = -4.91050630165 0.175275800529 y[1] (closed_form) = -4.91050629715 0.175284194054 absolute error = 8.394e-06 relative error = 0.0001708 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = -4.91081079975 0.175850808343 y[1] (closed_form) = -4.91081073881 0.175858901638 absolute error = 8.094e-06 relative error = 0.0001647 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4529 1.587 h = 0.001 0.001 y[1] (numeric) = -4.91098950589 0.176198266299 y[1] (closed_form) = -4.91098932692 0.17620634056 absolute error = 8.076e-06 relative error = 0.0001643 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = -4.91093922199 0.176375425152 y[1] (closed_form) = -4.91093898849 0.176383470379 absolute error = 8.049e-06 relative error = 0.0001638 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.55 Order of pole (given) = 0.5 0 NO 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=4178.3MB, alloc=52.3MB, time=50.75 x[1] = 10.454 1.592 h = 0.003 0.006 y[1] (numeric) = -4.91118156479 0.176836882828 y[1] (closed_form) = -4.91118157841 0.176844893354 absolute error = 8.011e-06 relative error = 0.000163 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.457 1.598 h = 0.0001 0.005 y[1] (numeric) = -4.91122208217 0.177710585989 y[1] (closed_form) = -4.91122210174 0.177719066991 absolute error = 8.481e-06 relative error = 0.0001726 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = -4.91153019728 0.178286995213 y[1] (closed_form) = -4.91153016088 0.178295176062 absolute error = 8.181e-06 relative error = 0.0001665 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4572 1.606 h = 0.001 0.001 y[1] (numeric) = -4.9117110628 0.178635324014 y[1] (closed_form) = -4.91171090846 0.178643485667 absolute error = 8.163e-06 relative error = 0.0001661 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO 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=4223.9MB, alloc=52.3MB, time=51.30 x[1] = 10.4582 1.607 h = 0.001 0.003 y[1] (numeric) = -4.91166124139 0.178813477566 y[1] (closed_form) = -4.9116610326 0.178821610121 absolute error = 8.135e-06 relative error = 0.0001655 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = -4.91173967273 0.179219770421 y[1] (closed_form) = -4.91173957726 0.179227957737 absolute error = 8.188e-06 relative error = 0.0001666 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4593 1.614 h = 0.003 0.006 y[1] (numeric) = -4.91198550817 0.179682619934 y[1] (closed_form) = -4.91198550235 0.17969074863 absolute error = 8.129e-06 relative error = 0.0001654 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.56 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = -4.91203011205 0.180560775222 y[1] (closed_form) = -4.9120301114 0.180569374102 absolute error = 8.599e-06 relative error = 0.0001749 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.57 Order of pole (given) = 0.5 0 NO 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=4269.4MB, alloc=52.3MB, time=51.86 x[1] = 10.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = -4.9123424008 0.181138875934 y[1] (closed_form) = -4.9123423447 0.181147174761 absolute error = 8.299e-06 relative error = 0.0001688 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4625 1.628 h = 0.001 0.001 y[1] (numeric) = -4.91252575741 0.181488254258 y[1] (closed_form) = -4.91252558348 0.181496533702 absolute error = 8.281e-06 relative error = 0.0001685 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4635 1.629 h = 0.001 0.003 y[1] (numeric) = -4.91247645509 0.181667570751 y[1] (closed_form) = -4.9124762268 0.181675821025 absolute error = 8.253e-06 relative error = 0.0001679 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = -4.91255708732 0.182075670164 y[1] (closed_form) = -4.91255697218 0.182083975353 absolute error = 8.306e-06 relative error = 0.000169 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4646 1.636 h = 0.003 0.006 y[1] (numeric) = -4.91280625345 0.182539892132 y[1] (closed_form) = -4.912806228 0.18254813889 absolute error = 8.247e-06 relative error = 0.0001677 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.57 Order of pole (given) = 0.5 0 NO 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=4315.0MB, alloc=52.3MB, time=52.41 x[1] = 10.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = -4.91285493371 0.183422503547 y[1] (closed_form) = -4.91285491264 0.183431220193 absolute error = 8.717e-06 relative error = 0.0001773 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = -4.91317139056 0.184002301669 y[1] (closed_form) = -4.91317131458 0.184010718363 absolute error = 8.417e-06 relative error = 0.0001712 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4678 1.65 h = 0.001 0.001 y[1] (numeric) = -4.91335723489 0.184352733022 y[1] (closed_form) = -4.91335704118 0.184361130148 absolute error = 8.399e-06 relative error = 0.0001708 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4688 1.651 h = 0.001 0.003 y[1] (numeric) = -4.91330844937 0.184533212577 y[1] (closed_form) = -4.91330820139 0.18454158046 absolute error = 8.372e-06 relative error = 0.0001703 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO 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=4360.6MB, alloc=52.3MB, time=52.96 x[1] = 10.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = -4.91339127803 0.184943121075 y[1] (closed_form) = -4.91339114304 0.184951544029 absolute error = 8.424e-06 relative error = 0.0001713 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4699 1.658 h = 0.003 0.006 y[1] (numeric) = -4.91364377039 0.185408720206 y[1] (closed_form) = -4.91364372512 0.185417084917 absolute error = 8.365e-06 relative error = 0.0001701 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = -4.91369651691 0.186295791709 y[1] (closed_form) = -4.91369647523 0.18630462601 absolute error = 8.834e-06 relative error = 0.0001797 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.473 1.669 h = 0.0001 0.003 y[1] (numeric) = -4.91401713632 0.186877293133 y[1] (closed_form) = -4.91401704027 0.186885827585 absolute error = 8.535e-06 relative error = 0.0001736 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4731 1.672 h = 0.001 0.001 y[1] (numeric) = -4.91420546498 0.187228781006 y[1] (closed_form) = -4.91420525132 0.187237295705 absolute error = 8.517e-06 relative error = 0.0001732 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.58 Order of pole (given) = 0.5 0 NO 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=4406.1MB, alloc=52.3MB, time=53.52 x[1] = 10.4741 1.673 h = 0.001 0.003 y[1] (numeric) = -4.91415719397 0.187410423737 y[1] (closed_form) = -4.91415692611 0.187418909121 absolute error = 8.490e-06 relative error = 0.0001726 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = -4.9142422146 0.187822143832 y[1] (closed_form) = -4.91424205958 0.18783068444 absolute error = 8.542e-06 relative error = 0.0001737 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4752 1.68 h = 0.003 0.006 y[1] (numeric) = -4.91449802872 0.188289124809 y[1] (closed_form) = -4.91449796346 0.188297607363 absolute error = 8.483e-06 relative error = 0.0001725 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = -4.91455483139 0.189180660321 y[1] (closed_form) = -4.91455476892 0.189189612165 absolute error = 8.952e-06 relative error = 0.000182 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO 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=4451.7MB, alloc=52.3MB, time=54.08 x[1] = 10.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = -4.91487960779 0.189763870917 y[1] (closed_form) = -4.91487949149 0.189772523016 absolute error = 8.653e-06 relative error = 0.0001759 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4784 1.694 h = 0.001 0.001 y[1] (numeric) = -4.91507041739 0.190116418786 y[1] (closed_form) = -4.91507018359 0.190125050948 absolute error = 8.635e-06 relative error = 0.0001756 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = -4.91502265861 0.190299224796 y[1] (closed_form) = -4.9150223707 0.190307827571 absolute error = 8.608e-06 relative error = 0.000175 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4795 1.699 h = 0.003 0.006 y[1] (numeric) = -4.91528118812 0.190767334145 y[1] (closed_form) = -4.91528114683 0.190775904342 absolute error = 8.570e-06 relative error = 0.0001742 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.59 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = -4.91534152732 0.191662667084 y[1] (closed_form) = -4.91534148814 0.191671706321 absolute error = 9.039e-06 relative error = 0.0001838 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 0 NO 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=4497.2MB, alloc=52.3MB, time=54.63 x[1] = 10.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = -4.91566989791 0.19224730413 y[1] (closed_form) = -4.91566980536 0.192256043707 absolute error = 8.740e-06 relative error = 0.0001777 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4827 1.713 h = 0.001 0.001 y[1] (numeric) = -4.915862853 0.19260073768 y[1] (closed_form) = -4.91586264304 0.192609457161 absolute error = 8.722e-06 relative error = 0.0001773 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4837 1.714 h = 0.001 0.003 y[1] (numeric) = -4.91581554715 0.192784539016 y[1] (closed_form) = -4.91581528316 0.192793229048 absolute error = 8.694e-06 relative error = 0.0001767 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = -4.91590465632 0.193199610708 y[1] (closed_form) = -4.91590450484 0.193208356249 absolute error = 8.747e-06 relative error = 0.0001778 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 0 NO 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=4542.7MB, alloc=52.3MB, time=55.18 x[1] = 10.4848 1.721 h = 0.003 0.006 y[1] (numeric) = -4.91616665612 0.193669135932 y[1] (closed_form) = -4.91616659449 0.193677823769 absolute error = 8.688e-06 relative error = 0.0001766 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.6 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = -4.91623103268 0.194568940193 y[1] (closed_form) = -4.91623097236 0.194578096766 absolute error = 9.157e-06 relative error = 0.0001861 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = -4.91656354994 0.195155297327 y[1] (closed_form) = -4.91656343681 0.195164154346 absolute error = 8.858e-06 relative error = 0.00018 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.488 1.735 h = 0.001 0.001 y[1] (numeric) = -4.9167589797 0.195509797338 y[1] (closed_form) = -4.91675874926 0.195518634078 absolute error = 8.840e-06 relative error = 0.0001796 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO 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=4588.3MB, alloc=52.3MB, time=55.74 x[1] = 10.489 1.736 h = 0.001 0.003 y[1] (numeric) = -4.91671218185 0.195694762154 y[1] (closed_form) = -4.91671189745 0.195703569375 absolute error = 8.812e-06 relative