|\^/| 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(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) + > c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2)))); > end; exact_soln_y := proc(x) return c(10.0)*(c(0.1)*c(x) + c(0.2))*arctan(sqrt(c(0.1)*c(x) + c(0.2))) - c(10.0)*sqrt(c(0.1)*c(x) + c(0.2)) + c(10.0)*arctan(sqrt(c(0.1)*c(x) + c(0.2))) 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, 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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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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_a1, array_tmp4_a2, 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_a1, > array_tmp4_a2, > 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 arctan $eq_no = 1 > array_tmp4[1] := arctan(array_tmp3[1]); > array_tmp4_a1[1] := sin(array_tmp4[1]); > array_tmp4_a2[1] := cos(array_tmp4[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 arctan $eq_no = 1 > array_tmp4[2] := (ats(2,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(1,array_tmp4_a1,array_tmp4,2) - att(1,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]); > array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp4,1); > array_tmp4_a2[2] := neg(att(1,array_tmp4_a1,array_tmp4,1)); > #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 arctan $eq_no = 1 > array_tmp4[3] := (ats(3,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(2,array_tmp4_a1,array_tmp4,2) - att(2,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]); > array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp4,1); > array_tmp4_a2[3] := neg(att(2,array_tmp4_a1,array_tmp4,1)); > #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 arctan $eq_no = 1 > array_tmp4[4] := (ats(4,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(3,array_tmp4_a1,array_tmp4,2) - att(3,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]); > array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp4,1); > array_tmp4_a2[4] := neg(att(3,array_tmp4_a1,array_tmp4,1)); > #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 arctan $eq_no = 1 > array_tmp4[5] := (ats(5,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(4,array_tmp4_a1,array_tmp4,2) - att(4,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]); > array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp4,1); > array_tmp4_a2[5] := neg(att(4,array_tmp4_a1,array_tmp4,1)); > #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 atan $eq_no = 1 > array_tmp4[kkk] := (ats(kkk,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(kkk-1,array_tmp4_a1,array_tmp4,2) - att(kkk-1,array_tmp4_a2,array_tmp4,2))/(array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]); > array_tmp4_a1[kkk] := att(kkk-1,array_tmp4_a2,array_tmp4,1); > array_tmp4_a2[kkk] := neg(att(kkk-1,array_tmp4_a1,array_tmp4,1)); > #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_a1, array_tmp4_a2, 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] := arctan(array_tmp3[1]); array_tmp4_a1[1] := sin(array_tmp4[1]); array_tmp4_a2[1] := cos(array_tmp4[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] := (ats(2, array_tmp3, array_tmp4_a2, 2) - array_tmp3[1]*att(1, array_tmp4_a1, array_tmp4, 2) - att(1, array_tmp4_a2, array_tmp4, 2))/( array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]); array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp4, 1); array_tmp4_a2[2] := neg(att(1, array_tmp4_a1, array_tmp4, 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] := (ats(3, array_tmp3, array_tmp4_a2, 2) - array_tmp3[1]*att(2, array_tmp4_a1, array_tmp4, 2) - att(2, array_tmp4_a2, array_tmp4, 2))/( array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]); array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp4, 1); array_tmp4_a2[3] := neg(att(2, array_tmp4_a1, array_tmp4, 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] := (ats(4, array_tmp3, array_tmp4_a2, 2) - array_tmp3[1]*att(3, array_tmp4_a1, array_tmp4, 2) - att(3, array_tmp4_a2, array_tmp4, 2))/( array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]); array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp4, 1); array_tmp4_a2[4] := neg(att(3, array_tmp4_a1, array_tmp4, 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] := (ats(5, array_tmp3, array_tmp4_a2, 2) - array_tmp3[1]*att(4, array_tmp4_a1, array_tmp4, 2) - att(4, array_tmp4_a2, array_tmp4, 2))/( array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]); array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp4, 1); array_tmp4_a2[5] := neg(att(4, array_tmp4_a1, array_tmp4, 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] := (ats(kkk, array_tmp3, array_tmp4_a2, 2) - array_tmp3[1]*att(kkk - 1, array_tmp4_a1, array_tmp4, 2) - att(kkk - 1, array_tmp4_a2, array_tmp4, 2))/( array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]); array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp4, 1); array_tmp4_a2[kkk] := neg(att(kkk - 1, array_tmp4_a1, array_tmp4, 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_a1, > array_tmp4_a2, > 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_a1:= Array(0..(40),[]); > array_tmp4_a2:= 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_a1[term] := c(0.0); > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 40) do # do number 1 > array_tmp4_a2[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_a1); > zero_ats_ar(array_tmp4_a2); > 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/arctan_sqrtpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = arctan ( 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 := -1.1 + 0.1 * I;"); > omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_max_h :=c(0.01);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"glob_type_given_pole := 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,"#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(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +"); > omniout_str(ALWAYS,"c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));"); > 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 := -1.1 + 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_max_h :=c(0.01); > 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 ) = arctan ( 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,"2017-11-26T14:35:50-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"arctan_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = arctan ( 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,"arctan_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"arctan_sqrt maple results") > ; > logitem_str(html_log_file,"Good Accuracy - Wasn't for Real") > ; > 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_a1, array_tmp4_a2, 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_a1 := Array(0 .. 40, []); array_tmp4_a2 := 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_a1[term] := c(0.); term := term + 1 end do; term := 1; while term <= 40 do array_tmp4_a2[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_a1); zero_ats_ar(array_tmp4_a2); 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/arctan_sqrtpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = arctan ( 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 := -1.1 + 0.1 * I;"); omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_max_h :=c(0.01);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_type_given_pole := 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, "#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(10.0) * (c(0.1) * c(x) + c(0.2)) * arct\ an(sqrt ( c(0.1) * c(x) +"); omniout_str(ALWAYS, "c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2\ )) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));"); 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 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0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 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 := -1.1 + 0.1*I; x_end := 99.0 + 99.0*I; array_y_init[1] := exact_soln_y(x_start); glob_look_poles := true; glob_max_h := c(0.01); 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 ) = arctan ( 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, "2017-11-26T14:35:50-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "arctan_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = ar\ ctan ( 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, "arctan_sqrt diffeq.mxt"); logitem_str(html_log_file, "arctan_sqrt maple results"); logitem_str(html_log_file, "Good Accuracy - Wasn't for Real"); 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=3.8MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/arctan_sqrtpostcpx.cpx################# diff ( y , x , 1 ) = arctan ( 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 := -1.1 + 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_max_h :=c(0.01); 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(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) + c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2)))); end; next_delta := proc() global glob_nxt, x_delta; x_delta := [ 0.001 + 0.00004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.0001 + 0.004 * I, 0.003 + 0.006 * I, 0.0001 + 0.005 * I, 0.0001 + 0.003 * I, 0.001 + 0.001 * I, 0.001 + 0.003 * I, 0.000 + 0.000 * I ]; glob_nxt := glob_nxt + 1; it := x_delta[glob_nxt]; return it; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion memory used=34.7MB, alloc=40.3MB, time=0.45 x[1] = -1.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 0.176115197062 0.029162139066 y[1] (closed_form) = 0.176115197062 0.029162139066 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 0.9055 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0999 0.105 h = 0.0001 0.003 y[1] (numeric) = 0.176066556187 0.0306235825185 y[1] (closed_form) = 0.176066176572 0.0306236155925 absolute error = 3.811e-07 relative error = 0.0002132 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9062 Order of pole (given) = 0.5 0 NO 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=80.2MB, alloc=44.3MB, time=1.02 x[1] = -1.0998 0.108 h = 0.001 0.001 y[1] (numeric) = 0.176046552583 0.0315013701346 y[1] (closed_form) = 0.176046627856 0.0315013564935 absolute error = 7.650e-08 relative error = 4.277e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0988 0.109 h = 0.001 0.003 y[1] (numeric) = 0.176321932456 0.0318101613941 y[1] (closed_form) = 0.176322222121 0.0318100486822 absolute error = 3.108e-07 relative error = 0.0001735 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9078 Order of pole (given) = 0.5 0 NO 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=125.6MB, alloc=44.3MB, time=1.58 x[1] = -1.0978 0.112 h = 0.0001 0.004 y[1] (numeric) = 0.176564167781 0.0327037687936 y[1] (closed_form) = 0.17656401296 0.0327038402137 absolute error = 1.705e-07 relative error = 9.495e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9091 Order of pole (given) = 0.5 0 NO 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=171.1MB, alloc=44.3MB, time=2.14 x[1] = -1.0977 0.116 h = 0.003 0.006 y[1] (numeric) = 0.17652427357 0.0338755016633 y[1] (closed_form) = 0.176523789201 0.033875330633 absolute error = 5.137e-07 relative error = 0.0002858 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9097 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0947 0.122 h = 0.0001 0.005 y[1] (numeric) = 0.1772939366 0.0356844116489 y[1] (closed_form) = 0.177293338495 0.0356860321252 absolute error = 1.727e-06 relative error = 0.0009551 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9135 Order of pole (given) = 0.5 0 NO 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=216.6MB, alloc=44.3MB, time=2.70 x[1] = -1.0946 0.127 h = 0.0001 0.003 y[1] (numeric) = 0.177228368222 0.0371525837223 y[1] (closed_form) = 0.177228037447 0.0371530730699 absolute error = 5.907e-07 relative error = 0.0003262 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9143 Order of pole (given) = 0.5 0 NO 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=262.0MB, alloc=44.3MB, time=3.27 x[1] = -1.0945 0.13 h = 0.001 0.001 y[1] (numeric) = 0.177198653306 0.0380338704785 y[1] (closed_form) = 0.177198774491 0.0380343071867 absolute error = 4.532e-07 relative error = 0.0002501 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9148 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0935 0.131 h = 0.001 0.003 y[1] (numeric) = 0.177471824073 0.0383469932792 y[1] (closed_form) = 0.177472157225 0.0383473285183 absolute error = 4.726e-07 relative error = 0.0002603 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9159 Order of pole (given) = 0.5 0 NO 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=307.4MB, alloc=44.3MB, time=3.83 x[1] = -1.0925 0.134 h = 0.0001 0.004 y[1] (numeric) = 0.177705317013 0.0392470477831 y[1] (closed_form) = 0.177705210418 0.0392475722233 absolute error = 5.352e-07 relative error = 0.0002941 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.9173 Order of pole (given) = 0.5 0 NO 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=352.9MB, alloc=44.3MB, time=4.40 x[1] = -1.0924 0.138 h = 0.003 0.006 y[1] (numeric) = 0.177652482442 0.0404233745912 y[1] (closed_form) = 0.177652044718 0.0404236622585 absolute error = 5.238e-07 relative error = 0.0002875 % Correct digits = 6 Radius of convergence (given) for eq 1 = 0.918 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0894 0.144 h = 0.0001 0.005 y[1] (numeric) = 0.17840582439 0.0422485165225 y[1] (closed_form) = 0.178405297568 0.0422505879716 absolute error = 2.137e-06 relative error = 0.001166 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9219 Order of pole (given) = 0.5 0 NO 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=398.5MB, alloc=44.3MB, time=4.96 x[1] = -1.0893 0.149 h = 0.0001 0.003 y[1] (numeric) = 0.178324149916 0.0437224416433 y[1] (closed_form) = 0.178323873935 0.0437233842958 absolute error = 9.822e-07 relative error = 0.000535 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0892 0.152 h = 0.001 0.001 y[1] (numeric) = 0.178284820787 0.0446073399822 y[1] (closed_form) = 0.178284993683 0.0446082242487 absolute error = 9.010e-07 relative error = 0.0004903 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9234 Order of pole (given) = 0.5 0 NO 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=444.0MB, alloc=44.3MB, time=5.52 x[1] = -1.0882 0.153 h = 0.001 0.003 y[1] (numeric) = 0.178555852027 0.0449248015374 y[1] (closed_form) = 0.178556234419 0.0449255820495 absolute error = 8.692e-07 relative error = 0.0004721 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9245 Order of pole (given) = 0.5 0 NO 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=489.5MB, alloc=44.3MB, time=6.09 x[1] = -1.0872 0.156 h = 0.0001 0.004 y[1] (numeric) = 0.1787807342 0.0458313870048 y[1] (closed_form) = 0.178780681684 0.0458323615616 absolute error = 9.760e-07 relative error = 0.0005288 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.926 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0871 0.16 h = 0.003 0.006 y[1] (numeric) = 0.178715088079 0.0470124567713 y[1] (closed_form) = 0.178714703061 0.0470132002048 absolute error = 8.372e-07 relative error = 0.0004531 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9268 Order of pole (given) = 0.5 0 NO 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=535.0MB, alloc=44.3MB, time=6.65 x[1] = -1.0841 0.166 h = 0.0001 0.005 y[1] (numeric) = 0.179452411351 0.0488539628905 y[1] (closed_form) = 0.179451961275 0.0488564816879 absolute error = 2.559e-06 relative error = 0.001376 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9308 Order of pole (given) = 0.5 0 NO 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=580.5MB, alloc=44.3MB, time=7.22 x[1] = -1.084 0.171 h = 0.0001 0.003 y[1] (numeric) = 0.17935479249 0.0503338236965 y[1] (closed_form) = 0.179354577075 0.0503352165292 absolute error = 1.409e-06 relative error = 0.0007566 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0839 0.174 h = 0.001 0.001 y[1] (numeric) = 0.179305948542 0.051222441313 y[1] (closed_form) = 0.17930617878 0.0512237701953 absolute error = 1.349e-06 relative error = 0.0007232 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9325 Order of pole (given) = 0.5 0 NO 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=626.0MB, alloc=44.3MB, time=7.78 x[1] = -1.0829 0.175 h = 0.001 0.003 y[1] (numeric) = 0.179574909086 0.0515442464695 y[1] (closed_form) = 0.17957534631 0.0515454694248 absolute error = 1.299e-06 relative error = 0.0006952 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9336 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0819 0.178 h = 0.0001 0.004 y[1] (numeric) = 0.179791312977 0.0524574412988 y[1] (closed_form) = 0.17979132022 0.0524588629169 absolute error = 1.422e-06 relative error = 0.0007591 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9352 Order of pole (given) = 0.5 0 NO 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=671.4MB, alloc=44.3MB, time=8.34 x[1] = -1.0818 0.182 h = 0.003 0.006 y[1] (numeric) = 0.179712987111 0.0536433967537 y[1] (closed_form) = 0.179712660678 0.0536445928601 absolute error = 1.240e-06 relative error = 0.0006611 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9361 Order of pole (given) = 0.5 0 NO 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=717.0MB, alloc=44.3MB, time=8.90 x[1] = -1.0788 0.188 h = 0.0001 0.005 y[1] (numeric) = 0.18043459404 0.0555013876371 y[1] (closed_form) = 0.180434225968 0.0555043500457 absolute error = 2.985e-06 relative error = 0.001581 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9402 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0787 0.193 h = 0.0001 0.003 y[1] (numeric) = 0.180321196 0.0569873589445 y[1] (closed_form) = 0.180321046737 0.056989198691 absolute error = 1.846e-06 relative error = 0.000976 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9413 Order of pole (given) = 0.5 0 NO 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=762.4MB, alloc=44.3MB, time=9.47 x[1] = -1.0786 0.196 h = 0.001 0.001 