error = 0.0001791 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.49 1.739 h = 0.0001 0.004 y[1] (numeric) = -4.91680347024 0.19611165258 y[1] (closed_form) = -4.9168032982 0.196120515462 absolute error = 8.865e-06 relative error = 0.0001801 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4901 1.743 h = 0.003 0.006 y[1] (numeric) = -4.91706877903 0.19658257299 y[1] (closed_form) = -4.91706869686 0.196591378355 absolute error = 8.806e-06 relative error = 0.0001789 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = -4.91713718282 0.197486852383 y[1] (closed_form) = -4.91713710119 0.197496126178 absolute error = 9.274e-06 relative error = 0.0001885 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = -4.91747384117 0.198074935398 y[1] (closed_form) = -4.91747370725 0.198083909748 absolute error = 8.975e-06 relative error = 0.0001824 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO 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=4633.8MB, alloc=52.3MB, time=56.28 x[1] = 10.4933 1.757 h = 0.001 0.001 y[1] (numeric) = -4.91767174218 0.198430505299 y[1] (closed_form) = -4.91767149108 0.198439459188 absolute error = 8.957e-06 relative error = 0.000182 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4943 1.758 h = 0.001 0.003 y[1] (numeric) = -4.91762545004 0.198616633679 y[1] (closed_form) = -4.91762514506 0.198625557978 absolute error = 8.930e-06 relative error = 0.0001814 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = -4.9177189132 0.19903534528 y[1] (closed_form) = -4.91771872042 0.199044325391 absolute error = 8.982e-06 relative error = 0.0001825 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4954 1.765 h = 0.003 0.006 y[1] (numeric) = -4.91798752646 0.199507665479 y[1] (closed_form) = -4.91798742358 0.199516588261 absolute error = 8.923e-06 relative error = 0.0001813 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO 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=4679.4MB, alloc=52.3MB, time=56.84 x[1] = 10.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = -4.91805994736 0.200416423775 y[1] (closed_form) = -4.91805984425 0.200425814678 absolute error = 9.391e-06 relative error = 0.0001908 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = -4.9184007412 0.201006238438 y[1] (closed_form) = -4.91840058632 0.201015330007 absolute error = 9.093e-06 relative error = 0.0001847 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4986 1.779 h = 0.001 0.001 y[1] (numeric) = -4.91860111005 0.201362881643 y[1] (closed_form) = -4.9186008381 0.20137195257 absolute error = 9.075e-06 relative error = 0.0001843 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.62 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.4996 1.78 h = 0.001 0.003 y[1] (numeric) = -4.91855532135 0.201550173662 y[1] (closed_form) = -4.91855499561 0.201559214928 absolute error = 9.047e-06 relative error = 0.0001838 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = -4.9186509548 0.201970708861 y[1] (closed_form) = -4.91865074109 0.201979806089 absolute error = 9.100e-06 relative error = 0.0001848 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO 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=4724.9MB, alloc=52.3MB, time=57.39 x[1] = 10.5007 1.787 h = 0.003 0.006 y[1] (numeric) = -4.91892286802 0.202444433431 y[1] (closed_form) = -4.91892274425 0.202453473518 absolute error = 9.041e-06 relative error = 0.0001836 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = -4.91899929592 0.203357674362 y[1] (closed_form) = -4.91899917113 0.20336718226 absolute error = 9.509e-06 relative error = 0.0001931 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = -4.91934421961 0.203949226413 y[1] (closed_form) = -4.9193440436 0.203958435089 absolute error = 9.210e-06 relative error = 0.0001871 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5039 1.801 h = 0.001 0.001 y[1] (numeric) = -4.91954705289 0.204306946322 y[1] (closed_form) = -4.91954675991 0.204316134174 absolute error = 9.193e-06 relative error = 0.0001867 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO 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=4770.5MB, alloc=52.3MB, time=57.94 x[1] = 10.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = -4.91950176535 0.204495402046 y[1] (closed_form) = -4.91950141867 0.204504560167 absolute error = 9.165e-06 relative error = 0.0001861 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.505 1.806 h = 0.003 0.006 y[1] (numeric) = -4.91977637612 0.204970273368 y[1] (closed_form) = -4.91977627553 0.204979401011 absolute error = 9.128e-06 relative error = 0.0001854 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.508 1.812 h = 0.0001 0.005 y[1] (numeric) = -4.91985629847 0.205887328193 y[1] (closed_form) = -4.91985619619 0.205896923388 absolute error = 9.596e-06 relative error = 0.0001949 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = -4.92020479328 0.206480331204 y[1] (closed_form) = -4.92020464023 0.206489627268 absolute error = 9.297e-06 relative error = 0.0001888 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5082 1.82 h = 0.001 0.001 y[1] (numeric) = -4.92040975799 0.206838951311 y[1] (closed_form) = -4.92040948807 0.206848226394 absolute error = 9.279e-06 relative error = 0.0001884 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.64 Order of pole (given) = 0.5 0 NO 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=4816.2MB, alloc=52.3MB, time=58.49 x[1] = 10.5092 1.821 h = 0.001 0.003 y[1] (numeric) = -4.92036491388 0.207028402829 y[1] (closed_form) = -4.92036459033 0.207037648122 absolute error = 9.251e-06 relative error = 0.0001878 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = -4.92046459563 0.207452311979 y[1] (closed_form) = -4.9204643838 0.207461613512 absolute error = 9.304e-06 relative error = 0.0001889 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5103 1.828 h = 0.003 0.006 y[1] (numeric) = -4.9207426541 0.207928622698 y[1] (closed_form) = -4.92074253228 0.207937867438 absolute error = 9.246e-06 relative error = 0.0001877 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.64 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = -4.92082656467 0.208850167122 y[1] (closed_form) = -4.92082644038 0.2088598791 absolute error = 9.713e-06 relative error = 0.0001972 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 0.5 0 NO 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=4861.7MB, alloc=52.3MB, time=59.04 x[1] = 10.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = -4.92117917892 0.2094449182 y[1] (closed_form) = -4.92117900439 0.209454331162 absolute error = 9.415e-06 relative error = 0.0001911 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5135 1.842 h = 0.001 0.001 y[1] (numeric) = -4.9213866017 0.209804621331 y[1] (closed_form) = -4.92138631042 0.209814013133 absolute error = 9.396e-06 relative error = 0.0001908 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5145 1.843 h = 0.001 0.003 y[1] (numeric) = -4.92134225454 0.209995236687 y[1] (closed_form) = -4.92134190972 0.210004598628 absolute error = 9.368e-06 relative error = 0.0001902 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = -4.92144409381 0.21042097632 y[1] (closed_form) = -4.92144386053 0.21043039465 absolute error = 9.421e-06 relative error = 0.0001913 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 0.5 0 NO 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=4907.3MB, alloc=52.3MB, time=59.60 x[1] = 10.5156 1.85 h = 0.003 0.006 y[1] (numeric) = -4.92172543932 0.210898704457 y[1] (closed_form) = -4.92172529609 0.210908066181 absolute error = 9.363e-06 relative error = 0.0001901 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.65 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = -4.92181332799 0.211824742101 y[1] (closed_form) = -4.92181318151 0.211834570746 absolute error = 9.830e-06 relative error = 0.0001995 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = -4.92217005603 0.212421246912 y[1] (closed_form) = -4.92216985984 0.212430776658 absolute error = 9.532e-06 relative error = 0.0001935 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5188 1.864 h = 0.001 0.001 y[1] (numeric) = -4.92237993345 0.21278203642 y[1] (closed_form) = -4.92237962062 0.212791544826 absolute error = 9.514e-06 relative error = 0.0001931 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5198 1.865 h = 0.001 0.003 y[1] (numeric) = -4.92233608097 0.212973815659 y[1] (closed_form) = -4.92233571469 0.212983294136 absolute error = 9.486e-06 relative error = 0.0001925 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO 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=4952.8MB, alloc=52.3MB, time=60.15 x[1] = 10.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = -4.92244007328 0.213401388128 y[1] (closed_form) = -4.92243981837 0.213410923141 absolute error = 9.538e-06 relative error = 0.0001936 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5209 1.872 h = 0.003 0.006 y[1] (numeric) = -4.92272470129 0.213880538184 y[1] (closed_form) = -4.92272453646 0.213890016778 absolute error = 9.480e-06 relative error = 0.0001924 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = -4.92281655794 0.214811072632 y[1] (closed_form) = -4.9228163891 0.214821017827 absolute error = 9.947e-06 relative error = 0.0002019 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.524 1.883 h = 0.0001 0.003 y[1] (numeric) = -4.9231773941 0.215409336814 y[1] (closed_form) = -4.92317717608 0.21541898323 absolute error = 9.649e-06 relative error = 0.0001958 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.66 Order of pole (given) = 0.5 0 NO 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=4998.4MB, alloc=52.3MB, time=60.71 x[1] = 10.5241 1.886 h = 0.001 0.001 y[1] (numeric) = -4.92338972271 0.215771216037 y[1] (closed_form) = -4.92338938815 0.215780840934 absolute error = 9.631e-06 relative error = 0.0001954 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5251 1.887 h = 0.001 0.003 y[1] (numeric) = -4.92334636266 0.215964159196 y[1] (closed_form) = -4.92334597474 0.215973754096 absolute error = 9.603e-06 relative error = 0.0001949 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = -4.92345250353 0.216393566837 y[1] (closed_form) = -4.92345222681 0.216403218418 absolute error = 9.656e-06 relative error = 0.0001959 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5262 1.894 h = 0.003 0.006 y[1] (numeric) = -4.92374040946 0.216874143291 y[1] (closed_form) = -4.92374022286 0.21688373864 absolute error = 9.597e-06 relative error = 0.0001947 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = -4.92383622399 0.217809178088 y[1] (closed_form) = -4.92383603261 0.217819239718 absolute error = 1.006e-05 relative error = 0.0002042 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO 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=5044.0MB, alloc=52.3MB, time=61.26 x[1] = 10.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = -4.92420116259 0.218409207255 y[1] (closed_form) = -4.92420092256 0.218418970225 absolute error = 9.766e-06 relative error = 0.0001981 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5294 1.908 h = 0.001 0.001 y[1] (numeric) = -4.92441593894 0.218772179513 y[1] (closed_form) = -4.92441558249 0.218781920787 absolute error = 9.748e-06 relative error = 0.0001978 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = -4.92437306906 0.218966286623 y[1] (closed_form) = -4.92437265932 0.218975997831 absolute error = 9.720e-06 relative error = 0.0001972 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.67 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5305 1.913 h = 0.003 0.006 y[1] (numeric) = -4.92466365454 0.2194480278 y[1] (closed_form) = -4.92466349034 0.219457710608 absolute error = 9.684e-06 relative error = 0.0001965 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO 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=5089.6MB, alloc=52.3MB, time=61.82 x[1] = 10.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = -4.92476292145 0.220386892176 y[1] (closed_form) = -4.9247627518 0.220397040996 absolute error = 1.015e-05 relative error = 0.0002059 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = -4.92513140786 0.220988396281 y[1] (closed_form) = -4.92513119001 0.22099824654 absolute error = 9.853e-06 relative error = 0.0001998 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5337 1.927 h = 0.001 0.001 y[1] (numeric) = -4.92534830144 0.221352282934 y[1] (closed_form) = -4.92534796727 0.221362111341 absolute error = 9.834e-06 relative error = 0.0001995 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5347 1.928 h = 0.001 0.003 y[1] (numeric) = -4.92530586554 0.22154738615 y[1] (closed_form) = -4.92530547816 0.221557184432 absolute error = 9.806e-06 relative error = 0.0001989 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = -4.92541601437 0.221980189303 y[1] (closed_form) = -4.92541573788 0.22199004454 absolute error = 9.859e-06 relative error = 0.0002 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO 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=5135.1MB, alloc=52.3MB, time=62.37 x[1] = 10.5358 1.935 h = 0.003 0.006 y[1] (numeric) = -4.92571002472 0.222463392884 y[1] (closed_form) = -4.92570983841 0.222473192236 absolute error = 9.801e-06 relative error = 0.0001988 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.68 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = -4.92581323073 0.223406764225 y[1] (closed_form) = -4.92581303821 0.223417029264 absolute error = 1.027e-05 relative error = 0.0002082 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = -4.92618580906 0.224010043757 y[1] (closed_form) = -4.92618556887 0.224020010357 absolute error = 9.969e-06 relative error = 0.0002022 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.539 1.949 h = 0.001 0.001 y[1] (numeric) = -4.92640514398 0.224375029623 y[1] (closed_form) = -4.92640478757 0.224384974195 absolute error = 9.951e-06 relative error = 0.0002018 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.69 Order of pole (given) = 0.5 0 NO 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=5180.7MB, alloc=52.3MB, time=62.92 x[1] = 10.54 1.95 h = 0.001 0.003 y[1] (numeric) = -4.92636319405 0.224571296853 y[1] (closed_form) = -4.92636278452 0.224581211233 absolute error = 9.923e-06 relative error = 0.0002012 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.541 1.953 h = 0.0001 0.004 y[1] (numeric) = -4.92647547864 0.225005941813 y[1] (closed_form) = -4.92647517984 0.225015913291 absolute error = 9.976e-06 relative error = 0.0002023 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5411 1.957 h = 0.003 0.006 y[1] (numeric) = -4.92677275388 0.225490584546 y[1] (closed_form) = -4.92677254528 0.225500500326 absolute error = 9.918e-06 relative error = 0.0002011 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.69 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = -4.92687988889 0.226438466288 y[1] (closed_form) = -4.92687967332 0.226448847428 absolute error = 1.038e-05 relative error = 0.0002105 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 0 NO 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=5226.2MB, alloc=52.3MB, time=63.48 x[1] = 10.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = -4.92725655344 0.227043526784 y[1] (closed_form) = -4.92725629072 0.22705360961 absolute error = 1.009e-05 relative error = 0.0002045 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5443 1.971 h = 0.001 0.001 y[1] (numeric) = -4.92747832621 0.227409615139 y[1] (closed_form) = -4.9274779474 0.22741967576 absolute error = 1.007e-05 relative error = 0.0002041 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5453 1.972 h = 0.001 0.003 y[1] (numeric) = -4.92743686002 0.227607046393 y[1] (closed_form) = -4.92743642817 0.227617076755 absolute error = 1.004e-05 relative error = 0.0002035 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = -4.92755127588 0.228043535425 y[1] (closed_form) = -4.92755095458 0.228053623029 absolute error = 1.009e-05 relative error = 0.0002046 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5464 1.979 h = 0.003 0.006 y[1] (numeric) = -4.92785181142 0.228529621708 y[1] (closed_form) = -4.92785158036 0.228539653801 absolute error = 1.003e-05 relative error = 0.0002034 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.7 Order of pole (given) = 0.5 0 NO 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=5271.8MB, alloc=52.3MB, time=64.03 x[1] = 10.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = -4.92796286532 0.229482017249 y[1] (closed_form) = -4.92796262652 0.229492514373 absolute error = 1.050e-05 relative error = 0.0002128 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = -4.92834361037 0.23008886422 y[1] (closed_form) = -4.92834332495 0.230099063156 absolute error = 1.020e-05 relative error = 0.0002068 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5496 1.993 h = 0.001 0.001 y[1] (numeric) = -4.92856781753 0.230456058324 y[1] (closed_form) = -4.92856741613 0.23046623488 absolute error = 1.018e-05 relative error = 0.0002064 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5506 1.994 h = 0.001 0.003 y[1] (numeric) = -4.92852683281 0.230654653603 y[1] (closed_form) = -4.92852637846 0.230664799833 absolute error = 1.016e-05 relative error = 0.0002058 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO 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=5317.3MB, alloc=52.3MB, time=64.58 x[1] = 10.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = -4.92864337545 0.231092988956 y[1] (closed_form) = -4.92864303149 0.23110319257 absolute error = 1.021e-05 relative error = 0.0002069 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5517 2.001 h = 0.003 0.006 y[1] (numeric) = -4.92894716669 0.231580523166 y[1] (closed_form) = -4.928946913 0.231590671455 absolute error = 1.015e-05 relative error = 0.0002057 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = -4.92906212939 0.232537435868 y[1] (closed_form) = -4.92906186719 0.232548048856 absolute error = 1.062e-05 relative error = 0.0002151 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = -4.92944694921 0.233146074799 y[1] (closed_form) = -4.92944664091 0.233156389727 absolute error = 1.032e-05 relative error = 0.0002091 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.71 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5549 2.015 h = 0.001 0.001 y[1] (numeric) = -4.92967358726 0.233514377896 y[1] (closed_form) = -4.92967316311 0.233524670268 absolute error = 1.030e-05 relative error = 0.0002087 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO 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=5362.8MB, alloc=52.3MB, time=65.13 x[1] = 10.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = -4.92963308179 0.233714137193 y[1] (closed_form) = -4.92963260477 0.233724399174 absolute error = 1.027e-05 relative error = 0.0002082 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.556 2.02 h = 0.003 0.006 y[1] (numeric) = -4.9299395344 0.234202853691 y[1] (closed_form) = -4.92993930233 0.234213089328 absolute error = 1.024e-05 relative error = 0.0002074 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.559 2.026 h = 0.0001 0.005 y[1] (numeric) = -4.93005790743 0.235163610878 y[1] (closed_form) = -4.9300576662 0.235174310937 absolute error = 1.070e-05 relative error = 0.0002168 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = -4.93044625152 0.235773748195 y[1] (closed_form) = -4.93044596464 0.235784150298 absolute error = 1.041e-05 relative error = 0.0002108 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO 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=5408.4MB, alloc=52.3MB, time=65.69 x[1] = 10.5592 2.034 h = 0.001 0.001 y[1] (numeric) = -4.93067499248 0.236142979561 y[1] (closed_form) = -4.93067458984 0.236153358957 absolute error = 1.039e-05 relative error = 0.0002104 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5602 2.035 h = 0.001 0.003 y[1] (numeric) = -4.93063491159 0.236343735124 y[1] (closed_form) = -4.93063445616 0.236354084071 absolute error = 1.036e-05 relative error = 0.0002099 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = -4.93075542178 0.236785486763 y[1] (closed_form) = -4.93075507642 0.23679589336 absolute error = 1.041e-05 relative error = 0.0002109 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5613 2.042 h = 0.003 0.006 y[1] (numeric) = -4.93106527622 0.237275688155 y[1] (closed_form) = -4.93106502118 0.237286039772 absolute error = 1.035e-05 relative error = 0.0002097 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = -4.93118753929 0.238240968774 y[1] (closed_form) = -4.93118727434 0.238251784479 absolute error = 1.082e-05 relative error = 0.0002191 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO 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=5454.1MB, alloc=52.3MB, time=66.24 x[1] = 10.