y[1] (numeric) = 0.180262938612 0.0578797987795 y[1] (closed_form) = 0.180263231651 0.0578815691964 absolute error = 1.795e-06 relative error = 0.0009478 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.942 Order of pole (given) = 0.5 0 NO 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=807.9MB, alloc=44.3MB, time=10.04 x[1] = -1.0776 0.197 h = 0.0001 0.004 y[1] (numeric) = 0.180529896431 0.0582059501177 y[1] (closed_form) = 0.180530393916 0.0582076125465 absolute error = 1.735e-06 relative error = 0.0009148 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9432 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0775 0.201 h = 0.003 0.006 y[1] (numeric) = 0.180441292822 0.0593959832509 y[1] (closed_form) = 0.180440866283 0.0593975133409 absolute error = 1.588e-06 relative error = 0.0008362 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9441 Order of pole (given) = 0.5 0 NO 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=853.3MB, alloc=44.3MB, time=10.60 x[1] = -1.0745 0.207 h = 0.0001 0.005 y[1] (numeric) = 0.181149415118 0.0612680692107 y[1] (closed_form) = 0.181148966705 0.0612713575941 absolute error = 3.319e-06 relative error = 0.001736 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9484 Order of pole (given) = 0.5 0 NO 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=898.8MB, alloc=44.3MB, time=11.16 x[1] = -1.0744 0.212 h = 0.0001 0.003 y[1] (numeric) = 0.181022494006 0.0627592490312 y[1] (closed_form) = 0.181022250988 0.0627614177662 absolute error = 2.182e-06 relative error = 0.001139 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9496 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0743 0.215 h = 0.001 0.001 y[1] (numeric) = 0.180956169203 0.0636549472611 y[1] (closed_form) = 0.18095636557 0.0636570421441 absolute error = 2.104e-06 relative error = 0.001097 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9503 Order of pole (given) = 0.5 0 NO 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=944.3MB, alloc=44.3MB, time=11.72 x[1] = -1.0733 0.216 h = 0.001 0.003 y[1] (numeric) = 0.181221405071 0.0639848172872 y[1] (closed_form) = 0.181221803701 0.0639868024658 absolute error = 2.025e-06 relative error = 0.001054 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9515 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0723 0.219 h = 0.0001 0.004 y[1] (numeric) = 0.181422306454 0.064910403693 y[1] (closed_form) = 0.1814222844 0.0649125955925 absolute error = 2.192e-06 relative error = 0.001138 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9532 Order of pole (given) = 0.5 0 NO 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=989.9MB, alloc=44.3MB, time=12.29 x[1] = -1.0722 0.223 h = 0.003 0.006 y[1] (numeric) = 0.181320683966 0.0661056614002 y[1] (closed_form) = 0.181320326499 0.0661076380873 absolute error = 2.009e-06 relative error = 0.001041 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9542 Order of pole (given) = 0.5 0 NO 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=1035.3MB, alloc=44.3MB, time=12.86 x[1] = -1.0692 0.229 h = 0.0001 0.005 y[1] (numeric) = 0.182013649063 0.0679944300634 y[1] (closed_form) = 0.182013291944 0.0679981549085 absolute error = 3.742e-06 relative error = 0.001926 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9586 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0691 0.234 h = 0.0001 0.003 y[1] (numeric) = 0.181871261926 0.0694920269778 y[1] (closed_form) = 0.181871095 0.0694946362783 absolute error = 2.615e-06 relative error = 0.001343 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9599 Order of pole (given) = 0.5 0 NO 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=1080.9MB, alloc=44.3MB, time=13.44 x[1] = -1.069 0.237 h = 0.001 0.001 y[1] (numeric) = 0.181795715477 0.0703917276485 y[1] (closed_form) = 0.181795984379 0.0703942580652 absolute error = 2.545e-06 relative error = 0.001305 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9607 Order of pole (given) = 0.5 0 NO 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=1126.5MB, alloc=44.3MB, time=14.00 x[1] = -1.068 0.238 h = 0.001 0.003 y[1] (numeric) = 0.182059072515 0.0707259437652 y[1] (closed_form) = 0.182059541099 0.0707283626204 absolute error = 2.464e-06 relative error = 0.001261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9619 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.067 0.241 h = 0.0001 0.004 y[1] (numeric) = 0.182251875938 0.0716583361263 y[1] (closed_form) = 0.182251928935 0.0716609656855 absolute error = 2.630e-06 relative error = 0.001343 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9636 Order of pole (given) = 0.5 0 NO 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=1171.9MB, alloc=44.3MB, time=14.56 x[1] = -1.0669 0.245 h = 0.003 0.006 y[1] (numeric) = 0.182137962209 0.0728588548596 y[1] (closed_form) = 0.182137679156 0.0728612746603 absolute error = 2.436e-06 relative error = 0.001242 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9647 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0639 0.251 h = 0.0001 0.005 y[1] (numeric) = 0.18281606906 0.0747643951778 y[1] (closed_form) = 0.182815807916 0.0747685524978 absolute error = 4.166e-06 relative error = 0.002109 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9692 Order of pole (given) = 0.5 0 NO 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=1217.6MB, alloc=44.3MB, time=15.12 x[1] = -1.0638 0.256 h = 0.0001 0.003 y[1] (numeric) = 0.182658388493 0.076268561848 y[1] (closed_form) = 0.182658302708 0.0762716081133 absolute error = 3.047e-06 relative error = 0.00154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9706 Order of pole (given) = 0.5 0 NO 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=1263.2MB, alloc=44.3MB, time=15.69 x[1] = -1.0637 0.259 h = 0.001 0.001 y[1] (numeric) = 0.182573725873 0.0771723544827 y[1] (closed_form) = 0.182574072268 0.0771753170199 absolute error = 2.983e-06 relative error = 0.001505 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0627 0.26 h = 0.001 0.003 y[1] (numeric) = 0.182835269117 0.0775109133579 y[1] (closed_form) = 0.1828358126 0.0775137625835 absolute error = 2.901e-06 relative error = 0.001461 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9727 Order of pole (given) = 0.5 0 NO 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=1308.7MB, alloc=44.3MB, time=16.25 x[1] = -1.0617 0.263 h = 0.0001 0.004 y[1] (numeric) = 0.183020107671 0.0784501699962 y[1] (closed_form) = 0.183020240698 0.0784532336929 absolute error = 3.067e-06 relative error = 0.00154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9745 Order of pole (given) = 0.5 0 NO 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=1354.4MB, alloc=44.3MB, time=16.82 x[1] = -1.0616 0.267 h = 0.003 0.006 y[1] (numeric) = 0.182894042397 0.0796560684534 y[1] (closed_form) = 0.182893838907 0.0796589277748 absolute error = 2.867e-06 relative error = 0.001437 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9756 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0586 0.273 h = 0.0001 0.005 y[1] (numeric) = 0.183557587719 0.0815784590393 y[1] (closed_form) = 0.183557427031 0.0815830447847 absolute error = 4.589e-06 relative error = 0.002284 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9802 Order of pole (given) = 0.5 0 NO 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=1399.9MB, alloc=44.3MB, time=17.39 x[1] = -1.0585 0.278 h = 0.0001 0.003 y[1] (numeric) = 0.183384787983 0.0830893405437 y[1] (closed_form) = 0.183384788198 0.0830928200814 absolute error = 3.480e-06 relative error = 0.001728 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0584 0.281 h = 0.001 0.001 y[1] (numeric) = 0.183291115552 0.0839973100878 y[1] (closed_form) = 0.183291544219 0.0840007012402 absolute error = 3.418e-06 relative error = 0.001695 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9826 Order of pole (given) = 0.5 0 NO 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=1445.5MB, alloc=44.3MB, time=17.95 x[1] = -1.0574 0.282 h = 0.001 0.003 y[1] (numeric) = 0.183550908862 0.0843402065385 y[1] (closed_form) = 0.183551532016 0.0843434827336 absolute error = 3.335e-06 relative error = 0.001651 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9839 Order of pole (given) = 0.5 0 NO 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=1491.1MB, alloc=44.3MB, time=18.52 x[1] = -1.0564 0.285 h = 0.0001 0.004 y[1] (numeric) = 0.183727915143 0.0852863809143 y[1] (closed_form) = 0.183728132996 0.0852898751361 absolute error = 3.501e-06 relative error = 0.001728 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9857 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0563 0.289 h = 0.003 0.006 y[1] (numeric) = 0.183589839159 0.0864977717488 y[1] (closed_form) = 0.18358972019 0.0865010669013 absolute error = 3.297e-06 relative error = 0.001625 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.987 Order of pole (given) = 0.5 0 NO 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=1536.6MB, alloc=44.3MB, time=19.08 x[1] = -1.0533 0.295 h = 0.0001 0.005 y[1] (numeric) = 0.184239116989 0.0884370812802 y[1] (closed_form) = 0.184239061043 0.0884420913507 absolute error = 5.010e-06 relative error = 0.002452 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9916 Order of pole (given) = 0.5 0 NO 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=1582.2MB, alloc=44.3MB, time=19.64 x[1] = -1.0532 0.3 h = 0.0001 0.003 y[1] (numeric) = 0.184051373594 0.0899548152487 y[1] (closed_form) = 0.184051464478 0.089958724287 absolute error = 3.910e-06 relative error = 0.001909 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9932 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0531 0.303 h = 0.001 0.001 y[1] (numeric) = 0.183948798347 0.0908670421595 y[1] (closed_form) = 0.183949313888 0.0908708583405 absolute error = 3.851e-06 relative error = 0.001877 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9942 Order of pole (given) = 0.5 0 NO 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=1627.7MB, alloc=44.3MB, time=20.21 x[1] = -1.0521 0.304 h = 0.0001 0.004 y[1] (numeric) = 0.184206904353 0.091214269262 y[1] (closed_form) = 0.184207611777 0.0912179689418 absolute error = 3.767e-06 relative error = 0.001832 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9955 Order of pole (given) = 0.5 0 NO 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=1673.3MB, alloc=44.3MB, time=20.78 x[1] = -1.052 0.308 h = 0.003 0.006 y[1] (numeric) = 0.184059102354 0.092430212901 y[1] (closed_form) = 0.184058906618 0.0924338377705 absolute error = 3.630e-06 relative error = 0.001763 % Correct digits = 5 Radius of convergence (given) for eq 1 = 0.9968 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.049 0.314 h = 0.0001 0.005 y[1] (numeric) = 0.184696129841 0.0943839681689 y[1] (closed_form) = 0.184696014138 0.0943892979871 absolute error = 5.331e-06 relative error = 0.00257 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.001 Order of pole (given) = 0.5 0 NO 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=1718.8MB, alloc=44.3MB, time=21.34 x[1] = -1.0489 0.319 h = 0.0001 0.003 y[1] (numeric) = 0.18449558093 0.095907530001 y[1] (closed_form) = 0.184495600187 0.0959117633224 absolute error = 4.233e-06 relative error = 0.002036 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.003 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0488 0.322 h = 0.001 0.001 y[1] (numeric) = 0.184385376494 0.0968233782777 y[1] (closed_form) = 0.184385817145 0.0968275149933 absolute error = 4.160e-06 relative error = 0.001998 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.004 Order of pole (given) = 0.5 0 NO 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=1764.3MB, alloc=44.3MB, time=21.90 x[1] = -1.0478 0.323 h = 0.001 0.003 y[1] (numeric) = 0.184642027856 0.0971743071607 y[1] (closed_form) = 0.184642658168 0.0971783260944 absolute error = 4.068e-06 relative error = 0.00195 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.005 Order of pole (given) = 0.5 0 NO 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=1809.8MB, alloc=44.3MB, time=22.47 x[1] = -1.0468 0.326 h = 0.0001 0.004 y[1] (numeric) = 0.184804726724 0.0981333905499 y[1] (closed_form) = 0.184804961314 0.0981376336431 absolute error = 4.250e-06 relative error = 0.002031 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.007 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0467 0.33 h = 0.003 0.006 y[1] (numeric) = 0.184644610692 0.099355141976 y[1] (closed_form) = 0.18464450824 0.0993591956496 absolute error = 4.055e-06 relative error = 0.001934 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.009 Order of pole (given) = 0.5 0 NO 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=1855.4MB, alloc=44.3MB, time=23.03 x[1] = -1.0437 0.336 h = 0.0001 0.005 y[1] (numeric) = 0.185267908788 0.10132592239 y[1] (closed_form) = 0.185267905347 0.10133166885 absolute error = 5.746e-06 relative error = 0.002721 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.014 Order of pole (given) = 0.5 0 NO 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=1901.0MB, alloc=44.3MB, time=23.60 x[1] = -1.0436 0.341 h = 0.0001 0.003 y[1] (numeric) = 0.185052743367 0.102856575623 y[1] (closed_form) = 0.185052861532 0.102861231304 absolute error = 4.657e-06 relative error = 0.0022 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.015 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0435 0.344 h = 0.001 0.001 y[1] (numeric) = 0.184933835286 0.10377682067 y[1] (closed_form) = 0.184934370949 0.103781375611 absolute error = 4.586e-06 relative error = 0.002163 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.016 Order of pole (given) = 0.5 0 NO 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=1946.6MB, alloc=44.3MB, time=24.16 x[1] = -1.0425 0.345 h = 0.001 0.003 y[1] (numeric) = 0.185188912576 0.104132063773 y[1] (closed_form) = 0.185189635304 0.10413649957 absolute error = 4.494e-06 relative error = 0.002115 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.018 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0415 0.348 h = 0.0001 0.004 y[1] (numeric) = 0.185344153412 0.105098194033 y[1] (closed_form) = 0.185344485584 0.105102856969 absolute error = 4.675e-06 relative error = 0.002194 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.02 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 memory used=1992.1MB, alloc=44.3MB, time=24.72 x[1] = -1.0414 0.352 h = 0.003 0.006 y[1] (numeric) = 0.185172431927 0.106325729566 y[1] (closed_form) = 0.185172427174 0.106330208142 absolute error = 4.479e-06 relative error = 0.002097 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.021 Order of pole (given) = 0.5 0 NO 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=2037.5MB, alloc=44.3MB, time=25.28 x[1] = -1.0384 0.358 h = 0.0001 0.005 y[1] (numeric) = 0.185782285043 0.108313577676 y[1] (closed_form) = 0.185782397614 0.108319736585 absolute error = 6.160e-06 relative error = 0.002864 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.026 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0383 0.363 h = 0.0001 0.003 y[1] (numeric) = 0.185552680205 0.109851439567 y[1] (closed_form) = 0.185552901421 0.109856513667 absolute error = 5.079e-06 relative error = 0.002355 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.028 Order of pole (given) = 0.5 0 NO 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=2083.1MB, alloc=44.3MB, time=25.85 x[1] = -1.0382 0.366 h = 0.001 0.001 y[1] (numeric) = 0.185425176123 0.110776149598 y[1] (closed_form) = 0.185425810899 0.110781119001 absolute error = 5.010e-06 relative error = 0.002319 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.029 Order of pole (given) = 0.5 0 NO 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=2128.8MB, alloc=44.3MB, time=26.42 x[1] = -1.0372 0.367 h = 0.001 0.003 y[1] (numeric) = 0.185678738237 0.111135695601 y[1] (closed_form) = 0.185679557494 0.111140544592 absolute error = 4.918e-06 relative error = 0.002273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.03 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] = -1.0362 0.37 h = 0.0001 0.004 y[1] (numeric) = 0.185826649879 0.112108909011 y[1] (closed_form) = 0.18582708373 0.112113987931 absolute error = 5.097e-06 relative error = 0.002349 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.032 Order of pole (given) = 0.5 0 NO 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=2174.4MB, alloc=44.3MB, time=26.98 x[1] = -1.0361 0.374 h = 0.003 0.006 y[1] (numeric) = 0.185643465382 0.113342319227 y[1] (closed_form) = 0.185643562556 0.113347218752 absolute error = 4.900e-06 relative error = 0.002253 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.034 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0331 0.38 h = 0.0001 0.005 y[1] (numeric) = 0.186240153937 0.115347269296 y[1] (closed_form) = 0.186240386092 0.115353836449 absolute error = 6.571e-06 relative error = 0.003 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.039 Order of pole (given) = 0.5 0 NO 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=2220.0MB, alloc=44.3MB, time=27.54 x[1] = -1.033 0.385 h = 0.0001 0.003 y[1] (numeric) = 0.185996286661 0.116892450354 y[1] (closed_form) = 0.185996614888 0.116897938895 absolute error = 5.498e-06 relative error = 0.002503 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.041 Order of pole (given) = 0.5 0 NO 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=2265.6MB, alloc=44.3MB, time=28.11 x[1] = -1.0329 0.388 h = 0.001 0.001 y[1] (numeric) = 0.185860294049 0.117821689539 y[1] (closed_form) = 0.18586103187 0.117827069599 absolute error = 5.430e-06 relative error = 0.002468 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.042 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0319 0.389 h = 0.001 0.003 y[1] (numeric) = 0.18611239852 0.118185525795 y[1] (closed_form) = 0.186113318252 0.118190784263 absolute error = 5.338e-06 relative error = 0.002421 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.043 Order of pole (given) = 0.5 0 NO 