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = -4.93157994753 0.238852908255 y[1] (closed_form) = -4.93157963745 0.238863426135 absolute error = 1.052e-05 relative error = 0.0002131 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5645 2.056 h = 0.001 0.001 y[1] (numeric) = -4.93181111293 0.23922325465 y[1] (closed_form) = -4.93181068721 0.239233749648 absolute error = 1.050e-05 relative error = 0.0002127 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5655 2.057 h = 0.001 0.003 y[1] (numeric) = -4.93177150712 0.239425174227 y[1] (closed_form) = -4.93177102868 0.23943563871 absolute error = 1.048e-05 relative error = 0.0002122 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = -4.93189413127 0.239868778574 y[1] (closed_form) = -4.93189376274 0.239879300848 absolute error = 1.053e-05 relative error = 0.0002132 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO 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=5499.7MB, alloc=52.3MB, time=66.79 x[1] = 10.5666 2.064 h = 0.003 0.006 y[1] (numeric) = -4.93220722825 0.240360440353 y[1] (closed_form) = -4.93220695007 0.240370907834 absolute error = 1.047e-05 relative error = 0.0002121 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = -4.93233337127 0.241330247658 y[1] (closed_form) = -4.93233308242 0.241341178889 absolute error = 1.094e-05 relative error = 0.0002214 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = -4.93272983791 0.241943994714 y[1] (closed_form) = -4.93272950445 0.241954628251 absolute error = 1.064e-05 relative error = 0.0002154 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5698 2.078 h = 0.001 0.001 y[1] (numeric) = -4.93296342425 0.242315459334 y[1] (closed_form) = -4.93296297526 0.242326069817 absolute error = 1.062e-05 relative error = 0.000215 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.74 Order of pole (given) = 0.5 0 NO 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=5545.3MB, alloc=52.3MB, time=67.35 x[1] = 10.5708 2.079 h = 0.001 0.003 y[1] (numeric) = -4.93292429128 0.242518542899 y[1] (closed_form) = -4.93292378967 0.242529122802 absolute error = 1.059e-05 relative error = 0.0002145 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = -4.9330490249 0.242964002134 y[1] (closed_form) = -4.93304863302 0.242974639967 absolute error = 1.065e-05 relative error = 0.0002155 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5719 2.086 h = 0.003 0.006 y[1] (numeric) = -4.93336535979 0.243457128597 y[1] (closed_form) = -4.93336505829 0.243467711822 absolute error = 1.059e-05 relative error = 0.0002143 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.74 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = -4.93349537266 0.244431465802 y[1] (closed_form) = -4.93349505975 0.244442512438 absolute error = 1.105e-05 relative error = 0.0002237 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.575 2.097 h = 0.0001 0.003 y[1] (numeric) = -4.93389589194 0.245047025815 y[1] (closed_form) = -4.93389553493 0.245057774892 absolute error = 1.076e-05 relative error = 0.0002177 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 0.5 0 NO 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=5590.8MB, alloc=52.3MB, time=67.90 x[1] = 10.5751 2.1 h = 0.001 0.001 y[1] (numeric) = -4.93413189571 0.245419611844 y[1] (closed_form) = -4.93413142329 0.245430337694 absolute error = 1.074e-05 relative error = 0.0002173 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5761 2.101 h = 0.001 0.003 y[1] (numeric) = -4.93409323335 0.245623859363 y[1] (closed_form) = -4.9340927084 0.245634554568 absolute error = 1.071e-05 relative error = 0.0002168 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = -4.93422007194 0.246071175646 y[1] (closed_form) = -4.93421965655 0.24608192892 absolute error = 1.076e-05 relative error = 0.0002178 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5772 2.108 h = 0.003 0.006 y[1] (numeric) = -4.93453964011 0.246565771068 y[1] (closed_form) = -4.93453931512 0.24657646992 absolute error = 1.070e-05 relative error = 0.0002166 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.75 Order of pole (given) = 0.5 0 NO 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=5636.4MB, alloc=52.3MB, time=68.46 x[1] = 10.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = -4.93467351275 0.247544641351 y[1] (closed_form) = -4.93467317561 0.247555803273 absolute error = 1.117e-05 relative error = 0.000226 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = -4.93507807889 0.248162019678 y[1] (closed_form) = -4.93507769816 0.248172884176 absolute error = 1.087e-05 relative error = 0.00022 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5804 2.122 h = 0.001 0.001 y[1] (numeric) = -4.93531649658 0.248535730283 y[1] (closed_form) = -4.93531600056 0.248546571381 absolute error = 1.085e-05 relative error = 0.0002196 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = -4.9352783026 0.248741141714 y[1] (closed_form) = -4.93527775413 0.248751952104 absolute error = 1.082e-05 relative error = 0.000219 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5815 2.127 h = 0.003 0.006 y[1] (numeric) = -4.93560051381 0.249236936583 y[1] (closed_form) = -4.93560020967 0.249247722661 absolute error = 1.079e-05 relative error = 0.0002183 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO 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=5681.9MB, alloc=52.3MB, time=69.01 x[1] = 10.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = -4.93573775478 0.25021966549 y[1] (closed_form) = -4.93573743785 0.250230914352 absolute error = 1.125e-05 relative error = 0.0002277 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = -4.93614582143 0.25083856512 y[1] (closed_form) = -4.93614546136 0.250849516668 absolute error = 1.096e-05 relative error = 0.0002217 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.76 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5847 2.141 h = 0.001 0.001 y[1] (numeric) = -4.93638632758 0.251213217548 y[1] (closed_form) = -4.93638585231 0.251224145548 absolute error = 1.094e-05 relative error = 0.0002213 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5857 2.142 h = 0.001 0.003 y[1] (numeric) = -4.93634854885 0.251419625254 y[1] (closed_form) = -4.93634802121 0.251430522489 absolute error = 1.091e-05 relative error = 0.0002207 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO 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=5727.6MB, alloc=52.3MB, time=69.56 x[1] = 10.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = -4.93647931453 0.251870377817 y[1] (closed_form) = -4.93647889613 0.251881333379 absolute error = 1.096e-05 relative error = 0.0002218 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5868 2.149 h = 0.003 0.006 y[1] (numeric) = -4.93680490431 0.252367679549 y[1] (closed_form) = -4.93680457637 0.252378581034 absolute error = 1.091e-05 relative error = 0.0002206 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = -4.93694598634 0.253354947467 y[1] (closed_form) = -4.93694564484 0.253366311392 absolute error = 1.137e-05 relative error = 0.00023 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = -4.93735808914 0.253975675379 y[1] (closed_form) = -4.93735770502 0.253986742128 absolute error = 1.107e-05 relative error = 0.000224 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.59 2.163 h = 0.001 0.001 y[1] (numeric) = -4.93760100269 0.254351458274 y[1] (closed_form) = -4.9376005035 0.254362501304 absolute error = 1.105e-05 relative error = 0.0002236 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.77 Order of pole (given) = 0.5 0 NO 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=5773.1MB, alloc=52.3MB, time=70.11 x[1] = 10.591 2.164 h = 0.001 0.003 y[1] (numeric) = -4.93756368821 0.254559029823 y[1] (closed_form) = -4.93756313674 0.254570042024 absolute error = 1.103e-05 relative error = 0.000223 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.592 2.167 h = 0.0001 0.004 y[1] (numeric) = -4.93769654603 0.255011645576 y[1] (closed_form) = -4.93769610362 0.255022716241 absolute error = 1.108e-05 relative error = 0.0002241 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5921 2.171 h = 0.003 0.006 y[1] (numeric) = -4.93802535582 0.255510428435 y[1] (closed_form) = -4.93802500389 0.255521445208 absolute error = 1.102e-05 relative error = 0.0002229 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = -4.93817026882 0.256502238435 y[1] (closed_form) = -4.9381699026 0.2565137173 absolute error = 1.148e-05 relative error = 0.0002323 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO 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=5818.6MB, alloc=52.3MB, time=70.66 x[1] = 10.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = -4.93858640197 0.25712479991 y[1] (closed_form) = -4.93858599364 0.25713598174 absolute error = 1.119e-05 relative error = 0.0002263 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5953 2.185 h = 0.001 0.001 y[1] (numeric) = -4.93883171941 0.257501716395 y[1] (closed_form) = -4.93883119612 0.257512874335 absolute error = 1.117e-05 relative error = 0.0002259 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5963 2.186 h = 0.001 0.003 y[1] (numeric) = -4.93879486696 0.257710451725 y[1] (closed_form) = -4.93879429147 0.257721578772 absolute error = 1.114e-05 relative error = 0.0002253 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = -4.93892981241 0.25816493276 y[1] (closed_form) = -4.93892934583 0.258176118408 absolute error = 1.120e-05 relative error = 0.0002264 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.79 Order of pole (given) = 0.5 0 NO 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=5864.2MB, alloc=52.3MB, time=71.22 x[1] = 10.5974 2.193 h = 0.003 0.006 y[1] (numeric) = -4.93926183755 0.25866520094 y[1] (closed_form) = -4.93926146147 0.25867633288 absolute error = 1.114e-05 relative error = 0.0002252 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = -4.93941057145 0.259661556056 y[1] (closed_form) = -4.93941018033 0.25967314974 absolute error = 1.160e-05 relative error = 0.0002345 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = -4.93983072913 0.26028595635 y[1] (closed_form) = -4.93983029642 0.26029725314 absolute error = 1.131e-05 relative error = 0.0002285 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6006 2.207 h = 0.001 0.001 y[1] (numeric) = -4.94007844692 0.26066400953 y[1] (closed_form) = -4.94007789937 0.260675282259 absolute error = 1.129e-05 relative error = 0.0002281 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.79 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6016 2.208 h = 0.001 0.003 y[1] (numeric) = -4.94004205429 0.260873908571 y[1] (closed_form) = -4.94004145463 0.260885150346 absolute error = 1.126e-05 relative error = 0.0002276 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.79 Order of pole (given) = 0.5 0 NO 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=5909.8MB, alloc=52.3MB, time=71.77 x[1] = 10.