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=2311.2MB, alloc=44.3MB, time=28.67 x[1] = -1.0309 0.392 h = 0.0001 0.004 y[1] (numeric) = 0.186253108415 0.119165854624 y[1] (closed_form) = 0.186253647871 0.119171345629 absolute error = 5.517e-06 relative error = 0.002495 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.045 Order of pole (given) = 0.5 0 NO 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=2356.9MB, alloc=44.3MB, time=29.24 x[1] = -1.0308 0.396 h = 0.003 0.006 y[1] (numeric) = 0.18605860311 0.120405224769 y[1] (closed_form) = 0.186058806257 0.120410541246 absolute error = 5.320e-06 relative error = 0.002401 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.047 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0278 0.402 h = 0.0001 0.005 y[1] (numeric) = 0.186642403295 0.122427303204 y[1] (closed_form) = 0.186642758434 0.122434274389 absolute error = 6.980e-06 relative error = 0.003127 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.052 Order of pole (given) = 0.5 0 NO 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=2402.5MB, alloc=44.3MB, time=29.80 x[1] = -1.0277 0.407 h = 0.0001 0.003 y[1] (numeric) = 0.186384450153 0.123979907407 y[1] (closed_form) = 0.186384889178 0.12398580638 absolute error = 5.915e-06 relative error = 0.002642 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.054 Order of pole (given) = 0.5 0 NO 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=2448.1MB, alloc=44.3MB, time=30.37 x[1] = -1.0276 0.41 h = 0.001 0.001 y[1] (numeric) = 0.186240076145 0.124913736004 y[1] (closed_form) = 0.186240920777 0.124919522883 absolute error = 5.848e-06 relative error = 0.002608 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.055 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0266 0.411 h = 0.0001 0.004 y[1] (numeric) = 0.18649077913 0.125281848638 y[1] (closed_form) = 0.18649180312 0.12528751283 absolute error = 5.756e-06 relative error = 0.002562 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.057 Order of pole (given) = 0.5 0 NO 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=2493.6MB, alloc=44.3MB, time=30.93 x[1] = -1.0265 0.415 h = 0.003 0.006 y[1] (numeric) = 0.186287111467 0.126526135208 y[1] (closed_form) = 0.18628725853 0.126531774435 absolute error = 5.641e-06 relative error = 0.002505 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.058 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0235 0.421 h = 0.0001 0.005 y[1] (numeric) = 0.186859831236 0.128562823501 y[1] (closed_form) = 0.186860144582 0.128570106361 absolute error = 7.290e-06 relative error = 0.003214 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.063 Order of pole (given) = 0.5 0 NO 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=2539.2MB, alloc=44.3MB, time=31.50 x[1] = -1.0234 0.426 h = 0.0001 0.003 y[1] (numeric) = 0.18658980435 0.130121730796 y[1] (closed_form) = 0.18659019132 0.130127946959 absolute error = 6.228e-06 relative error = 0.002738 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.065 Order of pole (given) = 0.5 0 NO 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=2584.7MB, alloc=44.3MB, time=32.06 x[1] = -1.0233 0.429 h = 0.001 0.001 y[1] (numeric) = 0.186438245759 0.131059457064 y[1] (closed_form) = 0.186439034932 0.131065558107 absolute error = 6.152e-06 relative error = 0.002699 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0223 0.43 h = 0.001 0.003 y[1] (numeric) = 0.186687735605 0.131431222874 y[1] (closed_form) = 0.186688701968 0.131437200325 absolute error = 6.055e-06 relative error = 0.002652 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.068 Order of pole (given) = 0.5 0 NO 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=2630.3MB, alloc=44.3MB, time=32.62 x[1] = -1.0213 0.433 h = 0.0001 0.004 y[1] (numeric) = 0.186815293164 0.132424782492 y[1] (closed_form) = 0.186815888685 0.132430996928 absolute error = 6.243e-06 relative error = 0.002726 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.07 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 memory used=2675.9MB, alloc=44.3MB, time=33.19 x[1] = -1.0212 0.437 h = 0.003 0.006 y[1] (numeric) = 0.186600026075 0.133675321154 y[1] (closed_form) = 0.186600286218 0.133681369861 absolute error = 6.054e-06 relative error = 0.002638 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.072 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0182 0.443 h = 0.0001 0.005 y[1] (numeric) = 0.187160359366 0.135729170666 y[1] (closed_form) = 0.187160801632 0.135736849767 absolute error = 7.692e-06 relative error = 0.003327 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.077 Order of pole (given) = 0.5 0 NO 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=2721.4MB, alloc=44.3MB, time=33.75 x[1] = -1.0181 0.448 h = 0.0001 0.003 y[1] (numeric) = 0.186876572149 0.137295680042 y[1] (closed_form) = 0.186877076561 0.137302299168 absolute error = 6.638e-06 relative error = 0.002863 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.079 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.018 0.451 h = 0.001 0.001 y[1] (numeric) = 0.186716829484 0.138238099177 y[1] (closed_form) = 0.186717732088 0.138244599872 absolute error = 6.563e-06 relative error = 0.002825 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.081 Order of pole (given) = 0.5 0 NO 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=2767.1MB, alloc=44.3MB, time=34.31 x[1] = -1.017 0.452 h = 0.001 0.003 y[1] (numeric) = 0.186965018841 0.138614113236 y[1] (closed_form) = 0.186966096122 0.138620489397 absolute error = 6.467e-06 relative error = 0.002778 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.082 Order of pole (given) = 0.5 0 NO 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=2812.6MB, alloc=44.3MB, time=34.88 x[1] = -1.016 0.455 h = 0.0001 0.004 y[1] (numeric) = 0.187085730257 0.139614861559 y[1] (closed_form) = 0.187086441727 0.139621476826 absolute error = 6.653e-06 relative error = 0.00285 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.084 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0159 0.459 h = 0.003 0.006 y[1] (numeric) = 0.186859545138 0.140871577843 y[1] (closed_form) = 0.186859921907 0.140878031962 absolute error = 6.465e-06 relative error = 0.002763 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.086 Order of pole (given) = 0.5 0 NO 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=2858.1MB, alloc=44.3MB, time=35.45 x[1] = -1.0129 0.465 h = 0.0001 0.005 y[1] (numeric) = 0.187407755121 0.142942594786 y[1] (closed_form) = 0.187408329243 0.142950665935 absolute error = 8.092e-06 relative error = 0.003433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.091 Order of pole (given) = 0.5 0 NO 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=2903.7MB, alloc=44.3MB, time=36.01 x[1] = -1.0128 0.47 h = 0.0001 0.003 y[1] (numeric) = 0.187110381688 0.144516792763 y[1] (closed_form) = 0.187111006852 0.144523810801 absolute error = 7.046e-06 relative error = 0.00298 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.093 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0127 0.473 h = 0.001 0.001 y[1] (numeric) = 0.186942560357 0.145463954598 y[1] (closed_form) = 0.186943579701 0.14547085105 absolute error = 6.971e-06 relative error = 0.002943 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.095 Order of pole (given) = 0.5 0 NO 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=2949.1MB, alloc=44.3MB, time=36.57 x[1] = -1.0117 0.474 h = 0.001 0.003 y[1] (numeric) = 0.187189501427 0.145844200021 y[1] (closed_form) = 0.187190692961 0.145850971073 absolute error = 6.875e-06 relative error = 0.002897 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.096 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0107 0.477 h = 0.0001 0.004 y[1] (numeric) = 0.18730348776 0.146852155548 y[1] (closed_form) = 0.187304318467 0.14685916767 absolute error = 7.061e-06 relative error = 0.002967 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.098 Order of pole (given) = 0.5 0 NO 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=2994.8MB, alloc=44.3MB, time=37.13 x[1] = -1.0106 0.481 h = 0.003 0.006 y[1] (numeric) = 0.18706652405 0.148115115801 y[1] (closed_form) = 0.187067020827 0.148121971255 absolute error = 6.873e-06 relative error = 0.002881 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.1 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=3040.4MB, alloc=44.3MB, time=37.70 x[1] = -1.0076 0.487 h = 0.0001 0.005 y[1] (numeric) = 0.187602869064 0.150203300137 y[1] (closed_form) = 0.187603577829 0.15021175916 absolute error = 8.489e-06 relative error = 0.003532 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.105 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0075 0.492 h = 0.0001 0.003 y[1] (numeric) = 0.187292082241 0.151785267581 y[1] (closed_form) = 0.187292831308 0.15179268048 absolute error = 7.451e-06 relative error = 0.003091 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.108 Order of pole (given) = 0.5 0 NO 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=3086.0MB, alloc=44.3MB, time=38.26 x[1] = -1.0074 0.495 h = 0.001 0.001 y[1] (numeric) = 0.187116286798 0.15273721858 y[1] (closed_form) = 0.187117426039 0.15274450689 absolute error = 7.377e-06 relative error = 0.003054 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.109 Order of pole (given) = 0.5 0 NO 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=3131.6MB, alloc=44.3MB, time=38.83 x[1] = -1.0064 0.496 h = 0.001 0.003 y[1] (numeric) = 0.187362030404 0.153121677605 y[1] (closed_form) = 0.187363339377 0.153128839722 absolute error = 7.281e-06 relative error = 0.003009 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.111 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0054 0.499 h = 0.0001 0.004 y[1] (numeric) = 0.187469410844 0.154136855711 y[1] (closed_form) = 0.187470363923 0.154144260711 absolute error = 7.466e-06 relative error = 0.003076 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.113 Order of pole (given) = 0.5 0 NO 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=3177.0MB, alloc=44.3MB, time=39.39 x[1] = -1.0053 0.503 h = 0.003 0.006 y[1] (numeric) = 0.187221806852 0.155406121842 y[1] (closed_form) = 0.187222426857 0.15541337455 absolute error = 7.279e-06 relative error = 0.002992 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.115 Order of pole (given) = 0.5 0 NO 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=3222.6MB, alloc=44.3MB, time=39.95 x[1] = -1.0023 0.509 h = 0.0001 0.005 y[1] (numeric) = 0.18774654032 0.157511467665 y[1] (closed_form) = 0.187747386368 0.157520310412 absolute error = 8.883e-06 relative error = 0.003625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.12 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] = -1.0022 0.514 h = 0.0001 0.003 y[1] (numeric) = 0.187422511466 0.159101280021 y[1] (closed_form) = 0.187423387438 0.159109083736 absolute error = 7.853e-06 relative error = 0.003194 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.122 Order of pole (given) = 0.5 0 NO 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=3268.2MB, alloc=44.3MB, time=40.52 x[1] = -1.0021 0.517 h = 0.001 0.001 y[1] (numeric) = 0.187238845515 0.160058063424 y[1] (closed_form) = 0.187240107664 0.160065739691 absolute error = 7.779e-06 relative error = 0.003158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -1.0011 0.518 h = 0.0001 0.004 y[1] (numeric) = 0.187483441113 0.160446717493 y[1] (closed_form) = 0.187484870564 0.160454266843 absolute error = 7.683e-06 relative error = 0.003114 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.125 Order of pole (given) = 0.5 0 NO 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=3313.7MB, alloc=44.3MB, time=41.08 x[1] = -1.001 0.522 h = 0.003 0.006 y[1] (numeric) = 0.187227227354 0.161721167318 y[1] (closed_form) = 0.187227809201 0.161728734064 absolute error = 7.589e-06 relative error = 0.003067 % Correct digits = 5 Radius of convergence (given) for eq 1 = 1.127 Order of pole (given) = 0.5 0 NO 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=3359.4MB, alloc=44.3MB, time=41.65 x[1] = -0.998 0.528 h = 0.0001 0.005 y[1] (numeric) = 0.187741960897 0.163841141948 y[1] (closed_form) = 0.187742780595 0.163850287206 absolute error = 9.182e-06 relative error = 0.003685 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.133 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9979 0.533 h = 0.0001 0.003 y[1] (numeric) = 0.187406575161 0.165437608398 y[1] (closed_form) = 0.187407416045 0.165445720682 absolute error = 8.156e-06 relative error = 0.003262 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.135 Order of pole (given) = 0.5 0 NO 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=3405.0MB, alloc=44.3MB, time=42.22 x[1] = -0.9978 0.536 h = 0.001 0.001 y[1] (numeric) = 0.187216158499 0.166398491542 y[1] (closed_form) = 0.187217382164 0.166406473984 absolute error = 8.076e-06 relative error = 0.003224 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.137 Order of pole (given) = 0.5 0 NO 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=3450.6MB, alloc=44.3MB, time=42.78 x[1] = -0.9968 0.537 h = 0.001 0.003 y[1] (numeric) = 0.187459754845 0.166790728256 y[1] (closed_form) = 0.187461143752 0.166798583183 absolute error = 7.977e-06 relative error = 0.003179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.138 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9958 0.54 h = 0.0001 0.004 y[1] (numeric) = 0.187555067519 0.167819301391 y[1] (closed_form) = 0.18755610955 0.167827402257 absolute error = 8.168e-06 relative error = 0.003245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.14 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=3496.3MB, alloc=44.3MB, time=43.34 x[1] = -0.9957 0.544 h = 0.003 0.006 y[1] (numeric) = 0.18728795149 0.169100328718 y[1] (closed_form) = 0.187288662197 0.169108285176 absolute error = 7.988e-06 relative error = 0.003166 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.142 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9927 0.55 h = 0.0001 0.005 y[1] (numeric) = 0.187791531996 0.171237442396 y[1] (closed_form) = 0.187792493574 0.171246963759 absolute error = 9.570e-06 relative error = 0.003765 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.148 Order of pole (given) = 0.5 0 NO 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=3541.9MB, alloc=44.3MB, time=43.91 x[1] = -0.9926 0.555 h = 0.0001 0.003 y[1] (numeric) = 0.187443217931 0.1728418825 y[1] (closed_form) = 0.187444190962 0.172850378137 absolute error = 8.551e-06 relative error = 0.003354 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.15 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=3587.5MB, alloc=44.3MB, time=44.48 x[1] = -0.9925 0.558 h = 0.001 0.001 y[1] (numeric) = 0.187245120277 0.173807671602 y[1] (closed_form) = 0.187246472123 0.173816034796 absolute error = 8.472e-06 relative error = 0.003316 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.152 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9915 0.559 h = 0.001 0.003 y[1] (numeric) = 0.187487657299 0.17420406752 y[1] (closed_form) = 0.187489172017 0.174212302596 absolute error = 8.373e-06 relative error = 0.003272 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.153 Order of pole (given) = 0.5 0 NO 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=3633.1MB, alloc=44.3MB, time=45.04 x[1] = -0.9905 0.562 h = 0.0001 0.004 y[1] (numeric) = 0.18757669419 0.175239892815 y[1] (closed_form) = 0.187577866803 0.175248375252 absolute error = 8.563e-06 relative error = 0.003336 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.155 Order of pole (given) = 0.5 0 NO 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=3678.9MB, alloc=44.3MB, time=45.61 x[1] = -0.9904 0.566 h = 0.003 0.006 y[1] (numeric) = 0.187299325622 0.176527381872 y[1] (closed_form) = 0.18730016798 0.176535723986 absolute error = 8.385e-06 relative error = 0.003258 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.157 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9874 0.572 h = 0.0001 0.005 y[1] (numeric) = 0.187791992256 0.178681613884 y[1] (closed_form) = 0.187793097971 0.178691507289 absolute error = 9.955e-06 relative error = 0.00384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.163 Order of pole (given) = 0.5 0 NO 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=3724.4MB, alloc=44.3MB, time=46.17 x[1] = -0.9873 0.577 h = 0.0001 0.003 y[1] (numeric) = 0.187430916307 0.180294088822 y[1] (closed_form) = 0.18743202408 0.18030296381 absolute error = 8.944e-06 relative error = 0.003439 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.166 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9872 0.58 h = 0.001 0.001 y[1] (numeric) = 0.18722523812 0.181264818645 y[1] (closed_form) = 0.187226720764 0.181273558722 absolute error = 8.865e-06 relative error = 0.003402 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.167 Order of pole (given) = 0.5 0 NO 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=3770.0MB, alloc=44.3MB, time=46.74 x[1] = -0.9862 0.581 h = 0.001 0.003 y[1] (numeric) = 0.187466761469 0.181665353326 y[1] (closed_form) = 0.187468404648 0.18167396474 absolute error = 8.767e-06 relative error = 0.003358 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.168 Order of pole (given) = 0.5 0 NO 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=3815.7MB, alloc=44.3MB, time=47.32 x[1] = -0.9852 0.584 h = 0.0001 0.004 y[1] (numeric) = 0.187549634138 0.182708435636 y[1] (closed_form) = 0.18755093992 0.182717295708 absolute error = 8.956e-06 relative error = 0.00342 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.171 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9851 0.588 h = 0.003 0.006 y[1] (numeric) = 0.187262145928 0.184002432909 y[1] (closed_form) = 0.187263122587 0.184011156644 absolute error = 8.778e-06 relative error = 0.003344 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.173 Order of pole (given) = 0.5 0 NO 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=3861.4MB, alloc=44.3MB, time=47.90 