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = -4.94017908289 0.261330256966 y[1] (closed_form) = -4.94017859195 0.261341557476 absolute error = 1.131e-05 relative error = 0.0002286 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6027 2.215 h = 0.003 0.006 y[1] (numeric) = -4.94051431869 0.261832014638 y[1] (closed_form) = -4.94051391829 0.261843261625 absolute error = 1.125e-05 relative error = 0.0002275 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = -4.94066686342 0.262832917867 y[1] (closed_form) = -4.94066644725 0.262844626248 absolute error = 1.172e-05 relative error = 0.0002368 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = -4.94109103982 0.26345916221 y[1] (closed_form) = -4.94109058256 0.263470573839 absolute error = 1.142e-05 relative error = 0.0002308 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO 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=5955.3MB, alloc=52.3MB, time=72.32 x[1] = 10.6059 2.229 h = 0.001 0.001 y[1] (numeric) = -4.94134115443 0.263838355174 y[1] (closed_form) = -4.94134058245 0.263849742574 absolute error = 1.140e-05 relative error = 0.0002304 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = -4.94130521939 0.26404941785 y[1] (closed_form) = -4.94130459539 0.264060774233 absolute error = 1.137e-05 relative error = 0.0002298 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.607 2.234 h = 0.003 0.006 y[1] (numeric) = -4.94164307976 0.264552391722 y[1] (closed_form) = -4.94164269944 0.264563725802 absolute error = 1.134e-05 relative error = 0.0002292 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.61 2.24 h = 0.0001 0.005 y[1] (numeric) = -4.94179895089 0.265557166954 y[1] (closed_form) = -4.94179855416 0.265568962134 absolute error = 1.180e-05 relative error = 0.0002385 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = -4.94222660385 0.266184954985 y[1] (closed_form) = -4.94222616648 0.26619645353 absolute error = 1.151e-05 relative error = 0.0002325 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.81 Order of pole (given) = 0.5 0 NO 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=6000.8MB, alloc=52.3MB, time=72.87 x[1] = 10.6102 2.248 h = 0.001 0.001 y[1] (numeric) = -4.94247879234 0.266565103006 y[1] (closed_form) = -4.94247824036 0.266576577175 absolute error = 1.149e-05 relative error = 0.0002321 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6112 2.249 h = 0.001 0.003 y[1] (numeric) = -4.94244326329 0.266777161819 y[1] (closed_form) = -4.94244265936 0.266788604916 absolute error = 1.146e-05 relative error = 0.0002315 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = -4.94258417847 0.267236965712 y[1] (closed_form) = -4.94258368294 0.267248467797 absolute error = 1.151e-05 relative error = 0.0002326 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.81 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6123 2.256 h = 0.003 0.006 y[1] (numeric) = -4.94292539398 0.267741467902 y[1] (closed_form) = -4.94292498902 0.267752916807 absolute error = 1.146e-05 relative error = 0.0002314 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.81 Order of pole (given) = 0.5 0 NO 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=6046.3MB, alloc=52.3MB, time=73.43 x[1] = 10.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = -4.94308505725 0.268750796846 y[1] (closed_form) = -4.94308463515 0.268762706496 absolute error = 1.192e-05 relative error = 0.0002407 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = -4.94351671814 0.269380438657 y[1] (closed_form) = -4.9435162559 0.269392051816 absolute error = 1.162e-05 relative error = 0.0002348 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6155 2.27 h = 0.001 0.001 y[1] (numeric) = -4.94377129688 0.26976173221 y[1] (closed_form) = -4.94377072016 0.269773320827 absolute error = 1.160e-05 relative error = 0.0002343 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6165 2.271 h = 0.001 0.003 y[1] (numeric) = -4.94373622133 0.269974954525 y[1] (closed_form) = -4.94373559274 0.269986512008 absolute error = 1.157e-05 relative error = 0.0002338 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = -4.94387920681 0.270436631674 y[1] (closed_form) = -4.94387868645 0.270448248278 absolute error = 1.163e-05 relative error = 0.0002349 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.82 Order of pole (given) = 0.5 0 NO 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=6091.9MB, alloc=52.3MB, time=73.98 x[1] = 10.6176 2.278 h = 0.003 0.006 y[1] (numeric) = -4.94422361962 0.270942635233 y[1] (closed_form) = -4.94422318986 0.27095419884 absolute error = 1.157e-05 relative error = 0.0002337 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.82 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = -4.94438706499 0.271956520779 y[1] (closed_form) = -4.94438661735 0.271968544777 absolute error = 1.203e-05 relative error = 0.000243 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = -4.94482272796 0.272588021524 y[1] (closed_form) = -4.94482224068 0.272599749177 absolute error = 1.174e-05 relative error = 0.000237 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6208 2.292 h = 0.001 0.001 y[1] (numeric) = -4.94507969341 0.272970463655 y[1] (closed_form) = -4.94507909177 0.272982166598 absolute error = 1.172e-05 relative error = 0.0002366 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO 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=6137.4MB, alloc=52.3MB, time=74.53 x[1] = 10.6218 2.293 h = 0.001 0.003 y[1] (numeric) = -4.94504506915 0.273184849375 y[1] (closed_form) = -4.94504441573 0.273196521123 absolute error = 1.169e-05 relative error = 0.000236 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = -4.94519012043 0.273648401789 y[1] (closed_form) = -4.94518957508 0.27366013279 absolute error = 1.174e-05 relative error = 0.0002371 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6229 2.3 h = 0.003 0.006 y[1] (numeric) = -4.94553772585 0.274155910807 y[1] (closed_form) = -4.9455372711 0.274167588996 absolute error = 1.169e-05 relative error = 0.000236 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = -4.94570494326 0.275174355812 y[1] (closed_form) = -4.94570446991 0.275186494033 absolute error = 1.215e-05 relative error = 0.0002452 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.83 Order of pole (given) = 0.5 0 NO 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=6183.0MB, alloc=52.3MB, time=75.08 x[1] = 10.626 2.311 h = 0.0001 0.003 y[1] (numeric) = -4.94614460245 0.275807720619 y[1] (closed_form) = -4.94614408998 0.275819562643 absolute error = 1.185e-05 relative error = 0.0002393 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6261 2.314 h = 0.001 0.001 y[1] (numeric) = -4.94640395105 0.276191314356 y[1] (closed_form) = -4.94640332433 0.276203131504 absolute error = 1.183e-05 relative error = 0.0002389 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6271 2.315 h = 0.001 0.003 y[1] (numeric) = -4.94636977589 0.276406863378 y[1] (closed_form) = -4.94636909748 0.276418649269 absolute error = 1.181e-05 relative error = 0.0002383 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = -4.94651688847 0.276872293048 y[1] (closed_form) = -4.94651631795 0.276884138324 absolute error = 1.186e-05 relative error = 0.0002394 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6282 2.322 h = 0.003 0.006 y[1] (numeric) = -4.94686768179 0.277381311597 y[1] (closed_form) = -4.9468672019 0.277393104244 absolute error = 1.180e-05 relative error = 0.0002382 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO 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=6228.7MB, alloc=52.3MB, time=75.64 x[1] = 10.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = -4.9470386612 0.278404318878 y[1] (closed_form) = -4.94703816197 0.278416571198 absolute error = 1.226e-05 relative error = 0.0002475 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = -4.94748231076 0.279039552849 y[1] (closed_form) = -4.94748177291 0.279051509122 absolute error = 1.197e-05 relative error = 0.0002415 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.84 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6314 2.336 h = 0.001 0.001 y[1] (numeric) = -4.94774403894 0.279424301206 y[1] (closed_form) = -4.94774338697 0.279436232436 absolute error = 1.195e-05 relative error = 0.0002411 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = -4.94771031068 0.279641013419 y[1] (closed_form) = -4.94770960711 0.279652913332 absolute error = 1.192e-05 relative error = 0.0002405 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO 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=6274.2MB, alloc=52.3MB, time=76.19 x[1] = 10.6325 2.341 h = 0.003 0.006 y[1] (numeric) = -4.94806370994 0.280151264513 y[1] (closed_form) = -4.94806324938 0.280163144109 absolute error = 1.189e-05 relative error = 0.0002399 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = -4.94823797389 0.281178156429 y[1] (closed_form) = -4.94823749338 0.281190495395 absolute error = 1.235e-05 relative error = 0.0002491 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = -4.94868507588 0.281814955942 y[1] (closed_form) = -4.94868455718 0.281826998984 absolute error = 1.205e-05 relative error = 0.0002432 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6357 2.355 h = 0.001 0.001 y[1] (numeric) = -4.94894886328 0.28220067227 y[1] (closed_form) = -4.94894823056 0.282212690126 absolute error = 1.203e-05 relative error = 0.0002428 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6367 2.356 h = 0.001 0.003 y[1] (numeric) = -4.9489155318 0.282418380338 y[1] (closed_form) = -4.94891484755 0.282430366824 absolute error = 1.201e-05 relative error = 0.0002422 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.85 Order of pole (given) = 0.5 0 NO 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=6319.8MB, alloc=52.3MB, time=76.75 x[1] = 10.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = -4.94906649043 0.282887283957 y[1] (closed_form) = -4.94906591375 0.282899330073 absolute error = 1.206e-05 relative error = 0.0002433 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6378 2.363 h = 0.003 0.006 y[1] (numeric) = -4.94942322123 0.283399084309 y[1] (closed_form) = -4.94942273522 0.283411078137 absolute error = 1.200e-05 relative error = 0.0002421 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = -4.94960122854 0.284430543769 y[1] (closed_form) = -4.94960072184 0.284442996605 absolute error = 1.246e-05 relative error = 0.0002514 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = -4.95005231002 0.28506922194 y[1] (closed_form) = -4.95005176564 0.285081379005 absolute error = 1.217e-05 relative error = 0.0002454 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.86 Order of pole (given) = 0.5 0 NO 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=6365.4MB, alloc=52.3MB, time=77.31 x[1] = 10.641 2.377 h = 0.001 0.001 y[1] (numeric) = -4.9503184704 0.285456098494 y[1] (closed_form) = -4.95031781213 0.285468230207 absolute error = 1.215e-05 relative error = 0.000245 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.642 2.378 h = 0.001 0.003 y[1] (numeric) = -4.95028558175 0.285674969557 y[1] (closed_form) = -4.95028487203 0.285687069839 absolute error = 1.212e-05 relative error = 0.0002444 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.86 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.643 2.381 h = 0.0001 0.004 y[1] (numeric) = -4.95043858884 0.286145756087 y[1] (closed_form) = -4.95043798652 0.286157916129 absolute error = 1.217e-05 relative error = 0.0002455 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6431 2.385 h = 0.003 0.006 y[1] (numeric) = -4.95079849408 0.286659077554 y[1] (closed_form) = -4.95079798245 0.286671185492 absolute error = 1.212e-05 relative error = 0.0002444 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = -4.95098023471 0.287695107272 y[1] (closed_form) = -4.95097970168 0.287707673853 absolute error = 1.258e-05 relative error = 0.0002536 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO 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=6410.9MB, alloc=52.3MB, time=77.87 x[1] = 10.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = -4.95143528981 0.28833566913 y[1] (closed_form) = -4.95143471959 0.288347940092 absolute error = 1.228e-05 relative error = 0.0002477 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6463 2.399 h = 0.001 0.001 y[1] (numeric) = -4.95170381961 0.288723708878 y[1] (closed_form) = -4.95170313561 0.288735954324 absolute error = 1.226e-05 relative error = 0.0002473 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6473 2.4 h = 0.001 0.003 y[1] (numeric) = -4.95167137159 0.288943742805 y[1] (closed_form) = -4.95167063624 0.288955956761 absolute error = 1.224e-05 relative error = 0.0002467 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = -4.95182642265 0.289416414171 y[1] (closed_form) = -4.95182579452 0.289428688016 absolute error = 1.229e-05 relative error = 0.0002478 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.87 Order of pole (given) = 0.5 0 NO 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=6456.4MB, alloc=52.3MB, time=78.42 x[1] = 10.6484 2.407 h = 0.003 0.006 y[1] (numeric) = -4.9521894976 0.289931260742 y[1] (closed_form) = -4.95218896018 0.289943482666 absolute error = 1.223e-05 relative error = 0.0002466 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = -4.95237496153 0.290971863398 y[1] (closed_form) = -4.95237440199 0.290984543598 absolute error = 1.269e-05 relative error = 0.0002559 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = -4.95283398435 0.291614313943 y[1] (closed_form) = -4.95283338813 0.291626698679 absolute error = 1.240e-05 relative error = 0.0002499 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6516 2.421 h = 0.001 0.001 y[1] (numeric) = -4.95310487998 0.292003519836 y[1] (closed_form) = -4.9531041701 0.292015878893 absolute error = 1.238e-05 relative error = 0.0002495 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO 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=6502.0MB, alloc=52.3MB, time=78.98 x[1] = 10.6526 2.422 h = 0.001 0.003 y[1] (numeric) = -4.95307287042 0.292224716491 y[1] (closed_form) = -4.95307210928 0.292237043998 absolute error = 1.235e-05 relative error = 0.0002489 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = -4.95322996094 0.292699274601 y[1] (closed_form) = -4.95322930685 0.292711662125 absolute error = 1.240e-05 relative error = 0.00025 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6537 2.429 h = 0.003 0.006 y[1] (numeric) = -4.95359620087 0.293215650245 y[1] (closed_form) = -4.95359563749 0.29322798603 absolute error = 1.235e-05 relative error = 0.0002489 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = -4.95378537808 0.29426082848 y[1] (closed_form) = -4.95378479187 0.294273622175 absolute error = 1.281e-05 relative error = 0.0002581 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = -4.95424836272 0.294905172687 y[1] (closed_form) = -4.95424774033 0.294917671073 absolute error = 1.251e-05 relative error = 0.0002521 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.89 Order of pole (given) = 0.5 0 NO 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=6547.6MB, alloc=52.3MB, time=79.53 x[1] = 10.6569 2.443 h = 0.001 0.001 y[1] (numeric) = -4.9545216206 0.295295547664 y[1] (closed_form) = -4.95452088468 0.295308020207 absolute error = 1.249e-05 relative error = 0.0002517 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = -4.95449004733 0.295517906903 y[1] (closed_form) = -4.95448926023 0.295530347838 absolute error = 1.247e-05 relative error = 0.0002512 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.658 2.448 h = 0.003 0.006 y[1] (numeric) = -4.95485887446 0.296035531034 y[1] (closed_form) = -4.95485832968 0.296047953612 absolute error = 1.243e-05 relative error = 0.0002505 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.89 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.661 2.454 h = 0.0001 0.005 y[1] (numeric) = -4.95505129446 0.297084605795 y[1] (closed_form) = -4.95505072623 0.297097485972 absolute error = 1.289e-05 relative error = 0.0002597 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 0 NO 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=6593.1MB, alloc=52.3MB, time=80.09 x[1] = 10.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = -4.95551770723 0.29773053687 y[1] (closed_form) = -4.95551710324 0.297743121868 absolute error = 1.260e-05 relative error = 0.0002538 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6612 2.462 h = 0.001 0.001 y[1] (numeric) = -4.95579300955 0.298121892412 y[1] (closed_form) = -4.95579229213 0.298134451426 absolute error = 1.258e-05 relative error = 0.0002534 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6622 2.463 h = 0.001 0.003 y[1] (numeric) = -4.95576182392 0.298345247083 y[1] (closed_form) = -4.9557610554 0.298357774438 absolute error = 1.255e-05 relative error = 0.0002528 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = -4.95592271996 0.298823296833 y[1] (closed_form) = -4.95592205817 0.298835884443 absolute error = 1.260e-05 relative error = 0.0002539 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6633 2.47 h = 0.003 0.006 y[1] (numeric) = -4.95629485486 0.299342490647 y[1] (closed_form) = -4.95629428383 0.299355026857 absolute error = 1.255e-05 relative error = 0.0002527 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.9 Order of pole (given) = 0.5 0 NO 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=6638.7MB, alloc=52.3MB, time=80.64 x[1] = 10.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = -4.95649096956 0.30039614593 y[1] (closed_form) = -4.95649037435 0.300409139368 absolute error = 1.301e-05 relative error = 0.0002619 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = -4.95696133321 0.301043979926 y[1] (closed_form) = -4.95696070274 0.301056678343 absolute error = 1.271e-05 relative error = 0.000256 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6665 2.484 h = 0.001 0.001 y[1] (numeric) = -4.95723899114 0.301436510014 y[1] (closed_form) = -4.95723824737 0.301449182287 absolute error = 1.269e-05 relative error = 0.0002556 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6675 2.485 h = 0.001 0.003 y[1] (numeric) = -4.95720823775 0.30166102701 y[1] (closed_form) = -4.95720744297 0.301673667565 absolute error = 1.267e-05 relative error = 0.000255 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.91 Order of pole (given) = 0.5 0 NO 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=6684.3MB, alloc=52.3MB, time=81.20 x[1] = 10.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = -4.95737116041 0.30214096892 y[1] (closed_form) = -4.95737047218 0.302153669855 absolute error = 1.272e-05 relative error = 0.0002561 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6686 2.492 h = 0.003 0.006 y[1] (numeric) = -4.95774644674 0.302661703101 y[1] (closed_form) = -4.95774584929 0.302674352819 absolute error = 1.266e-05 relative error = 0.000255 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.91 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = -4.95794624613 0.303719941446 y[1] (closed_form) = -4.95794562379 0.303733048018 absolute error = 1.312e-05 relative error = 0.0002642 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = -4.95842055475 0.304369683263 y[1] (closed_form) = -4.95841989765 0.304382494975 absolute error = 1.283e-05 relative error = 0.0002582 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6718 2.506 h = 0.001 0.001 y[1] (numeric) = -4.95870056469 0.30476339079 y[1] (closed_form) = -4.95869979441 0.304776176196 absolute error = 1.281e-05 relative error = 0.0002578 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6728 2.507 h = 0.001 0.003 y[1] (numeric) = -4.95867024137 0.304989069949 y[1] (closed_form) = -4.95866942017 0.305001823578 absolute error = 1.278e-05 relative error = 0.0002572 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = -4.95883518615 0.305470905859 y[1] (closed_form) = -4.95883447133 0.305483719995 absolute error = 1.283e-05 relative error = 0.0002583 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6739 2.514 h = 0.003 0.006 y[1] (numeric) = -4.95921361917 0.305993184295 y[1] (closed_form) = -4.95921299513 0.306005947395 absolute error = 1.278e-05 relative error = 0.0002572 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = -4.95941709325 0.307056008206 y[1] (closed_form) = -4.95941644362 0.307069227786 absolute error = 1.324e-05 relative error = 0.0002664 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.92 Order of pole (given) = 0.5 0 NO 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=6772.2MB, alloc=84.3MB, time=82.34 x[1] = 10.677 2.525 h = 0.0001 0.003 y[1] (numeric) = -4.95989534091 0.30770766272 y[1] (closed_form) = -4.95989465701 0.307720587601 absolute error = 1.294e-05 relative error = 0.0002605 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6771 2.528 h = 0.001 0.001 y[1] (numeric) = -4.96017769926 0.308102550562 y[1] (closed_form) = -4.96017690232 0.308115448975 absolute error = 1.292e-05 relative error = 0.00026 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6781 2.529 h = 0.001 0.003 y[1] (numeric) = -4.96014780385 0.308329391714 y[1] (closed_form) = -4.96014695607 0.308342258293 absolute error = 1.289e-05 relative error = 0.0002595 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = -4.96031476626 0.308813123449 y[1] (closed_form) = -4.96031402468 0.30882605066 absolute error = 1.295e-05 relative error = 0.0002605 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6792 2.536 h = 0.003 0.006 y[1] (numeric) = -4.96069634119 0.309336950007 y[1] (closed_form) = -4.96069569041 0.309349826364 absolute error = 1.289e-05 relative error = 0.0002594 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = -4.96090347998 0.310404361954 y[1] (closed_form) = -4.9609028029 0.310417694414 absolute error = 1.335e-05 relative error = 0.0002686 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = -4.96138566074 0.311057934013 y[1] (closed_form) = -4.96138494989 0.311070971936 absolute error = 1.306e-05 relative error = 0.0002627 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6824 2.55 h = 0.001 0.001 y[1] (numeric) = -4.96167036391 0.311454005029 y[1] (closed_form) = -4.96166954013 0.311467016325 absolute error = 1.304e-05 relative error = 0.0002622 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO 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=6860.3MB, alloc=84.3MB, time=83.46 x[1] = 10.