x[1] = -0.9821 0.594 h = 0.0001 0.005 y[1] (numeric) = 0.187744132821 0.186173758048 y[1] (closed_form) = 0.187745384809 0.186184019469 absolute error = 1.034e-05 relative error = 0.00391 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.179 Order of pole (given) = 0.5 0 NO 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=3907.0MB, alloc=44.3MB, time=48.46 x[1] = -0.982 0.599 h = 0.0001 0.003 y[1] (numeric) = 0.187370459478 0.187794324451 y[1] (closed_form) = 0.187371704454 0.187803574811 absolute error = 9.334e-06 relative error = 0.003518 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.181 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9819 0.602 h = 0.001 0.001 y[1] (numeric) = 0.187157299982 0.188770027065 y[1] (closed_form) = 0.187158915913 0.188779140171 absolute error = 9.255e-06 relative error = 0.003482 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.183 Order of pole (given) = 0.5 0 NO 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=3952.5MB, alloc=44.3MB, time=49.03 x[1] = -0.9809 0.603 h = 0.001 0.003 y[1] (numeric) = 0.187397854016 0.18917467954 y[1] (closed_form) = 0.187399628178 0.189183663497 absolute error = 9.157e-06 relative error = 0.003439 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.184 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9799 0.606 h = 0.0001 0.004 y[1] (numeric) = 0.187474671973 0.190225021382 y[1] (closed_form) = 0.187476113381 0.190234255175 absolute error = 9.346e-06 relative error = 0.003499 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.187 Order of pole (given) = 0.5 0 NO 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=3998.1MB, alloc=44.3MB, time=49.59 x[1] = -0.9798 0.61 h = 0.003 0.006 y[1] (numeric) = 0.187177195392 0.191525569805 y[1] (closed_form) = 0.187178308865 0.191534671147 absolute error = 9.169e-06 relative error = 0.003424 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.189 Order of pole (given) = 0.5 0 NO 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=4043.7MB, alloc=44.3MB, time=50.16 x[1] = -0.9768 0.616 h = 0.0001 0.005 y[1] (numeric) = 0.187648731656 0.193713958685 y[1] (closed_form) = 0.187650131933 0.193724584138 absolute error = 1.072e-05 relative error = 0.003974 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.194 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9767 0.621 h = 0.0001 0.003 y[1] (numeric) = 0.187262623362 0.195342668853 y[1] (closed_form) = 0.187264007875 0.195352290635 absolute error = 9.721e-06 relative error = 0.003592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.197 Order of pole (given) = 0.5 0 NO 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=4089.4MB, alloc=44.3MB, time=50.72 x[1] = -0.9766 0.624 h = 0.001 0.001 y[1] (numeric) = 0.187042080497 0.196323373758 y[1] (closed_form) = 0.18704383208 0.196332856064 absolute error = 9.643e-06 relative error = 0.003556 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.199 Order of pole (given) = 0.5 0 NO 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=4135.0MB, alloc=44.3MB, time=51.28 x[1] = -0.9756 0.625 h = 0.0001 0.004 y[1] (numeric) = 0.187281708307 0.196732122596 y[1] (closed_form) = 0.187283615852 0.196741475321 absolute error = 9.545e-06 relative error = 0.003514 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.2 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] = -0.9755 0.629 h = 0.003 0.006 y[1] (numeric) = 0.186976149221 0.198038042809 y[1] (closed_form) = 0.186977239853 0.198047448492 absolute error = 9.469e-06 relative error = 0.003476 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.202 Order of pole (given) = 0.5 0 NO 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=4180.5MB, alloc=44.3MB, time=51.85 x[1] = -0.9725 0.635 h = 0.0001 0.005 y[1] (numeric) = 0.187438666874 0.200240972227 y[1] (closed_form) = 0.187440053964 0.200251890498 absolute error = 1.101e-05 relative error = 0.004013 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.208 Order of pole (given) = 0.5 0 NO 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=4226.3MB, alloc=44.3MB, time=52.42 x[1] = -0.9724 0.64 h = 0.0001 0.003 y[1] (numeric) = 0.187041885673 0.201876585469 y[1] (closed_form) = 0.187043249624 0.20188650635 absolute error = 1.001e-05 relative error = 0.003639 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.211 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9723 0.643 h = 0.001 0.001 y[1] (numeric) = 0.186815004848 0.202861531551 y[1] (closed_form) = 0.186816732575 0.202871311091 absolute error = 9.931e-06 relative error = 0.003601 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.212 Order of pole (given) = 0.5 0 NO 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=4271.9MB, alloc=44.3MB, time=52.98 x[1] = -0.9713 0.644 h = 0.001 0.003 y[1] (numeric) = 0.187053820513 0.203273778569 y[1] (closed_form) = 0.187055702282 0.20328342817 absolute error = 9.831e-06 relative error = 0.003559 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.214 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9703 0.647 h = 0.0001 0.004 y[1] (numeric) = 0.187119570029 0.204337558859 y[1] (closed_form) = 0.187121127496 0.204347460248 absolute error = 1.002e-05 relative error = 0.003617 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.216 Order of pole (given) = 0.5 0 NO 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=4317.5MB, alloc=44.3MB, time=53.55 x[1] = -0.9702 0.651 h = 0.003 0.006 y[1] (numeric) = 0.186803771876 0.205650284873 y[1] (closed_form) = 0.186805003707 0.205660060799 absolute error = 9.853e-06 relative error = 0.003546 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.218 Order of pole (given) = 0.5 0 NO 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=4363.2MB, alloc=44.3MB, time=54.12 x[1] = -0.9672 0.657 h = 0.0001 0.005 y[1] (numeric) = 0.187256252432 0.207870215856 y[1] (closed_form) = 0.187257791315 0.207881490878 absolute error = 1.138e-05 relative error = 0.004067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.224 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9671 0.662 h = 0.0001 0.003 y[1] (numeric) = 0.186847332351 0.209514061229 y[1] (closed_form) = 0.18684883991 0.20952434629 absolute error = 1.039e-05 relative error = 0.003703 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.227 Order of pole (given) = 0.5 0 NO 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=4408.8MB, alloc=44.3MB, time=54.68 x[1] = -0.967 0.665 h = 0.001 0.001 y[1] (numeric) = 0.186613246565 0.210504059228 y[1] (closed_form) = 0.186615114075 0.21051420094 absolute error = 1.031e-05 relative error = 0.003666 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.229 Order of pole (given) = 0.5 0 NO 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=4454.5MB, alloc=44.3MB, time=55.24 x[1] = -0.966 0.666 h = 0.001 0.003 y[1] (numeric) = 0.186851213177 0.210920362163 y[1] (closed_form) = 0.186853232527 0.210930373596 absolute error = 1.021e-05 relative error = 0.003624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.23 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] = -0.965 0.669 h = 0.0001 0.004 y[1] (numeric) = 0.186911209939 0.211991398772 y[1] (closed_form) = 0.186912909437 0.212001662865 absolute error = 1.040e-05 relative error = 0.003681 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.232 Order of pole (given) = 0.5 0 NO 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=4500.0MB, alloc=44.3MB, time=55.81 x[1] = -0.9649 0.673 h = 0.003 0.006 y[1] (numeric) = 0.186585789047 0.213310782127 y[1] (closed_form) = 0.186587164233 0.213320924368 absolute error = 1.024e-05 relative error = 0.003611 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.235 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9619 0.679 h = 0.0001 0.005 y[1] (numeric) = 0.187028447502 0.215547674905 y[1] (closed_form) = 0.187030139887 0.215559302818 absolute error = 1.175e-05 relative error = 0.004117 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.24 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=4545.6MB, alloc=44.3MB, time=56.37 x[1] = -0.9618 0.684 h = 0.0001 0.003 y[1] (numeric) = 0.186607544814 0.217199793417 y[1] (closed_form) = 0.186609197979 0.217210438804 absolute error = 1.077e-05 relative error = 0.003762 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.243 Order of pole (given) = 0.5 0 NO 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=4591.2MB, alloc=44.3MB, time=56.94 x[1] = -0.9617 0.687 h = 0.001 0.001 y[1] (numeric) = 0.186366348161 0.218194866161 y[1] (closed_form) = 0.186368357492 0.218205366296 absolute error = 1.069e-05 relative error = 0.003725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.245 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9607 0.688 h = 0.001 0.003 y[1] (numeric) = 0.186603505345 0.218615202536 y[1] (closed_form) = 0.186605664349 0.218625572099 absolute error = 1.059e-05 relative error = 0.003685 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.246 Order of pole (given) = 0.5 0 NO 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=4636.7MB, alloc=44.3MB, time=57.50 x[1] = -0.9597 0.691 h = 0.0001 0.004 y[1] (numeric) = 0.186657850937 0.219693490239 y[1] (closed_form) = 0.18665969447 0.219704113236 absolute error = 1.078e-05 relative error = 0.00374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.249 Order of pole (given) = 0.5 0 NO 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=4682.5MB, alloc=44.3MB, time=58.07 x[1] = -0.9596 0.695 h = 0.003 0.006 y[1] (numeric) = 0.18632293182 0.221019561679 y[1] (closed_form) = 0.186324452404 0.221030066344 absolute error = 1.061e-05 relative error = 0.003672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.251 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9566 0.701 h = 0.0001 0.005 y[1] (numeric) = 0.186755978325 0.22327337339 y[1] (closed_form) = 0.186757825821 0.223285350382 absolute error = 1.212e-05 relative error = 0.004163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.257 Order of pole (given) = 0.5 0 NO 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=4727.9MB, alloc=44.3MB, time=58.63 x[1] = -0.9565 0.706 h = 0.0001 0.003 y[1] (numeric) = 0.186323247037 0.224933802487 y[1] (closed_form) = 0.186325047699 0.224944804382 absolute error = 1.115e-05 relative error = 0.003817 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.26 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] = -0.9564 0.709 h = 0.001 0.001 y[1] (numeric) = 0.186075032209 0.225933970702 y[1] (closed_form) = 0.186077185291 0.225944825545 absolute error = 1.107e-05 relative error = 0.003781 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.262 Order of pole (given) = 0.5 0 NO 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=4773.6MB, alloc=44.3MB, time=59.20 x[1] = -0.9554 0.71 h = 0.001 0.003 y[1] (numeric) = 0.186311418432 0.226358317774 y[1] (closed_form) = 0.186313719056 0.226369041796 absolute error = 1.097e-05 relative error = 0.003741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.263 Order of pole (given) = 0.5 0 NO 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=4819.3MB, alloc=44.3MB, time=59.76 x[1] = -0.9544 0.713 h = 0.0001 0.004 y[1] (numeric) = 0.186360212401 0.227443849652 y[1] (closed_form) = 0.186362201864 0.227454827793 absolute error = 1.116e-05 relative error = 0.003794 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.266 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9543 0.717 h = 0.003 0.006 y[1] (numeric) = 0.186015917726 0.228776637149 y[1] (closed_form) = 0.186017585638 0.228787500384 absolute error = 1.099e-05 relative error = 0.003727 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.268 Order of pole (given) = 0.5 0 NO 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=4864.9MB, alloc=44.3MB, time=60.33 x[1] = -0.9513 0.723 h = 0.0001 0.005 y[1] (numeric) = 0.186439557652 0.231047322087 y[1] (closed_form) = 0.186441561776 0.231059644392 absolute error = 1.248e-05 relative error = 0.004205 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.274 Order of pole (given) = 0.5 0 NO 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=4910.6MB, alloc=44.3MB, time=60.89 x[1] = -0.9512 0.728 h = 0.0001 0.003 y[1] (numeric) = 0.185995149478 0.232716095833 y[1] (closed_form) = 0.185997099426 0.232727450461 absolute error = 1.152e-05 relative error = 0.003867 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.277 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9511 0.731 h = 0.001 0.001 y[1] (numeric) = 0.18574000775 0.233721378253 y[1] (closed_form) = 0.185742306411 0.233732584127 absolute error = 1.144e-05 relative error = 0.003832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.278 Order of pole (given) = 0.5 0 NO 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=4956.3MB, alloc=44.3MB, time=61.46 x[1] = -0.9501 0.732 h = 0.0001 0.004 y[1] (numeric) = 0.185975660352 0.234149713054 y[1] (closed_form) = 0.185978104463 0.234160787896 absolute error = 1.134e-05 relative error = 0.003793 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.28 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] = -0.95 0.736 h = 0.003 0.006 y[1] (numeric) = 0.185623777597 0.235487997553 y[1] (closed_form) = 0.185625435657 0.235499155 absolute error = 1.128e-05 relative error = 0.003762 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.282 Order of pole (given) = 0.5 0 NO 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=5001.9MB, alloc=44.3MB, time=62.02 x[1] = -0.947 0.742 h = 0.0001 0.005 y[1] (numeric) = 0.186039281312 0.237773058989 y[1] (closed_form) = 0.186041283424 0.237785664276 absolute error = 1.276e-05 relative error = 0.004227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.288 Order of pole (given) = 0.5 0 NO 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=5047.5MB, alloc=44.3MB, time=62.59 x[1] = -0.9469 0.747 h = 0.0001 0.003 y[1] (numeric) = 0.18558484189 0.239448903681 y[1] (closed_form) = 0.18558678363 0.239460547578 absolute error = 1.180e-05 relative error = 0.003896 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9468 0.75 h = 0.001 0.001 y[1] (numeric) = 0.185323748528 0.240458520737 y[1] (closed_form) = 0.185326035844 0.240470014447 absolute error = 1.172e-05 relative error = 0.00386 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.293 Order of pole (given) = 0.5 0 NO 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=5093.1MB, alloc=44.3MB, time=63.16 x[1] = -0.9458 0.751 h = 0.001 0.003 y[1] (numeric) = 0.185558751591 0.240890261352 y[1] (closed_form) = 0.185561182585 0.240901623857 absolute error = 1.162e-05 relative error = 0.003821 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.294 Order of pole (given) = 0.5 0 NO 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=5138.8MB, alloc=44.3MB, time=63.72 x[1] = -0.9448 0.754 h = 0.0001 0.004 y[1] (numeric) = 0.185597387295 0.241989185795 y[1] (closed_form) = 0.185599514955 0.242000803516 absolute error = 1.181e-05 relative error = 0.003873 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.297 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9447 0.758 h = 0.0001 0.004 y[1] (numeric) = 0.185235886314 0.243334427525 y[1] (closed_form) = 0.185237695065 0.243345936502 absolute error = 1.165e-05 relative error = 0.003809 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.299 Order of pole (given) = 0.5 0 NO 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=5184.3MB, alloc=44.3MB, time=64.29 x[1] = -0.9446 0.762 h = 0.003 0.006 y[1] (numeric) = 0.184872244633 0.244680395649 y[1] (closed_form) = 0.184874053444 0.244691904731 absolute error = 1.165e-05 relative error = 0.003799 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.302 Order of pole (given) = 0.5 0 NO 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=5230.0MB, alloc=44.3MB, time=64.86 x[1] = -0.9416 0.768 h = 0.0001 0.005 y[1] (numeric) = 0.185276547944 0.246984806651 y[1] (closed_form) = 0.1852787113 0.246997748558 absolute error = 1.312e-05 relative error = 0.00425 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.308 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9415 0.773 h = 0.0001 0.003 y[1] (numeric) = 0.184808438747 0.248670088406 y[1] (closed_form) = 0.184810533437 0.248682077328 absolute error = 1.217e-05 relative error = 0.003928 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.311 Order of pole (given) = 0.5 0 NO 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=5275.6MB, alloc=44.3MB, time=65.42 x[1] = -0.9414 0.776 h = 0.001 0.001 y[1] (numeric) = 0.184539233075 0.249685492872 y[1] (closed_form) = 0.184541669146 0.249697329686 absolute error = 1.208e-05 relative error = 0.003892 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.313 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9404 0.777 h = 0.001 0.003 y[1] (numeric) = 0.184773311811 0.250121834193 y[1] (closed_form) = 0.184775889192 0.250133539568 absolute error = 1.199e-05 relative error = 0.003854 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.314 Order of pole (given) = 0.5 0 NO 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=5321.2MB, alloc=44.3MB, time=65.99 x[1] = -0.9394 0.78 h = 0.0001 0.004 y[1] (numeric) = 0.184805499134 0.251229028754 y[1] (closed_form) = 0.184807777978 0.251240990018 absolute error = 1.218e-05 relative error = 0.003904 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.317 Order of pole (given) = 0.5 0 NO 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=5367.0MB, alloc=44.3MB, time=66.56 x[1] = -0.9393 0.784 h = 0.003 0.006 y[1] (numeric) = 0.184433160458 0.252581896194 y[1] (closed_form) = 0.184435122013 0.25259375249 absolute error = 1.202e-05 relative error = 0.003842 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.319 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9363 0.79 h = 0.0001 0.005 y[1] (numeric) = 0.184828654434 0.254903035921 y[1] (closed_form) = 0.184830978665 0.254916312084 absolute error = 1.348e-05 relative error = 0.00428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.325 Order of pole (given) = 0.5 0 NO 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=5412.5MB, alloc=44.3MB, time=67.12 x[1] = -0.9362 0.795 h = 0.0001 0.003 y[1] (numeric) = 0.184349313236 0.256596753797 y[1] (closed_form) = 0.18435156223 0.256609084327 absolute error = 1.253e-05 relative error = 0.003967 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.328 Order of pole (given) = 0.5 0 NO 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=5458.3MB, alloc=44.3MB, time=67.68 x[1] = -0.9361 0.798 h = 0.001 0.001 y[1] (numeric) = 0.184073448194 0.2576173224 y[1] (closed_form) = 0.184076034992 0.257629499395 absolute error = 1.245e-05 relative error = 0.003932 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.33 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] = -0.9351 0.799 h = 0.001 0.003 y[1] (numeric) = 0.18430690116 0.258057582428 y[1] (closed_form) = 0.184309627282 0.258069627886 absolute error = 1.235e-05 relative error = 0.003894 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.331 Order of pole (given) = 0.5 0 NO 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=5504.0MB, alloc=44.3MB, time=68.25 x[1] = -0.9341 0.802 h = 0.0001 0.004 y[1] (numeric) = 0.18433391876 0.259171982785 y[1] (closed_form) = 0.184336350375 0.259184284494 absolute error = 1.254e-05 relative error = 0.003943 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.334 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.934 0.806 h = 0.003 0.006 y[1] (numeric) = 0.18395267945 0.260531659396 y[1] (closed_form) = 0.183954795282 0.26054385922 absolute error = 1.238e-05 relative error = 0.003882 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.336 Order of pole (given) = 0.5 0 NO 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=5549.6MB, alloc=44.3MB, time=68.82 x[1] = -0.931 0.812 h = 0.0001 0.005 y[1] (numeric) = 0.184339551101 0.262869472648 y[1] (closed_form) = 0.184342037386 0.262883079501 absolute error = 1.383e-05 relative error = 0.004308 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.342 Order of pole (given) = 0.5 0 NO 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=5595.4MB, alloc=44.3MB, time=69.38 x[1] = -0.9309 0.817 h = 0.0001 0.003 y[1] (numeric) = 0.183849120354 0.264571648676 y[1] (closed_form) = 0.183851525067 0.264584317211 absolute error = 1.289e-05 relative error = 0.004002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.346 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9308 0.82 h = 0.001 0.001 y[1] (numeric) = 0.183566681519 0.265597393072 y[1] (closed_form) = 0.183569420504 0.265609906724 absolute error = 1.281e-05 relative error = 0.003967 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.347 Order of pole (given) = 0.5 0 NO 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=5641.1MB, alloc=44.3MB, time=69.95 x[1] = -0.9298 0.821 h = 0.001 0.003 y[1] (numeric) = 0.183799541823 0.26604154825 y[1] (closed_form) = 0.183802418183 0.2660539303 absolute error = 1.271e-05 relative error = 0.003931 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.349 Order of pole (given) = 0.5 0 NO 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=5686.7MB, alloc=44.3MB, time=70.52 x[1] = -0.9288 0.824 h = 0.0001 0.004 y[1] (numeric) = 0.183821479379 0.2671631405 y[1] (closed_form) = 0.18382406519 0.267175779095 absolute error = 1.290e-05 relative error = 0.003978 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.351 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9287 0.828 h = 0.003 0.006 y[1] (numeric) = 0.18343145274 0.268529642269 y[1] (closed_form) = 0.183433724293 0.268542181982 absolute error = 1.274e-05 relative error = 0.003919 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.354 Order of pole (given) = 0.5 0 NO 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=5732.4MB, alloc=44.3MB, time=71.08 x[1] = -0.9257 0.834 h = 0.0001 0.005 y[1] (numeric) = 0.183809884714 0.270884072036 y[1] (closed_form) = 0.18381253416 0.270898006063 absolute error = 1.418e-05 relative error = 0.004333 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.36 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] = -0.9256 0.839 h = 0.0001 0.003 y[1] (numeric) = 0.183308504535 0.272594725679 y[1] (closed_form) = 0.183311066301 0.272607728661 absolute error = 1.325e-05 relative error = 0.004034 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.363 Order of pole (given) = 0.5 0 NO 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=5778.1MB, alloc=44.3MB, time=71.65 x[1] = -0.9255 0.842 h = 0.001 0.001 y[1] (numeric) = 0.183019576055 0.273625656015 y[1] (closed_form) = 0.183022468606 0.273638502845 absolute error = 1.317e-05 relative error = 0.004 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.365 Order of pole (given) = 0.5 0 NO 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=5823.9MB, alloc=44.3MB, time=72.22 x[1] = -0.9245 0.843 h = 0.001 0.003 y[1] (numeric) = 0.183251875832 0.274073682733 y[1] (closed_form) = 0.183254903845 0.274086397925 absolute error = 1.307e-05 relative error = 0.003964 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.367 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9235 0.846 h = 0.0001 0.004 y[1] (numeric) = 0.183268821133 0.275202451888 y[1] (closed_form) = 0.183271562486 0.275215423857 absolute error = 1.326e-05 relative error = 0.00401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.369 Order of pole (given) = 0.5 0 NO 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=5869.5MB, alloc=44.3MB, time=72.79 x[1] = -0.9234 0.85 h = 0.003 0.006 y[1] (numeric) = 0.182870118591 0.276575792813 y[1] (closed_form) = 0.182872547227 0.276588668822 absolute error = 1.310e-05 relative error = 0.003952 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.372 Order of pole (given) = 0.5 0 NO 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=5915.1MB, alloc=44.3MB, time=73.35 x[1] = -0.9204 0.856 h = 0.0001 0.005 y[1] (numeric) = 0.183240289273 0.278946780436 y[1] (closed_form) = 0.183243102914 0.278961038173 absolute error = 1.453e-05 relative error = 0.004354 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.378 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9203 0.861 h = 0.0001 0.003 y[1] (numeric) = 0.182728097454 0.280665928733 y[1] (closed_form) = 0.182730817528 0.280679262651 absolute error = 1.361e-05 relative error = 0.004063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.381 Order of pole (given) = 0.5 0 NO 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=5960.8MB, alloc=44.3MB, time=73.92 x[1] = -0.9202 0.864 h = 0.001 0.001 y[1] (numeric) = 0.182432762054 0.281702053735 y[1] (closed_form) = 0.182435809473 0.281715230306 absolute error = 1.352e-05 relative error = 0.00403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.383 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9192 0.865 h = 0.0001 0.004 y[1] (numeric) = 0.182664532496 0.282153928351 y[1] (closed_form) = 0.182667713498 0.282166973277 absolute error = 1.343e-05 relative error = 0.003995 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.384 Order of pole (given) = 0.5 0 NO 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=6006.4MB, alloc=44.3MB, time=74.48 x[1] = -0.9191 0.869 h = 0.003 0.006 y[1] (numeric) = 0.182258805536 0.283532858159 y[1] (closed_form) = 0.182261237752 0.283546015826 absolute error = 1.338e-05 relative error = 0.00397 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.387 Order of pole (given) = 0.5 0 NO 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=6052.1MB, alloc=44.3MB, time=75.05 x[1] = -0.9161 0.875 h = 0.0001 0.005 y[1] (numeric) = 0.182621808575 0.285917954526 y[1] (closed_form) = 0.182624631818 0.285932483272 absolute error = 1.480e-05 relative error = 0.004362 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.393 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.916 0.88 h = 0.0001 0.003 y[1] (numeric) = 0.182100317614 0.287644300029 y[1] (closed_form) = 0.182103042306 0.287657911069 absolute error = 1.388e-05 relative error = 0.004077 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.396 Order of pole (given) = 0.5 0 NO 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=6097.8MB, alloc=44.3MB, time=75.62 x[1] = -0.9159 0.883 h = 0.001 0.001 y[1] (numeric) = 0.181799470522 0.288684827384 y[1] (closed_form) = 0.181802519649 0.288698280064 absolute error = 1.379e-05 relative error = 0.004043 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.398 Order of pole (given) = 0.5 0 NO 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=6143.5MB, alloc=44.3MB, time=76.18 x[1] = -0.9149 0.884 h = 0.001 0.003 y[1] (numeric) = 0.182030764155 0.28913998939 y[1] (closed_form) = 0.182033945275 0.289153310418 absolute error = 1.370e-05 relative error = 0.004008 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.4 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] = -0.9139 0.887 h = 0.0001 0.004 y[1] (numeric) = 0.182038562339 0.290282012737 y[1] (closed_form) = 0.182041463853 0.290295590857 absolute error = 1.388e-05 relative error = 0.004052 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.402 Order of pole (given) = 0.5 0 NO 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=6189.1MB, alloc=44.3MB, time=76.75 x[1] = -0.9138 0.891 h = 0.003 0.006 y[1] (numeric) = 0.18162392436 0.291668010317 y[1] (closed_form) = 0.181626516024 0.291681497736 absolute error = 1.373e-05 relative error = 0.003997 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.405 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9108 0.897 h = 0.0001 0.005 y[1] (numeric) = 0.181978987757 0.29406955355 y[1] (closed_form) = 0.181981976991 0.294084399707 absolute error = 1.514e-05 relative error = 0.004379 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.411 Order of pole (given) = 0.5 0 NO 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=6234.7MB, alloc=44.3MB, time=77.31 x[1] = -0.9107 0.902 h = 0.0001 0.003 y[1] (numeric) = 0.181446935288 0.295804420981 y[1] (closed_form) = 0.18144982047 0.295818356563 absolute error = 1.423e-05 relative error = 0.004101 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.414 Order of pole (given) = 0.5 0 NO 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=6280.5MB, alloc=44.3MB, time=77.88 x[1] = -0.9106 0.905 h = 0.001 0.001 y[1] (numeric) = 0.181139831401 0.296850156672 y[1] (closed_form) = 0.181143037664 0.296863932828 absolute error = 1.414e-05 relative error = 0.004067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.416 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9096 0.906 h = 0.001 0.003 y[1] (numeric) = 0.181370651605 0.297309122932 y[1] (closed_form) = 0.181373988048 0.297322767478 absolute error = 1.405e-05 relative error = 0.004033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.418 Order of pole (given) = 0.5 0 NO 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=6326.1MB, alloc=44.3MB, time=78.44 x[1] = -0.9086 0.909 h = 0.0001 0.004 y[1] (numeric) = 0.181373698776 0.298458275999 y[1] (closed_form) = 0.181376759306 0.298472177703 absolute error = 1.423e-05 relative error = 0.004076 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.42 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=6371.8MB, alloc=44.3MB, time=79.01 x[1] = -0.9085 0.913 h = 0.003 0.006 y[1] (numeric) = 0.180950693288 0.299851143993 y[1] (closed_form) = 0.180953445543 0.299864957707 absolute error = 1.409e-05 relative error = 0.004022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.423 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9055 0.919 h = 0.0001 0.005 y[1] (numeric) = 0.181297983778 0.302269071509 y[1] (closed_form) = 0.181301139859 0.302284231756 absolute error = 1.549e-05 relative error = 0.004393 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.429 Order of pole (given) = 0.5 0 NO 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=6417.4MB, alloc=44.3MB, time=79.58 x[1] = -0.9054 0.924 h = 0.0001 0.003 y[1] (numeric) = 0.180755501069 0.304012471653 y[1] (closed_form) = 0.180758547793 0.304026728401 absolute error = 1.458e-05 relative error = 0.004122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.432 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9053 0.927 h = 0.001 0.001 y[1] (numeric) = 0.18044221913 0.305063420747 y[1] (closed_form) = 0.18044558363 0.305077517068 absolute error = 1.449e-05 relative error = 0.004089 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.434 Order of pole (given) = 0.5 0 NO 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=6463.1MB, alloc=44.3MB, time=80.14 x[1] = -0.9043 0.928 h = 0.001 0.003 y[1] (numeric) = 0.180672594557 0.305526167652 y[1] (closed_form) = 0.180676087453 0.305540132427 absolute error = 1.439e-05 relative error = 0.004055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.436 Order of pole (given) = 0.5 0 NO 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=6508.8MB, alloc=44.3MB, time=80.70 x[1] = -0.9033 0.931 h = 0.0001 0.004 y[1] (numeric) = 0.180670971551 0.30668243196 y[1] (closed_form) = 0.180674192165 0.30669665391 absolute error = 1.458e-05 relative error = 0.004097 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.439 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9032 0.935 h = 0.003 0.006 y[1] (numeric) = 0.180239702871 0.30808217764 y[1] (closed_form) = 0.18024261679 0.30809631424 absolute error = 1.443e-05 relative error = 0.004044 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.441 Order of pole (given) = 0.5 0 NO 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=6554.4MB, alloc=44.3MB, time=81.27 x[1] = -0.9002 0.941 h = 0.0001 0.005 y[1] (numeric) = 0.1805793833 0.310516425762 y[1] (closed_form) = 0.180582707026 0.31053189683 absolute error = 1.582e-05 relative error = 0.004405 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.447 Order of pole (given) = 0.5 0 NO 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=6600.0MB, alloc=44.3MB, time=81.83 x[1] = -0.9001 0.946 h = 0.0001 0.003 y[1] (numeric) = 0.180026599373 0.312268367457 y[1] (closed_form) = 0.180029808627 0.312282942044 absolute error = 1.492e-05 relative error = 0.00414 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.451 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.9 0.949 h = 0.001 0.001 y[1] (numeric) = 0.17970721676 0.313324533887 y[1] (closed_form) = 0.179710740529 0.313338947107 absolute error = 1.484e-05 relative error = 0.004108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.453 Order of pole (given) = 0.5 0 NO 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=6645.7MB, alloc=44.3MB, time=82.41 x[1] = -0.899 0.95 h = 0.001 0.003 y[1] (numeric) = 0.179937175224 0.313791037875 y[1] (closed_form) = 0.179940825643 0.313805319636 absolute error = 1.474e-05 relative error = 0.004075 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.454 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.898 0.953 h = 0.0001 0.004 y[1] (numeric) = 0.179930961166 0.314954394217 y[1] (closed_form) = 0.179934342864 0.31496893312 absolute error = 1.493e-05 relative error = 0.004115 % Correct digits = 4 memory used=6691.4MB, alloc=44.3MB, time=82.98 Radius of convergence (given) for eq 1 = 1.457 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8979 0.957 h = 0.003 0.006 y[1] (numeric) = 0.179491531812 0.316361023349 y[1] (closed_form) = 0.179494608403 0.316375479475 absolute error = 1.478e-05 relative error = 0.004063 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.46 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=6737.1MB, alloc=52.3MB, time=83.56 x[1] = -0.8949 0.963 h = 0.0001 0.005 y[1] (numeric) = 0.179823761234 0.318811527423 y[1] (closed_form) = 0.179827253348 0.318827306093 absolute error = 1.616e-05 relative error = 0.004415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.466 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8948 0.968 h = 0.0001 0.003 y[1] (numeric) = 0.179260802894 0.320572017673 y[1] (closed_form) = 0.179264175602 0.320586906819 absolute error = 1.527e-05 relative error = 0.004156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.469 Order of pole (given) = 0.5 0 NO 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=6782.8MB, alloc=52.3MB, time=84.12 x[1] = -0.8947 0.971 h = 0.001 0.001 y[1] (numeric) = 0.178935395635 0.321633404302 y[1] (closed_form) = 0.178939079646 0.321648131197 absolute error = 1.518e-05 relative error = 0.004124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.471 Order of pole (given) = 0.5 0 NO 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=6828.5MB, alloc=52.3MB, time=84.67 x[1] = -0.8937 0.972 h = 0.0001 0.004 y[1] (numeric) = 0.179164964146 0.32210364188 y[1] (closed_form) = 0.179168773091 0.322118237425 absolute error = 1.508e-05 relative error = 0.004092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.473 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8936 0.976 h = 0.003 0.006 y[1] (numeric) = 0.178718925129 0.323515891118 y[1] (closed_form) = 0.178722014208 0.323530618958 absolute error = 1.505e-05 relative error = 0.004071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.475 Order of pole (given) = 0.5 0 NO 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=6874.0MB, alloc=52.3MB, time=85.23 x[1] = -0.8906 0.982 h = 0.0001 0.005 y[1] (numeric) = 0.17904467294 0.325980249093 y[1] (closed_form) = 0.1790481824 0.32599628939 absolute error = 1.642e-05 relative error = 0.004415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.482 Order of pole (given) = 0.5 0 NO 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=6919.7MB, alloc=52.3MB, time=85.79 x[1] = -0.8905 0.987 h = 0.0001 0.003 y[1] (numeric) = 0.178472954762 0.327747982755 y[1] (closed_form) = 0.17847634063 0.327763139409 absolute error = 1.553e-05 relative error = 0.004161 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.485 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8904 0.99 h = 0.001 0.001 y[1] (numeric) = 0.178142359343 0.328813793717 y[1] (closed_form) = 0.178146053796 0.32882878737 absolute error = 1.544e-05 relative error = 0.004129 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.487 Order of pole (given) = 0.5 0 NO 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=6965.3MB, alloc=52.3MB, time=86.34 x[1] = -0.8894 0.991 h = 0.001 0.003 y[1] (numeric) = 0.178371569133 0.329287222074 y[1] (closed_form) = 0.178375387066 0.329302084465 absolute error = 1.534e-05 relative error = 0.004097 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.488 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8884 0.994 h = 0.0001 0.004 y[1] (numeric) = 0.17835693316 0.330463669102 y[1] (closed_form) = 0.178360488832 0.330478788499 absolute error = 1.553e-05 relative error = 0.004136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.491 Order of pole (given) = 0.5 0 NO 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=7011.0MB, alloc=52.3MB, time=86.90 x[1] = -0.8883 0.998 h = 0.003 0.006 y[1] (numeric) = 0.177902503396 0.331883022871 y[1] (closed_form) = 0.177905756896 0.331898064122 absolute error = 1.539e-05 relative error = 0.004087 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.494 Order of pole (given) = 0.5 0 NO 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=7056.7MB, alloc=52.3MB, time=87.46 x[1] = -0.8853 1.004 h = 0.0001 0.005 y[1] (numeric) = 0.178221087199 0.334363516066 y[1] (closed_form) = 0.178224766333 0.334379858113 absolute error = 1.675e-05 relative error = 0.004421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.5 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] = -0.8852 1.009 h = 0.0001 0.003 y[1] (numeric) = 0.177639424726 0.336139808231 y[1] (closed_form) = 0.177642975655 0.336155273475 absolute error = 1.587e-05 relative error = 0.004173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.504 Order of pole (given) = 0.5 0 NO 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=7102.3MB, alloc=52.3MB, time=88.02 x[1] = -0.8851 1.012 h = 0.001 0.001 y[1] (numeric) = 0.177302942601 0.337210842944 y[1] (closed_form) = 0.177306798988 0.337226144407 absolute error = 1.578e-05 relative error = 0.004142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.506 Order of pole (given) = 0.5 0 NO 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=7148.1MB, alloc=52.3MB, time=88.58 x[1] = -0.8841 1.013 h = 0.001 0.003 y[1] (numeric) = 0.177531810915 0.337687961707 y[1] (closed_form) = 0.177535789126 0.337703132051 absolute error = 1.568e-05 relative error = 0.004111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.507 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8831 1.016 h = 0.0001 0.004 y[1] (numeric) = 0.177512801365 0.338871443163 y[1] (closed_form) = 0.177516520697 0.33888687036 absolute error = 1.587e-05 relative error = 0.004148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.51 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=7193.6MB, alloc=52.3MB, time=89.13 x[1] = -0.883 1.02 h = 0.003 0.006 y[1] (numeric) = 0.177050494475 0.340297690471 y[1] (closed_form) = 0.177053913229 0.340313041909 absolute error = 1.573e-05 relative error = 0.0041 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.513 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.88 1.026 h = 0.0001 0.005 y[1] (numeric) = 0.177362063021 0.342794251992 y[1] (closed_form) = 0.177365912429 0.342810892707 absolute error = 1.708e-05 relative error = 0.004425 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.519 Order of pole (given) = 0.5 0 NO 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=7239.3MB, alloc=52.3MB, time=89.69 x[1] = -0.8799 1.031 h = 0.0001 0.003 y[1] (numeric) = 0.1767705769 0.344579104942 y[1] (closed_form) = 0.176774293656 0.34459487563 absolute error = 1.620e-05 relative error = 0.004184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.522 Order of pole (given) = 0.5 0 NO 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=7285.0MB, alloc=52.3MB, time=90.25 x[1] = -0.8798 1.034 h = 0.001 0.001 y[1] (numeric) = 0.176428280359 0.345655363519 y[1] (closed_form) = 0.176432299492 0.345670969696 absolute error = 1.612e-05 relative error = 0.004152 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.524 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8788 1.035 h = 0.001 0.003 y[1] (numeric) = 0.176656832042 0.346136149458 y[1] (closed_form) = 0.176660971373 0.346151624677 absolute error = 1.602e-05 relative error = 0.004122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.526 Order of pole (given) = 0.5 0 NO 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=7330.7MB, alloc=52.3MB, time=90.80 x[1] = -0.8778 1.038 h = 0.0001 0.004 y[1] (numeric) = 0.176633521777 0.347326643815 y[1] (closed_form) = 0.17663740555 0.347342375696 absolute error = 1.620e-05 relative error = 0.004158 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.529 Order of pole (given) = 0.5 0 NO 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=7376.4MB, alloc=52.3MB, time=91.36 x[1] = -0.8777 1.042 h = 0.003 0.006 y[1] (numeric) = 0.176163433583 0.34875978536 y[1] (closed_form) = 0.176167018372 0.34877544381 absolute error = 1.606e-05 relative error = 0.004111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.531 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8747 1.048 h = 0.0001 0.005 y[1] (numeric) = 0.1764681322 0.351272347727 y[1] (closed_form) = 0.176472152441 0.351289284079 absolute error = 1.741e-05 relative error = 0.004428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.538 Order of pole (given) = 0.5 0 NO 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=7422.1MB, alloc=52.3MB, time=91.92 x[1] = -0.8746 1.053 h = 0.0001 0.003 y[1] (numeric) = 0.175866940987 0.353065762283 y[1] (closed_form) = 0.175870824283 0.353081835315 absolute error = 1.654e-05 relative error = 0.004192 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.541 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8745 1.056 h = 0.001 0.001 y[1] (numeric) = 0.175518901048 0.354147243987 y[1] (closed_form) = 0.175523083686 0.354163151828 absolute error = 1.645e-05 relative error = 0.004161 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.543 Order of pole (given) = 0.5 0 NO 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=7467.7MB, alloc=52.3MB, time=92.47 x[1] = -0.8735 1.057 h = 0.001 0.003 y[1] (numeric) = 0.175747160235 0.354631673989 y[1] (closed_form) = 0.175751461476 0.354647451047 absolute error = 1.635e-05 relative error = 0.004132 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.545 Order of pole (given) = 0.5 0 NO 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=7513.4MB, alloc=52.3MB, time=93.03 x[1] = -0.8725 1.06 h = 0.0001 0.004 y[1] (numeric) = 0.175719620589 0.355829159244 y[1] (closed_form) = 0.175723669531 0.355845192739 absolute error = 1.654e-05 relative error = 0.004167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.548 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8724 1.064 h = 0.003 0.006 y[1] (numeric) = 0.175241845238 0.357269194599 y[1] (closed_form) = 0.175245596791 0.357285156931 absolute error = 1.640e-05 relative error = 0.00412 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.55 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=7559.1MB, alloc=52.3MB, time=93.59 x[1] = -0.8694 1.07 h = 0.0001 0.005 y[1] (numeric) = 0.175539815926 0.359797689831 y[1] (closed_form) = 0.175544007514 0.359814918834 absolute error = 1.773e-05 relative error = 0.004429 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.557 Order of pole (given) = 0.5 0 NO 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=7604.7MB, alloc=52.3MB, time=94.14 x[1] = -0.8693 1.075 h = 0.0001 0.003 y[1] (numeric) = 0.174929036115 0.361599665434 y[1] (closed_form) = 0.174933086617 0.361616037756 absolute error = 1.687e-05 relative error = 0.004199 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.56 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] = -0.8692 1.078 h = 0.001 0.001 y[1] (numeric) = 0.17457532255 0.362686368729 y[1] (closed_form) = 0.174579669403 0.362702575227 absolute error = 1.678e-05 relative error = 0.004168 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.562 Order of pole (given) = 0.5 0 NO 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=7650.4MB, alloc=52.3MB, time=94.70 x[1] = -0.8682 1.079 h = 0.0001 0.004 y[1] (numeric) = 0.174803312691 0.363174419809 y[1] (closed_form) = 0.174807776582 0.363190495715 absolute error = 1.668e-05 relative error = 0.004139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.564 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8681 1.083 h = 0.003 0.006 y[1] (numeric) = 0.174319308795 0.364620080109 y[1] (closed_form) = 0.174323080383 0.364636304565 absolute error = 1.666e-05 relative error = 0.004121 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.567 Order of pole (given) = 0.5 0 NO 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=7696.0MB, alloc=52.3MB, time=95.27 x[1] = -0.8651 1.089 h = 0.0001 0.005 y[1] (numeric) = 0.174611410857 0.367162157156 y[1] (closed_form) = 0.174615626392 0.367179638781 absolute error = 1.798e-05 relative error = 0.004423 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.573 Order of pole (given) = 0.5 0 NO 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=7741.7MB, alloc=52.3MB, time=95.82 x[1] = -0.865 1.094 h = 0.0001 0.003 y[1] (numeric) = 0.173992367295 0.368971388013 y[1] (closed_form) = 0.173996438218 0.368988018571 absolute error = 1.712e-05 relative error = 0.004197 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8649 1.097 h = 0.001 0.001 y[1] (numeric) = 0.173633762835 0.370062517598 y[1] (closed_form) = 0.173638127578 0.370078981786 absolute error = 1.703e-05 relative error = 0.004167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.579 Order of pole (given) = 0.5 0 NO 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=7787.3MB, alloc=52.3MB, time=96.38 x[1] = -0.8639 1.098 h = 0.001 0.003 y[1] (numeric) = 0.173861496899 0.370553664443 y[1] (closed_form) = 0.173865977352 0.370569998197 absolute error = 1.694e-05 relative error = 0.004138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.58 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=7833.2MB, alloc=52.3MB, time=96.94 x[1] = -0.8629 1.101 h = 0.0001 0.004 y[1] (numeric) = 0.173826189485 0.371764049678 y[1] (closed_form) = 0.173830423552 0.371780639399 absolute error = 1.712e-05 relative error = 0.004172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.583 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8628 1.105 h = 0.003 0.006 y[1] (numeric) = 0.173334273045 0.373216819073 y[1] (closed_form) = 0.173338212658 0.373233341719 absolute error = 1.699e-05 relative error = 0.004128 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.586 Order of pole (given) = 0.5 0 NO 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=7878.8MB, alloc=52.3MB, time=97.50 x[1] = -0.8598 1.111 h = 0.0001 0.005 y[1] (numeric) = 0.173619903674 0.375774703018 y[1] (closed_form) = 0.173624291442 0.375792471867 absolute error = 1.830e-05 relative error = 0.004421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.592 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8597 1.116 h = 0.0001 0.003 y[1] (numeric) = 0.172991482969 0.377592491816 y[1] (closed_form) = 0.172995722251 0.377609416111 absolute error = 1.745e-05 relative error = 0.004201 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.596 Order of pole (given) = 0.5 0 NO 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=7924.5MB, alloc=52.3MB, time=98.06 x[1] = -0.8596 1.119 h = 0.001 0.001 y[1] (numeric) = 0.172627331504 0.378688838963 y[1] (closed_form) = 0.172631861697 0.378705596334 absolute error = 1.736e-05 relative error = 0.004171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.598 Order of pole (given) = 0.5 0 NO 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=7970.3MB, alloc=52.3MB, time=98.62 x[1] = -0.8586 1.12 h = 0.001 0.003 y[1] (numeric) = 0.172854838683 0.379183564747 y[1] (closed_form) = 0.172859483074 0.3792001919 absolute error = 1.726e-05 relative error = 0.004143 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.599 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8576 1.123 h = 0.0001 0.004 y[1] (numeric) = 0.172815498103 0.380400876483 y[1] (closed_form) = 0.172819899202 0.38041775929 absolute error = 1.745e-05 relative error = 0.004176 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.602 Order of pole (given) = 0.5 0 NO 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=8015.9MB, alloc=52.3MB, time=99.18 x[1] = -0.8575 1.127 h = 0.003 0.006 y[1] (numeric) = 0.172316154916 0.381860533861 y[1] (closed_form) = 0.172320263147 0.381877351702 absolute error = 1.731e-05 relative error = 0.004132 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.605 Order of pole (given) = 0.5 0 NO 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=8061.4MB, alloc=52.3MB, time=99.73 x[1] = -0.8545 1.133 h = 0.0001 0.005 y[1] (numeric) = 0.172595447084 0.384434155666 y[1] (closed_form) = 0.17260000749 0.384452208884 absolute error = 1.862e-05 relative error = 0.004418 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.611 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8544 1.138 h = 0.0001 0.003 y[1] (numeric) = 0.171957760055 0.386260498306 y[1] (closed_form) = 0.171962168234 0.386277713414 absolute error = 1.777e-05 relative error = 0.004203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.615 Order of pole (given) = 0.5 0 NO 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=8107.2MB, alloc=52.3MB, time=100.29 x[1] = -0.8543 1.141 h = 0.001 0.001 y[1] (numeric) = 0.171588127919 0.387362059428 y[1] (closed_form) = 0.171592824145 0.387379107098 absolute error = 1.768e-05 relative error = 0.004174 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.617 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8533 1.142 h = 0.001 0.003 y[1] (numeric) = 0.171815429826 0.387860341571 y[1] (closed_form) = 0.171820238766 0.387877259252 absolute error = 1.759e-05 relative error = 0.004146 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.618 Order of pole (given) = 0.5 0 NO 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=8152.9MB, alloc=52.3MB, time=100.85 x[1] = -0.8523 1.145 h = 0.0001 0.004 y[1] (numeric) = 0.171772121847 0.389084556341 y[1] (closed_form) = 0.171776690533 0.389101729334 absolute error = 1.777e-05 relative error = 0.004178 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.621 Order of pole (given) = 0.5 0 NO 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=8198.6MB, alloc=52.3MB, time=101.41 x[1] = -0.8522 1.149 h = 0.003 0.006 y[1] (numeric) = 0.171265439892 0.390551097484 y[1] (closed_form) = 0.171269717292 0.390568207567 absolute error = 1.764e-05 relative error = 0.004135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.624 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8492 1.155 h = 0.0001 0.005 y[1] (numeric) = 0.171538523584 0.393140387877 y[1] (closed_form) = 0.171543256996 0.393158722653 absolute error = 1.894e-05 relative error = 0.004414 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.63 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=8244.3MB, alloc=52.3MB, time=101.97 x[1] = -0.8491 1.16 h = 0.0001 0.003 y[1] (numeric) = 0.170891679129 0.39497527917 y[1] (closed_form) = 0.170896256704 0.394992782209 absolute error = 1.809e-05 relative error = 0.004204 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.634 Order of pole (given) = 0.5 0 NO 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=8290.1MB, alloc=52.3MB, time=102.53 x[1] = -0.849 1.163 h = 0.001 0.001 y[1] (numeric) = 0.170516631497 0.396082050051 y[1] (closed_form) = 0.170521494297 0.396099385177 absolute error = 1.800e-05 relative error = 0.004175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.636 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.848 1.164 h = 0.001 0.003 y[1] (numeric) = 0.170743749145 0.396583866128 y[1] (closed_form) = 0.170748723202 0.396601071505 absolute error = 1.791e-05 relative error = 0.004148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.638 Order of pole (given) = 0.5 0 NO 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=8335.7MB, alloc=52.3MB, time=103.08 x[1] = -0.847 1.167 h = 0.0001 0.004 y[1] (numeric) = 0.17069653818 0.397814960177 y[1] (closed_form) = 0.170701274967 0.397832420498 absolute error = 1.809e-05 relative error = 0.004179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.641 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8469 1.171 h = 0.003 0.006 y[1] (numeric) = 0.170182603907 0.399288380025 y[1] (closed_form) = 0.170187050984 0.399305779443 absolute error = 1.796e-05 relative error = 0.004137 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.643 Order of pole (given) = 0.5 0 NO 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=8381.4MB, alloc=52.3MB, time=103.64 x[1] = -0.8439 1.177 h = 0.0001 0.005 y[1] (numeric) = 0.170449606201 0.401893269565 y[1] (closed_form) = 0.170454512956 0.401911883132 absolute error = 1.925e-05 relative error = 0.004409 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.65 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=8427.2MB, alloc=52.3MB, time=104.20 x[1] = -0.8438 1.182 h = 0.0001 0.003 y[1] (numeric) = 0.16979371134 0.403736703291 y[1] (closed_form) = 0.169798458772 0.403754491425 absolute error = 1.841e-05 relative error = 0.004203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.653 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8437 1.185 h = 0.001 0.001 y[1] (numeric) = 0.169413312249 0.40484867912 y[1] (closed_form) = 0.169418342126 0.404866298903 absolute error = 1.832e-05 relative error = 0.004175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.656 Order of pole (given) = 0.5 0 NO 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=8472.9MB, alloc=52.3MB, time=104.76 x[1] = -0.8427 1.186 h = 0.0001 0.004 y[1] (numeric) = 0.169640266069 0.405354006871 y[1] (closed_form) = 0.169645405774 0.405371497155 absolute error = 1.823e-05 relative error = 0.004148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.657 Order