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = -4.96164089425 0.311682007998 y[1] (closed_form) = -4.96164001972 0.311694987403 absolute error = 1.301e-05 relative error = 0.0002617 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6835 2.555 h = 0.003 0.006 y[1] (numeric) = -4.96202503752 0.312207098582 y[1] (closed_form) = -4.9620244046 0.312220061566 absolute error = 1.298e-05 relative error = 0.000261 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = -4.96223537747 0.313278418216 y[1] (closed_form) = -4.96223471764 0.313291836986 absolute error = 1.343e-05 relative error = 0.0002702 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = -4.96272096189 0.313933597942 y[1] (closed_form) = -4.96272026871 0.31394672231 absolute error = 1.314e-05 relative error = 0.0002643 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6867 2.569 h = 0.001 0.001 y[1] (numeric) = -4.96300769464 0.3143306618 y[1] (closed_form) = -4.96300688864 0.314343759403 absolute error = 1.312e-05 relative error = 0.0002639 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.94 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6877 2.57 h = 0.001 0.003 y[1] (numeric) = -4.96297860356 0.314559659641 y[1] (closed_form) = -4.96297774688 0.314572725302 absolute error = 1.309e-05 relative error = 0.0002633 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = -4.96314933098 0.315046899956 y[1] (closed_form) = -4.96314858019 0.31506002648 absolute error = 1.315e-05 relative error = 0.0002644 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6888 2.577 h = 0.003 0.006 y[1] (numeric) = -4.96353675812 0.315573580136 y[1] (closed_form) = -4.96353609815 0.315586656144 absolute error = 1.309e-05 relative error = 0.0002632 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = -4.96375074424 0.316649492425 y[1] (closed_form) = -4.96375005666 0.316663023839 absolute error = 1.355e-05 relative error = 0.0002724 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO 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=6948.2MB, alloc=84.3MB, time=84.59 x[1] = 10.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = -4.96424025076 0.31730659872 y[1] (closed_form) = -4.96423953033 0.317319835897 absolute error = 1.326e-05 relative error = 0.0002665 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.692 2.591 h = 0.001 0.001 y[1] (numeric) = -4.96452932165 0.317704851076 y[1] (closed_form) = -4.96452848852 0.317718061329 absolute error = 1.324e-05 relative error = 0.0002661 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.693 2.592 h = 0.001 0.003 y[1] (numeric) = -4.9645006523 0.317935010414 y[1] (closed_form) = -4.96449976859 0.31794818867 absolute error = 1.321e-05 relative error = 0.0002655 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.95 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.694 2.595 h = 0.0001 0.004 y[1] (numeric) = -4.96467338452 0.318424151735 y[1] (closed_form) = -4.96467260651 0.318437390976 absolute error = 1.326e-05 relative error = 0.0002666 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6941 2.599 h = 0.003 0.006 y[1] (numeric) = -4.96506393996 0.318952391041 y[1] (closed_form) = -4.96506325279 0.318965579947 absolute error = 1.321e-05 relative error = 0.0002654 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = -4.96528156228 0.320032898355 y[1] (closed_form) = -4.9652808468 0.320046542285 absolute error = 1.366e-05 relative error = 0.0002746 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = -4.96577498496 0.320691935993 y[1] (closed_form) = -4.96577423711 0.320705285853 absolute error = 1.337e-05 relative error = 0.0002687 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6973 2.613 h = 0.001 0.001 y[1] (numeric) = -4.96606639036 0.321091379663 y[1] (closed_form) = -4.96606552995 0.32110470244 absolute error = 1.335e-05 relative error = 0.0002683 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.96 Order of pole (given) = 0.5 0 NO 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=7036.1MB, alloc=84.3MB, time=85.73 x[1] = 10.6983 2.614 h = 0.001 0.003 y[1] (numeric) = -4.96603814061 0.321322700304 y[1] (closed_form) = -4.96603722969 0.321335991028 absolute error = 1.332e-05 relative error = 0.0002677 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.96 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = -4.96621287313 0.321813744388 y[1] (closed_form) = -4.96621206775 0.321827096219 absolute error = 1.338e-05 relative error = 0.0002688 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.6994 2.621 h = 0.003 0.006 y[1] (numeric) = -4.96660655207 0.322343546608 y[1] (closed_form) = -4.96660583755 0.322356848284 absolute error = 1.332e-05 relative error = 0.0002676 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = -4.96682780064 0.32342865128 y[1] (closed_form) = -4.96682705711 0.323442407598 absolute error = 1.378e-05 relative error = 0.0002768 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = -4.96732513351 0.32408962501 y[1] (closed_form) = -4.9673243581 0.324103087425 absolute error = 1.348e-05 relative error = 0.0002709 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7026 2.635 h = 0.001 0.001 y[1] (numeric) = -4.96761886982 0.324490262793 y[1] (closed_form) = -4.96761798197 0.324503697968 absolute error = 1.346e-05 relative error = 0.0002705 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7036 2.636 h = 0.001 0.003 y[1] (numeric) = -4.96759103751 0.324722744536 y[1] (closed_form) = -4.96759009924 0.324736147602 absolute error = 1.344e-05 relative error = 0.0002699 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = -4.96776776584 0.325215693127 y[1] (closed_form) = -4.96776693293 0.325229157421 absolute error = 1.349e-05 relative error = 0.000271 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7047 2.643 h = 0.003 0.006 y[1] (numeric) = -4.96816456351 0.325747062027 y[1] (closed_form) = -4.96816382147 0.325760476347 absolute error = 1.343e-05 relative error = 0.0002698 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO 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=7124.0MB, alloc=84.3MB, time=86.85 x[1] = 10.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = -4.96838942837 0.326836766355 y[1] (closed_form) = -4.96838865663 0.326850634932 absolute error = 1.389e-05 relative error = 0.000279 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = -4.96889066548 0.3274996809 y[1] (closed_form) = -4.96888986234 0.327513255743 absolute error = 1.360e-05 relative error = 0.0002731 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7079 2.657 h = 0.001 0.001 y[1] (numeric) = -4.96918672907 0.32790151558 y[1] (closed_form) = -4.96918581362 0.327915063026 absolute error = 1.358e-05 relative error = 0.0002727 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = -4.96915931206 0.328135158217 y[1] (closed_form) = -4.96915834628 0.328148673499 absolute error = 1.355e-05 relative error = 0.0002721 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.709 2.662 h = 0.003 0.006 y[1] (numeric) = -4.96955865913 0.328667806282 y[1] (closed_form) = -4.9695579342 0.328681307053 absolute error = 1.352e-05 relative error = 0.0002715 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.98 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.712 2.668 h = 0.0001 0.005 y[1] (numeric) = -4.96978668363 0.329761428739 y[1] (closed_form) = -4.96978592841 0.329775383442 absolute error = 1.398e-05 relative error = 0.0002806 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = -4.97029129978 0.330425971224 y[1] (closed_form) = -4.97029051358 0.330439632335 absolute error = 1.368e-05 relative error = 0.0002747 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7122 2.676 h = 0.001 0.001 y[1] (numeric) = -4.97058937803 0.330828810708 y[1] (closed_form) = -4.97058847962 0.330842444286 absolute error = 1.366e-05 relative error = 0.0002743 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.99 Order of pole (given) = 0.5 0 NO 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=7211.9MB, alloc=84.3MB, time=87.98 x[1] = 10.7132 2.677 h = 0.001 0.003 y[1] (numeric) = -4.9705623306 0.33106344752 y[1] (closed_form) = -4.97056138195 0.331077048885 absolute error = 1.363e-05 relative error = 0.0002737 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = -4.97074278347 0.331559920887 y[1] (closed_form) = -4.97074193984 0.331573583704 absolute error = 1.369e-05 relative error = 0.0002748 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7143 2.684 h = 0.003 0.006 y[1] (numeric) = -4.97114539035 0.332094177949 y[1] (closed_form) = -4.97114463762 0.332107791128 absolute error = 1.363e-05 relative error = 0.0002737 % Correct digits = 6 Radius of convergence (given) for eq 1 = 12.99 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = -4.97137701268 0.333192404365 y[1] (closed_form) = -4.97137622895 0.33320647109 absolute error = 1.409e-05 relative error = 0.0002828 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = -4.971885522 0.333858896456 y[1] (closed_form) = -4.97188470778 0.333872669758 absolute error = 1.380e-05 relative error = 0.0002769 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7175 2.698 h = 0.001 0.001 y[1] (numeric) = -4.97218592082 0.33426293802 y[1] (closed_form) = -4.97218499452 0.334276683634 absolute error = 1.378e-05 relative error = 0.0002765 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7185 2.699 h = 0.001 0.003 y[1] (numeric) = -4.97215928472 0.334498735348 y[1] (closed_form) = -4.97215830826 0.334512448694 absolute error = 1.375e-05 relative error = 0.0002759 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = -4.97234172057 0.334997118167 y[1] (closed_form) = -4.97234084898 0.335010893085 absolute error = 1.380e-05 relative error = 0.000277 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7196 2.706 h = 0.003 0.006 y[1] (numeric) = -4.9727474325 0.335532952626 y[1] (closed_form) = -4.9727466518 0.335546678085 absolute error = 1.375e-05 relative error = 0.0002758 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13 Order of pole (given) = 0.5 0 NO 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=7300.0MB, alloc=84.3MB, time=89.10 x[1] = 10.