of pole (given) = 0.5 0 NO 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=8518.6MB, alloc=52.3MB, time=105.32 x[1] = -0.8426 1.19 h = 0.003 0.006 y[1] (numeric) = 0.169120453282 0.406833036724 y[1] (closed_form) = 0.169124926807 0.406850689094 absolute error = 1.821e-05 relative error = 0.004133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.66 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] = -0.8396 1.196 h = 0.0001 0.005 y[1] (numeric) = 0.169382135824 0.409451227356 y[1] (closed_form) = 0.169387072172 0.409470084953 absolute error = 1.949e-05 relative error = 0.004399 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.666 Order of pole (given) = 0.5 0 NO 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=8564.2MB, alloc=52.3MB, time=105.88 x[1] = -0.8395 1.201 h = 0.0001 0.003 y[1] (numeric) = 0.168718433326 0.411301902296 y[1] (closed_form) = 0.168723207373 0.41131993979 absolute error = 1.866e-05 relative error = 0.004197 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.67 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] = -0.8394 1.204 h = 0.001 0.001 y[1] (numeric) = 0.168333416392 0.412418291366 y[1] (closed_form) = 0.168338470531 0.412436160125 absolute error = 1.857e-05 relative error = 0.004169 % Correct digits = 4 memory used=8609.8MB, alloc=52.3MB, time=106.44 Radius of convergence (given) for eq 1 = 1.672 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8384 1.205 h = 0.001 0.003 y[1] (numeric) = 0.168560203655 0.412926622518 y[1] (closed_form) = 0.168565366408 0.412944361986 absolute error = 1.848e-05 relative error = 0.004142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.674 Order of pole (given) = 0.5 0 NO 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=8655.4MB, alloc=52.3MB, time=106.99 x[1] = -0.8374 1.208 h = 0.0001 0.004 y[1] (numeric) = 0.168505815814 0.414170408472 y[1] (closed_form) = 0.168510746712 0.414188402172 absolute error = 1.866e-05 relative error = 0.004172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.677 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8373 1.212 h = 0.003 0.006 y[1] (numeric) = 0.167978529896 0.415656527823 y[1] (closed_form) = 0.167983173976 0.41567446424 absolute error = 1.853e-05 relative error = 0.004133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.68 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=8701.0MB, alloc=52.3MB, time=107.55 x[1] = -0.8343 1.218 h = 0.0001 0.005 y[1] (numeric) = 0.168234360877 0.418290189545 y[1] (closed_form) = 0.168239471141 0.418309320901 absolute error = 1.980e-05 relative error = 0.004392 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.686 Order of pole (given) = 0.5 0 NO 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=8746.7MB, alloc=52.3MB, time=108.11 x[1] = -0.8342 1.223 h = 0.0001 0.003 y[1] (numeric) = 0.16756180233 0.420149394039 y[1] (closed_form) = 0.167566747029 0.420167711466 absolute error = 1.897e-05 relative error = 0.004194 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.69 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] = -0.8341 1.226 h = 0.001 0.001 y[1] (numeric) = 0.167171550222 0.421270978383 y[1] (closed_form) = 0.16717677231 0.4212891267 absolute error = 1.888e-05 relative error = 0.004167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.692 Order of pole (given) = 0.5 0 NO 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=8792.3MB, alloc=52.3MB, time=108.67 x[1] = -0.8331 1.227 h = 0.001 0.003 y[1] (numeric) = 0.16739821046 0.421782780462 y[1] (closed_form) = 0.167403539779 0.421800799758 absolute error = 1.879e-05 relative error = 0.004141 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.693 Order of pole (given) = 0.5 0 NO 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=8837.9MB, alloc=52.3MB, time=109.22 x[1] = -0.8321 1.23 h = 0.0001 0.004 y[1] (numeric) = 0.167340097013 0.423033377132 y[1] (closed_form) = 0.167345197313 0.423051650227 absolute error = 1.897e-05 relative error = 0.00417 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.696 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.832 1.234 h = 0.003 0.006 y[1] (numeric) = 0.166805798017 0.424526357482 y[1] (closed_form) = 0.166810613055 0.424544575164 absolute error = 1.884e-05 relative error = 0.004131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.699 Order of pole (given) = 0.5 0 NO 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=8883.5MB, alloc=52.3MB, time=109.78 x[1] = -0.829 1.24 h = 0.0001 0.005 y[1] (numeric) = 0.167055896645 0.42717542061 y[1] (closed_form) = 0.167061181075 0.427194823078 absolute error = 2.011e-05 relative error = 0.004384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.706 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8289 1.245 h = 0.0001 0.003 y[1] (numeric) = 0.166374583906 0.429043145801 y[1] (closed_form) = 0.166379699617 0.429061740446 absolute error = 1.929e-05 relative error = 0.004191 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.709 Order of pole (given) = 0.5 0 NO 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=8929.2MB, alloc=52.3MB, time=110.34 x[1] = -0.8288 1.248 h = 0.001 0.001 y[1] (numeric) = 0.165979157541 0.430169919092 y[1] (closed_form) = 0.165984547979 0.430188344284 absolute error = 1.920e-05 relative error = 0.004163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.711 Order of pole (given) = 0.5 0 NO 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=8974.9MB, alloc=52.3MB, time=110.90 x[1] = -0.8278 1.249 h = 0.001 0.003 y[1] (numeric) = 0.166205709628 0.430685170321 y[1] (closed_form) = 0.166211205941 0.430703466768 absolute error = 1.910e-05 relative error = 0.004138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.713 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8268 1.252 h = 0.0001 0.004 y[1] (numeric) = 0.166143930077 0.4319425531 y[1] (closed_form) = 0.166149200154 0.431961102894 absolute error = 1.928e-05 relative error = 0.004167 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.716 Order of pole (given) = 0.5 0 NO 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=9020.5MB, alloc=52.3MB, time=111.45 x[1] = -0.8267 1.256 h = 0.003 0.006 y[1] (numeric) = 0.165602698844 0.433442386573 y[1] (closed_form) = 0.165607685209 0.433460882779 absolute error = 1.916e-05 relative error = 0.004128 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.719 Order of pole (given) = 0.5 0 NO 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=9066.2MB, alloc=52.3MB, time=112.01 x[1] = -0.8237 1.262 h = 0.0001 0.005 y[1] (numeric) = 0.165847181726 0.436106781436 y[1] (closed_form) = 0.165852640543 0.436126452411 absolute error = 2.041e-05 relative error = 0.004375 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.725 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8236 1.267 h = 0.0001 0.003 y[1] (numeric) = 0.16515721491 0.437983017658 y[1] (closed_form) = 0.165162501963 0.438001886845 absolute error = 1.960e-05 relative error = 0.004186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.729 Order of pole (given) = 0.5 0 NO 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=9111.9MB, alloc=52.3MB, time=112.57 x[1] = -0.8235 1.27 h = 0.001 0.001 y[1] (numeric) = 0.164756674158 0.439114973104 y[1] (closed_form) = 0.164762233316 0.439133672523 absolute error = 1.951e-05 relative error = 0.004159 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.731 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8225 1.271 h = 0.001 0.003 y[1] (numeric) = 0.164983136461 0.439633651883 y[1] (closed_form) = 0.164988800162 0.439652222844 absolute error = 1.942e-05 relative error = 0.004135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.733 Order of pole (given) = 0.5 0 NO 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=9157.5MB, alloc=52.3MB, time=113.12 x[1] = -0.8215 1.274 h = 0.0001 0.004 y[1] (numeric) = 0.16491774911 0.440897796008 y[1] (closed_form) = 0.164923189309 0.440916619846 absolute error = 1.959e-05 relative error = 0.004162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.735 Order of pole (given) = 0.5 0 NO 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=9203.1MB, alloc=52.3MB, time=113.68 x[1] = -0.8214 1.278 h = 0.003 0.006 y[1] (numeric) = 0.164369665102 0.442404474109 y[1] (closed_form) = 0.16437482313 0.442423246139 absolute error = 1.947e-05 relative error = 0.004125 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.738 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8184 1.284 h = 0.0001 0.005 y[1] (numeric) = 0.164608646315 0.445084131088 y[1] (closed_form) = 0.164614279716 0.445104068004 absolute error = 2.072e-05 relative error = 0.004366 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.745 Order of pole (given) = 0.5 0 NO 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=9248.8MB, alloc=52.3MB, time=114.24 x[1] = -0.8183 1.289 h = 0.0001 0.003 y[1] (numeric) = 0.163910123837 0.446968867912 y[1] (closed_form) = 0.163915582532 0.446988009006 absolute error = 1.990e-05 relative error = 0.004181 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.749 Order of pole (given) = 0.5 0 NO 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=9294.5MB, alloc=52.3MB, time=114.80 x[1] = -0.8182 1.292 h = 0.001 0.001 y[1] (numeric) = 0.163504527541 0.448105998285 y[1] (closed_form) = 0.163510255758 0.448124969325 absolute error = 1.982e-05 relative error = 0.004154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.751 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8172 1.293 h = 0.0001 0.004 y[1] (numeric) = 0.163730917935 0.448628083195 y[1] (closed_form) = 0.163736749385 0.44864692607 absolute error = 1.972e-05 relative error = 0.00413 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.752 Order of pole (given) = 0.5 0 NO 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=9340.2MB, alloc=52.3MB, time=115.36 x[1] = -0.8171 1.297 h = 0.003 0.006 y[1] (numeric) = 0.16317727713 0.45014034163 y[1] (closed_form) = 0.163182467077 0.450159357888 absolute error = 1.971e-05 relative error = 0.004117 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.755 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8141 1.303 h = 0.0001 0.005 y[1] (numeric) = 0.163411431486 0.452833016316 y[1] (closed_form) = 0.163417099327 0.452853189092 absolute error = 2.095e-05 relative error = 0.004352 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.762 Order of pole (given) = 0.5 0 NO 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=9385.8MB, alloc=52.3MB, time=115.91 x[1] = -0.814 1.308 h = 0.0001 0.003 y[1] (numeric) = 0.162705521038 0.454724960925 y[1] (closed_form) = 0.162711011651 0.454744342925 absolute error = 2.014e-05 relative error = 0.004171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.766 Order of pole (given) = 0.5 0 NO 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=9431.5MB, alloc=52.3MB, time=116.47 x[1] = -0.8139 1.311 h = 0.001 0.001 y[1] (numeric) = 0.162295557933 0.455866480314 y[1] (closed_form) = 0.162301315879 0.455885692007 absolute error = 2.006e-05 relative error = 0.004145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.768 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8129 1.312 h = 0.001 0.003 y[1] (numeric) = 0.162521860149 0.45639147952 y[1] (closed_form) = 0.162527720217 0.45641056329 absolute error = 1.996e-05 relative error = 0.004121 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.769 Order of pole (given) = 0.5 0 NO 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=9477.2MB, alloc=52.3MB, time=117.03 x[1] = -0.8119 1.315 h = 0.0001 0.004 y[1] (numeric) = 0.162449830905 0.457668097201 y[1] (closed_form) = 0.16245547244 0.457687432961 absolute error = 2.014e-05 relative error = 0.004147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.772 Order of pole (given) = 0.5 0 NO 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=9522.9MB, alloc=52.3MB, time=117.58 x[1] = -0.8118 1.319 h = 0.003 0.006 y[1] (numeric) = 0.16188912109 0.459187407511 y[1] (closed_form) = 0.161894483278 0.459206694682 absolute error = 2.002e-05 relative error = 0.004111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.775 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8088 1.325 h = 0.0001 0.005 y[1] (numeric) = 0.162117980387 0.461895216321 y[1] (closed_form) = 0.162123823141 0.461915650368 absolute error = 2.125e-05 relative error = 0.004341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.782 Order of pole (given) = 0.5 0 NO 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=9568.5MB, alloc=52.3MB, time=118.14 x[1] = -0.8087 1.33 h = 0.0001 0.003 y[1] (numeric) = 0.161403693143 0.463795641382 y[1] (closed_form) = 0.16140935591 0.463815290493 absolute error = 2.045e-05 relative error = 0.004164 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.786 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8086 1.333 h = 0.001 0.001 y[1] (numeric) = 0.160988781431 0.46494232185 y[1] (closed_form) = 0.160994709019 0.46496180042 absolute error = 2.036e-05 relative error = 0.004138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.788 Order of pole (given) = 0.5 0 NO 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=9614.2MB, alloc=52.3MB, time=118.70 x[1] = -0.8076 1.334 h = 0.001 0.003 y[1] (numeric) = 0.161215043992 0.46547068802 y[1] (closed_form) = 0.161221072436 0.465490038972 absolute error = 2.027e-05 relative error = 0.004114 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.789 Order of pole (given) = 0.5 0 NO 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=9659.9MB, alloc=52.3MB, time=119.26 x[1] = -0.8066 1.337 h = 0.0001 0.004 y[1] (numeric) = 0.161139567726 0.466753996199 y[1] (closed_form) = 0.161145380238 0.466773598623 absolute error = 2.045e-05 relative error = 0.00414 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.792 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8065 1.341 h = 0.003 0.006 y[1] (numeric) = 0.160572225207 0.46828012462 y[1] (closed_form) = 0.160577759886 0.468299680119 absolute error = 2.032e-05 relative error = 0.004105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.795 Order of pole (given) = 0.5 0 NO 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=9705.6MB, alloc=52.3MB, time=119.82 x[1] = -0.8035 1.347 h = 0.0001 0.005 y[1] (numeric) = 0.160795896671 0.471002998247 y[1] (closed_form) = 0.160801914466 0.471023691109 absolute error = 2.155e-05 relative error = 0.00433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.802 Order of pole (given) = 0.5 0 NO 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=9751.3MB, alloc=52.3MB, time=120.38 x[1] = -0.8034 1.352 h = 0.0001 0.003 y[1] (numeric) = 0.160073326384 0.472911891379 y[1] (closed_form) = 0.160079161526 0.472931805076 absolute error = 2.075e-05 relative error = 0.004156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.805 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8033 1.355 h = 0.001 0.001 y[1] (numeric) = 0.159653522099 0.474063724583 y[1] (closed_form) = 0.159659619587 0.474083467529 absolute error = 2.066e-05 relative error = 0.004131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.808 Order of pole (given) = 0.5 0 NO 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=9796.9MB, alloc=52.3MB, time=120.93 x[1] = -0.8023 1.356 h = 0.001 0.003 y[1] (numeric) = 0.159879761558 0.474595436819 y[1] (closed_form) = 0.159885958659 0.474615052459 absolute error = 2.057e-05 relative error = 0.004108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.809 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8013 1.359 h = 0.0001 0.004 y[1] (numeric) = 0.159800892252 0.475885410319 y[1] (closed_form) = 0.159806875976 0.475905276902 absolute error = 2.075e-05 relative error = 0.004133 % Correct digits = 4 memory used=9842.7MB, alloc=52.3MB, time=121.49 Radius of convergence (given) for eq 1 = 1.812 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.8012 1.363 h = 0.003 0.006 y[1] (numeric) = 0.15922699143 0.477418346278 y[1] (closed_form) = 0.159232698827 0.477438167559 absolute error = 2.063e-05 relative error = 0.004098 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.815 Order of pole (given) = 0.5 0 NO 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=9888.4MB, alloc=52.3MB, time=122.04 x[1] = -0.7982 1.369 h = 0.0001 0.005 y[1] (numeric) = 0.159445580025 0.480156215591 y[1] (closed_form) = 0.159451772968 0.48017716485 absolute error = 2.185e-05 relative error = 0.004318 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.822 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7981 1.374 h = 0.0001 0.003 y[1] (numeric) = 0.158714818883 0.482073563816 y[1] (closed_form) = 0.158720826596 0.482093739615 absolute error = 2.105e-05 relative error = 0.004148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.825 Order of pole (given) = 0.5 0 NO 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=9934.0MB, alloc=52.3MB, time=122.60 x[1] = -0.798 1.377 h = 0.001 0.001 y[1] (numeric) = 0.158290177116 0.483230541075 y[1] (closed_form) = 0.158296444737 0.483250545935 absolute error = 2.096e-05 relative error = 0.004123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.828 Order of pole (given) = 0.5 0 NO 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=9979.8MB, alloc=52.3MB, time=123.16 x[1] = -0.797 1.378 h = 0.001 0.003 y[1] (numeric) = 0.158516409593 0.483765578667 y[1] (closed_form) = 0.158522775605 0.483785456538 absolute error = 2.087e-05 relative error = 0.0041 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.829 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.796 1.381 h = 0.0001 0.004 y[1] (numeric) = 0.158434200178 0.485062192253 y[1] (closed_form) = 0.158440355325 0.485082320523 absolute error = 2.105e-05 relative error = 0.004125 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.832 Order of pole (given) = 0.5 0 NO 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=10025.5MB, alloc=52.3MB, time=123.72 x[1] = -0.7959 1.385 h = 0.003 0.006 y[1] (numeric) = 0.157853814213 0.486601924719 y[1] (closed_form) = 0.157859694529 0.486622009275 