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = -4.97298264272 0.336635785202 y[1] (closed_form) = -4.97298183033 0.336649963816 absolute error = 1.420e-05 relative error = 0.0002849 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = -4.97349503923 0.337304231547 y[1] (closed_form) = -4.97349419684 0.337318116912 absolute error = 1.391e-05 relative error = 0.0002791 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7228 2.72 h = 0.001 0.001 y[1] (numeric) = -4.97379775499 0.337709477931 y[1] (closed_form) = -4.97379680064 0.337723335453 absolute error = 1.389e-05 relative error = 0.0002786 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7238 2.721 h = 0.001 0.003 y[1] (numeric) = -4.97377152808 0.337946435549 y[1] (closed_form) = -4.97377052367 0.337960260748 absolute error = 1.386e-05 relative error = 0.0002781 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = -4.97395594245 0.338446729498 y[1] (closed_form) = -4.97395504271 0.338460616388 absolute error = 1.392e-05 relative error = 0.0002791 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7249 2.728 h = 0.003 0.006 y[1] (numeric) = -4.9743647546 0.33898414504 y[1] (closed_form) = -4.97436394577 0.338997982651 absolute error = 1.386e-05 relative error = 0.000278 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = -4.97460354278 0.340091585939 y[1] (closed_form) = -4.97460270159 0.340105876314 absolute error = 1.432e-05 relative error = 0.0002871 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.728 2.739 h = 0.0001 0.003 y[1] (numeric) = -4.9751198205 0.340761991162 y[1] (closed_form) = -4.97511894978 0.340775988462 absolute error = 1.402e-05 relative error = 0.0002812 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7281 2.742 h = 0.001 0.001 y[1] (numeric) = -4.97542484957 0.34116844509 y[1] (closed_form) = -4.97542386702 0.341182414392 absolute error = 1.400e-05 relative error = 0.0002808 % Correct digits = 6 memory used=7387.3MB, alloc=340.3MB, time=90.25 Radius of convergence (given) for eq 1 = 13.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7291 2.743 h = 0.001 0.003 y[1] (numeric) = -4.97539902973 0.341406562765 y[1] (closed_form) = -4.97539799721 0.341420499691 absolute error = 1.398e-05 relative error = 0.0002802 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = -4.97558541812 0.341908769507 y[1] (closed_form) = -4.9755844901 0.341922768241 absolute error = 1.403e-05 relative error = 0.0002813 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7302 2.75 h = 0.003 0.006 y[1] (numeric) = -4.97599732569 0.342447769798 y[1] (closed_form) = -4.97599648859 0.342461719431 absolute error = 1.397e-05 relative error = 0.0002802 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = -4.97623968193 0.34355982115 y[1] (closed_form) = -4.97623881177 0.343574223157 absolute error = 1.443e-05 relative error = 0.0002893 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.03 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = -4.97675983485 0.344232189849 y[1] (closed_form) = -4.97675893565 0.344246298954 absolute error = 1.414e-05 relative error = 0.0002834 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.03 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7334 2.764 h = 0.001 0.001 y[1] (numeric) = -4.97706717359 0.34463985403 y[1] (closed_form) = -4.9770661627 0.344653934984 absolute error = 1.412e-05 relative error = 0.000283 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.03 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = -4.97704175871 0.344879131524 y[1] (closed_form) = -4.97704069791 0.344893180048 absolute error = 1.409e-05 relative error = 0.0002824 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.03 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7345 2.769 h = 0.003 0.006 y[1] (numeric) = -4.97745619663 0.345419425718 y[1] (closed_form) = -4.97745537592 0.345433461617 absolute error = 1.406e-05 relative error = 0.0002818 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.03 Order of pole (given) = 0.5 0 NO 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=7475.2MB, alloc=340.3MB, time=91.36 x[1] = 10.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = -4.97770167115 0.346535404934 y[1] (closed_form) = -4.9777008168 0.346549892875 absolute error = 1.451e-05 relative error = 0.0002909 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = -4.97822517838 0.347209421324 y[1] (closed_form) = -4.9782242954 0.34722361651 absolute error = 1.422e-05 relative error = 0.000285 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7377 2.783 h = 0.001 0.001 y[1] (numeric) = -4.97853451676 0.347618101955 y[1] (closed_form) = -4.9785335222 0.347632268856 absolute error = 1.420e-05 relative error = 0.0002846 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7387 2.784 h = 0.001 0.003 y[1] (numeric) = -4.97850946255 0.347858372796 y[1] (closed_form) = -4.97850841817 0.347872507221 absolute error = 1.417e-05 relative error = 0.000284 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = -4.97869953504 0.348364119775 y[1] (closed_form) = -4.97869859483 0.348378316225 absolute error = 1.423e-05 relative error = 0.0002851 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7398 2.791 h = 0.003 0.006 y[1] (numeric) = -4.97911720862 0.348906041862 y[1] (closed_form) = -4.97911635934 0.348920189546 absolute error = 1.417e-05 relative error = 0.000284 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.04 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = -4.97936623279 0.350026635523 y[1] (closed_form) = -4.97936534919 0.350041234853 absolute error = 1.463e-05 relative error = 0.000293 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = -4.97989360412 0.350702623946 y[1] (closed_form) = -4.97989269237 0.350716930699 absolute error = 1.434e-05 relative error = 0.0002872 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.743 2.805 h = 0.001 0.001 y[1] (numeric) = -4.98020524544 0.351112519873 y[1] (closed_form) = -4.98020422223 0.351126798189 absolute error = 1.431e-05 relative error = 0.0002867 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 0.5 0 NO 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=7563.2MB, alloc=340.3MB, time=92.47 x[1] = 10.744 2.806 h = 0.001 0.003 y[1] (numeric) = -4.98018059223 0.351353950098 y[1] (closed_form) = -4.98017951929 0.351368195884 absolute error = 1.429e-05 relative error = 0.0002861 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.745 2.809 h = 0.0001 0.004 y[1] (numeric) = -4.98037262594 0.351861614584 y[1] (closed_form) = -4.980371657 0.351875922511 absolute error = 1.434e-05 relative error = 0.0002872 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7451 2.813 h = 0.003 0.006 y[1] (numeric) = -4.98079338119 0.35240513185 y[1] (closed_form) = -4.9807925032 0.352419391189 absolute error = 1.429e-05 relative error = 0.0002861 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.05 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = -4.98104594512 0.353530341989 y[1] (closed_form) = -4.98104503213 0.353545052577 absolute error = 1.474e-05 relative error = 0.0002952 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = -4.98157717455 0.35420830697 y[1] (closed_form) = -4.98157623388 0.35422272516 absolute error = 1.445e-05 relative error = 0.0002893 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7483 2.827 h = 0.001 0.001 y[1] (numeric) = -4.98189111515 0.354619420858 y[1] (closed_form) = -4.98189006315 0.354633810459 absolute error = 1.443e-05 relative error = 0.0002889 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7493 2.828 h = 0.001 0.003 y[1] (numeric) = -4.98186686084 0.354862010209 y[1] (closed_form) = -4.9818657592 0.354876367227 absolute error = 1.440e-05 relative error = 0.0002883 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = -4.98206085129 0.3553715938 y[1] (closed_form) = -4.98205985348 0.355386013074 absolute error = 1.445e-05 relative error = 0.0002894 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.06 Order of pole (given) = 0.5 0 NO 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=7651.2MB, alloc=340.3MB, time=93.60 x[1] = 10.7504 2.835 h = 0.003 0.006 y[1] (numeric) = -4.98248468339 0.355916709832 y[1] (closed_form) = -4.98248377652 0.355931080697 absolute error = 1.440e-05 relative error = 0.0002883 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.06 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = -4.98274077719 0.357046538447 y[1] (closed_form) = -4.98273983465 0.357061360163 absolute error = 1.485e-05 relative error = 0.0002973 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = -4.9832758587 0.357726484485 y[1] (closed_form) = -4.98327488896 0.357741013982 absolute error = 1.456e-05 relative error = 0.0002915 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7536 2.849 h = 0.001 0.001 y[1] (numeric) = -4.98359209494 0.358138818983 y[1] (closed_form) = -4.983591014 0.35815331974 absolute error = 1.454e-05 relative error = 0.000291 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7546 2.85 h = 0.001 0.003 y[1] (numeric) = -4.98356823742 0.358382567197 y[1] (closed_form) = -4.98356710692 0.358397035319 absolute error = 1.451e-05 relative error = 0.0002905 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = -4.98376418014 0.358894071475 y[1] (closed_form) = -4.98376315329 0.358908601966 absolute error = 1.457e-05 relative error = 0.0002915 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7557 2.857 h = 0.003 0.006 y[1] (numeric) = -4.98419108425 0.359440789839 y[1] (closed_form) = -4.98419014836 0.359455272099 absolute error = 1.451e-05 relative error = 0.0002904 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.07 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = -4.98445069806 0.360575238896 y[1] (closed_form) = -4.98444972582 0.360590171608 absolute error = 1.496e-05 relative error = 0.0002994 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.08 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = -4.98498962562 0.361257170463 y[1] (closed_form) = -4.98498862666 0.361271811137 absolute error = 1.467e-05 relative error = 0.0002936 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.08 Order of pole (given) = 0.5 0 NO 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=7739.1MB, alloc=340.3MB, time=94.72 x[1] = 10.7589 2.871 h = 0.001 0.001 y[1] (numeric) = -4.98530815387 0.361670728205 y[1] (closed_form) = -4.98530704383 0.361685339988 absolute error = 1.465e-05 relative error = 0.0002932 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.08 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 10.7599 2.872 h = 0.001 0.003 y[1] (numeric) = -4.98528469102 0.361915635015 y[1] (closed_form) = -4.98528353152 0.36193021411 absolute error = 1.463e-05 relative error = 0.0002926 % Correct digits = 6 Radius of convergence (given) for eq 1 = 13.08 Order of pole (given) = 0.5 0 NO 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 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 754 Total Elapsed Time = 1 Minutes 34 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 1 Minutes 34 Seconds > quit memory used=7768.5MB, alloc=340.3MB, time=95.06