absolute error = 2.093e-05 relative error = 0.004091 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.835 Order of pole (given) = 0.5 0 NO 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=10071.2MB, alloc=52.3MB, time=124.28 x[1] = -0.7929 1.391 h = 0.0001 0.005 y[1] (numeric) = 0.158067422701 0.489354720789 y[1] (closed_form) = 0.158073790877 0.489375924062 absolute error = 2.214e-05 relative error = 0.004305 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.842 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7928 1.396 h = 0.0001 0.003 y[1] (numeric) = 0.157328561362 0.491280510572 y[1] (closed_form) = 0.157334741819 0.491300946021 absolute error = 2.135e-05 relative error = 0.004138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.846 Order of pole (given) = 0.5 0 NO 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=10116.8MB, alloc=52.3MB, time=124.83 x[1] = -0.7927 1.399 h = 0.001 0.001 y[1] (numeric) = 0.156899136282 0.492442622883 y[1] (closed_form) = 0.156905574244 0.492462887231 absolute error = 2.126e-05 relative error = 0.004114 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.848 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7917 1.4 h = 0.003 0.006 y[1] (numeric) = 0.157125377479 0.49298096531 y[1] (closed_form) = 0.157131912633 0.493001102991 absolute error = 2.117e-05 relative error = 0.004092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.849 Order of pole (given) = 0.5 0 NO 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=10162.4MB, alloc=52.3MB, time=125.39 x[1] = -0.7887 1.406 h = 0.0001 0.005 y[1] (numeric) = 0.157336801007 0.495743394214 y[1] (closed_form) = 0.157343017003 0.495765361913 absolute error = 2.283e-05 relative error = 0.004389 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.856 Order of pole (given) = 0.5 0 NO 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=10208.2MB, alloc=52.3MB, time=125.94 x[1] = -0.7886 1.411 h = 0.0001 0.003 y[1] (numeric) = 0.156592631701 0.49767518409 y[1] (closed_form) = 0.156598658451 0.497696387865 absolute error = 2.204e-05 relative error = 0.004225 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.86 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] = -0.7885 1.414 h = 0.001 0.001 y[1] (numeric) = 0.156160076282 0.498840942264 y[1] (closed_form) = 0.156166358902 0.498861974897 absolute error = 2.195e-05 relative error = 0.004199 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.862 Order of pole (given) = 0.5 0 NO 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=10253.9MB, alloc=52.3MB, time=126.50 x[1] = -0.7875 1.415 h = 0.001 0.003 y[1] (numeric) = 0.156386415021 0.499381545556 y[1] (closed_form) = 0.156392794027 0.499402451776 absolute error = 2.186e-05 relative error = 0.004177 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.863 Order of pole (given) = 0.5 0 NO 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=10299.6MB, alloc=52.3MB, time=127.06 x[1] = -0.7865 1.418 h = 0.0001 0.004 y[1] (numeric) = 0.156298850973 0.500689390811 y[1] (closed_form) = 0.156305023242 0.500710546425 absolute error = 2.204e-05 relative error = 0.004201 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.866 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7864 1.422 h = 0.003 0.006 y[1] (numeric) = 0.155707851941 0.502240728258 y[1] (closed_form) = 0.15571375192 0.502261842717 absolute error = 2.192e-05 relative error = 0.004169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.869 Order of pole (given) = 0.5 0 NO 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=10345.2MB, alloc=52.3MB, time=127.61 x[1] = -0.7834 1.428 h = 0.0001 0.005 y[1] (numeric) = 0.15591365395 0.505018683282 y[1] (closed_form) = 0.155920045224 0.505040901052 absolute error = 2.312e-05 relative error = 0.004374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.876 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7833 1.433 h = 0.0001 0.003 y[1] (numeric) = 0.15516153372 0.50695888849 y[1] (closed_form) = 0.155167733394 0.506980347861 absolute error = 2.234e-05 relative error = 0.004213 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.88 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=10390.8MB, alloc=52.3MB, time=128.17 x[1] = -0.7832 1.436 h = 0.001 0.001 y[1] (numeric) = 0.154724284145 0.508129764547 y[1] (closed_form) = 0.154730737347 0.508151052647 absolute error = 2.224e-05 relative error = 0.004188 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.882 Order of pole (given) = 0.5 0 NO 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=10436.6MB, alloc=52.3MB, time=128.73 x[1] = -0.7822 1.437 h = 0.001 0.003 y[1] (numeric) = 0.15495065669 0.508673638086 y[1] (closed_form) = 0.154957205113 0.508694800102 absolute error = 2.215e-05 relative error = 0.004166 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.884 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7812 1.44 h = 0.0001 0.004 y[1] (numeric) = 0.154859889175 0.509988054161 y[1] (closed_form) = 0.154866233259 0.510009464999 absolute error = 2.233e-05 relative error = 0.00419 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.887 Order of pole (given) = 0.5 0 NO 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=10482.2MB, alloc=52.3MB, time=129.29 x[1] = -0.7811 1.444 h = 0.003 0.006 y[1] (numeric) = 0.154262595383 0.511546154679 y[1] (closed_form) = 0.154268668644 0.511567525854 absolute error = 2.222e-05 relative error = 0.004158 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.89 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=10527.9MB, alloc=52.3MB, time=129.84 x[1] = -0.7781 1.45 h = 0.0001 0.005 y[1] (numeric) = 0.154463681345 0.514338849944 y[1] (closed_form) = 0.154470247933 0.514361315497 absolute error = 2.341e-05 relative error = 0.004358 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.896 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.778 1.455 h = 0.0001 0.003 y[1] (numeric) = 0.153703696887 0.516287455648 y[1] (closed_form) = 0.153710069601 0.516309168262 absolute error = 2.263e-05 relative error = 0.004201 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.9 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=10573.6MB, alloc=52.3MB, time=130.40 x[1] = -0.7779 1.458 h = 0.001 0.001 y[1] (numeric) = 0.153261804944 0.517463439853 y[1] (closed_form) = 0.153268428876 0.517484981087 absolute error = 2.254e-05 relative error = 0.004176 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.902 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7769 1.459 h = 0.001 0.003 y[1] (numeric) = 0.153488225943 0.518010563632 y[1] (closed_form) = 0.153494943952 0.518031979115 absolute error = 2.244e-05 relative error = 0.004154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.904 Order of pole (given) = 0.5 0 NO 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=10619.2MB, alloc=52.3MB, time=130.96 x[1] = -0.7759 1.462 h = 0.0001 0.004 y[1] (numeric) = 0.153394304253 0.51933152522 y[1] (closed_form) = 0.15340082028 0.519353188943 absolute error = 2.262e-05 relative error = 0.004177 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.907 Order of pole (given) = 0.5 0 NO 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=10664.9MB, alloc=52.3MB, time=131.52 x[1] = -0.7758 1.466 h = 0.003 0.006 y[1] (numeric) = 0.152790784499 0.520896376363 y[1] (closed_form) = 0.15279703116 0.520918001881 absolute error = 2.251e-05 relative error = 0.004146 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.91 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] = -0.7728 1.472 h = 0.0001 0.005 y[1] (numeric) = 0.152987249583 0.523703743922 y[1] (closed_form) = 0.152993991507 0.523726455005 absolute error = 2.369e-05 relative error = 0.004342 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.916 Order of pole (given) = 0.5 0 NO 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=10710.5MB, alloc=52.3MB, time=132.08 x[1] = -0.7727 1.477 h = 0.0001 0.003 y[1] (numeric) = 0.152219486187 0.525660734844 y[1] (closed_form) = 0.152226032035 0.525682698383 absolute error = 2.292e-05 relative error = 0.004188 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.92 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=10756.2MB, alloc=52.3MB, time=132.64 x[1] = -0.7726 1.48 h = 0.001 0.001 y[1] (numeric) = 0.151773002813 0.526841817215 y[1] (closed_form) = 0.151779797606 0.526863609284 absolute error = 2.283e-05 relative error = 0.004163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.923 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7716 1.481 h = 0.0001 0.004 y[1] (numeric) = 0.151999486546 0.527392171414 y[1] (closed_form) = 0.152006374288 0.527413838069 absolute error = 2.274e-05 relative error = 0.004142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.924 Order of pole (given) = 0.5 0 NO 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=10801.9MB, alloc=52.3MB, time=133.19 x[1] = -0.7715 1.485 h = 0.003 0.006 y[1] (numeric) = 0.151390915003 0.528962524212 y[1] (closed_form) = 0.151397201329 0.528984379676 absolute error = 2.274e-05 relative error = 0.004133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.927 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7685 1.491 h = 0.0001 0.005 y[1] (numeric) = 0.151583303649 0.531782413471 y[1] (closed_form) = 0.151590086929 0.531805347028 absolute error = 2.392e-05 relative error = 0.004325 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.934 Order of pole (given) = 0.5 0 NO 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=10847.7MB, alloc=52.3MB, time=133.75 x[1] = -0.7684 1.496 h = 0.0001 0.003 y[1] (numeric) = 0.150808812016 0.533746518253 y[1] (closed_form) = 0.150815397321 0.533768708834 absolute error = 2.315e-05 relative error = 0.004173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.938 Order of pole (given) = 0.5 0 NO 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=10893.5MB, alloc=52.3MB, time=134.31 x[1] = -0.7683 1.499 h = 0.001 0.001 y[1] (numeric) = 0.150358356086 0.534931926901 y[1] (closed_form) = 0.150365188405 0.534953945924 absolute error = 2.305e-05 relative error = 0.004149 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.94 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] = -0.7673 1.5 h = 0.001 0.003 y[1] (numeric) = 0.150584866814 0.535485046983 y[1] (closed_form) = 0.150591791125 0.53550694087 absolute error = 2.296e-05 relative error = 0.004128 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.942 Order of pole (given) = 0.5 0 NO 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=10939.2MB, alloc=52.3MB, time=134.87 x[1] = -0.7663 1.503 h = 0.0001 0.004 y[1] (numeric) = 0.150485126711 0.536818084676 y[1] (closed_form) = 0.150491853332 0.536840225723 absolute error = 2.314e-05 relative error = 0.00415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.944 Order of pole (given) = 0.5 0 NO 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=10984.8MB, alloc=52.3MB, time=135.42 x[1] = -0.7662 1.507 h = 0.003 0.006 y[1] (numeric) = 0.149870121143 0.538395390621 y[1] (closed_form) = 0.149876581064 0.538417496108 absolute error = 2.303e-05 relative error = 0.004121 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.948 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7632 1.513 h = 0.0001 0.005 y[1] (numeric) = 0.150058061715 0.54122982762 y[1] (closed_form) = 0.150065020353 0.541253002598 absolute error = 2.420e-05 relative error = 0.004308 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.954 Order of pole (given) = 0.5 0 NO 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=11030.6MB, alloc=52.3MB, time=135.98 x[1] = -0.7631 1.518 h = 0.0001 0.003 y[1] (numeric) = 0.149275946395 0.543202289091 y[1] (closed_form) = 0.149282704989 0.543224726373 absolute error = 2.343e-05 relative error = 0.004159 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.958 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.763 1.521 h = 0.001 0.001 y[1] (numeric) = 0.148820991755 0.544392777309 y[1] (closed_form) = 0.148827995148 0.544415042976 absolute error = 2.334e-05 relative error = 0.004136 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.961 Order of pole (given) = 0.5 0 NO 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=11076.3MB, alloc=52.3MB, time=136.54 x[1] = -0.762 1.522 h = 0.001 0.003 y[1] (numeric) = 0.149047591069 0.544949091588 y[1] (closed_form) = 0.149054685365 0.544971232463 absolute error = 2.325e-05 relative error = 0.004115 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.962 Order of pole (given) = 0.5 0 NO 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=11122.1MB, alloc=52.3MB, time=137.10 x[1] = -0.761 1.525 h = 0.0001 0.004 y[1] (numeric) = 0.148944833062 0.546288603003 y[1] (closed_form) = 0.148951731914 0.54631099043 absolute error = 2.343e-05 relative error = 0.004137 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.965 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7609 1.529 h = 0.003 0.006 y[1] (numeric) = 0.148323792417 0.547872622968 y[1] (closed_form) = 0.148330425996 0.547894976203 absolute error = 2.332e-05 relative error = 0.004108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.968 Order of pole (given) = 0.5 0 NO 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=11167.7MB, alloc=52.3MB, time=137.66 x[1] = -0.7579 1.535 h = 0.0001 0.005 y[1] (numeric) = 0.14850737471 0.550721540621 y[1] (closed_form) = 0.148514508679 0.550744954859 absolute error = 2.448e-05 relative error = 0.004291 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.975 Order of pole (given) = 0.5 0 NO 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=11213.5MB, alloc=52.3MB, time=138.22 x[1] = -0.7578 1.54 h = 0.0001 0.003 y[1] (numeric) = 0.147717717132 0.552702342377 y[1] (closed_form) = 0.147724649059 0.552725024137 absolute error = 2.372e-05 relative error = 0.004145 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.979 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7577 1.543 h = 0.001 0.001 y[1] (numeric) = 0.147258312403 0.553897899552 y[1] (closed_form) = 0.147265486946 0.553920409656 absolute error = 2.363e-05 relative error = 0.004122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.981 Order of pole (given) = 0.5 0 NO 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=11259.1MB, alloc=52.3MB, time=138.78 x[1] = -0.7567 1.544 h = 0.001 0.003 y[1] (numeric) = 0.147485013585 0.554457388739 y[1] (closed_form) = 0.147492277958 0.554479774397 absolute error = 2.353e-05 relative error = 0.004102 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.982 Order of pole (given) = 0.5 0 NO 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=11304.9MB, alloc=52.3MB, time=139.33 x[1] = -0.7557 1.547 h = 0.0001 0.004 y[1] (numeric) = 0.147379283513 0.555803348627 y[1] (closed_form) = 0.147386354654 0.555825980224 absolute error = 2.371e-05 relative error = 0.004123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.985 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7556 1.551 h = 0.003 0.006 y[1] (numeric) = 0.146752272409 0.557394068979 y[1] (closed_form) = 0.146759079691 0.557416667721 absolute error = 2.360e-05 relative error = 0.004095 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.989 Order of pole (given) = 0.5 0 NO 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=11350.6MB, alloc=52.3MB, time=139.89 x[1] = -0.7526 1.557 h = 0.0001 0.005 y[1] (numeric) = 0.146931584438 0.560257400534 y[1] (closed_form) = 0.146938893701 0.560281051902 absolute error = 2.476e-05 relative error = 0.004274 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.995 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7525 1.562 h = 0.0001 0.003 y[1] (numeric) = 0.146134464743 0.562246525833 y[1] (closed_form) = 0.146141570029 0.562269449879 absolute error = 2.400e-05 relative error = 0.004131 % Correct digits = 4 Radius of convergence (given) for eq 1 = 1.999 Order of pole (given) = 0.5 0 NO 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=11396.3MB, alloc=52.3MB, time=140.45 x[1] = -0.7524 1.565 h = 0.001 0.001 y[1] (numeric) = 0.145670657768 0.563447141162 y[1] (closed_form) = 0.145678003518 0.563469893528 absolute error = 2.391e-05 relative error = 0.004108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.001 Order of pole (given) = 0.5 0 NO 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=11442.1MB, alloc=52.3MB, time=141.01 x[1] = -0.7514 1.566 h = 0.001 0.003 y[1] (numeric) = 0.14589747377 0.564009786151 y[1] (closed_form) = 0.145904908296 0.56403241442 absolute error = 2.382e-05 relative error = 0.004088 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.003 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7504 1.569 h = 0.0001 0.004 y[1] (numeric) = 0.145788816636 0.565362169309 y[1] (closed_form) = 0.145796060105 0.565385042895 absolute error = 2.399e-05 relative error = 0.004109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.006 Order of pole (given) = 0.5 0 NO 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=11487.7MB, alloc=52.3MB, time=141.57 x[1] = -0.7503 1.573 h = 0.003 0.006 y[1] (numeric) = 0.145155898666 0.566959576155 y[1] (closed_form) = 0.145162879681 0.566982418195 absolute error = 2.389e-05 relative error = 0.004081 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.009 Order of pole (given) = 0.5 0 NO 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=11533.5MB, alloc=52.3MB, time=142.13 x[1] = -0.7473 1.579 h = 0.0001 0.005 y[1] (numeric) = 0.145331026715 0.569837255209 y[1] (closed_form) = 0.14533851122 0.569861141606 absolute error = 2.503e-05 relative error = 0.004256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.016 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7472 1.584 h = 0.0001 0.003 y[1] (numeric) = 0.144526523778 0.571834686991 y[1] (closed_form) = 0.144533802434 0.571857851162 absolute error = 2.428e-05 relative error = 0.004117 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.02 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 memory used=11579.2MB, alloc=52.3MB, time=142.68 x[1] = -0.7471 1.587 h = 0.001 0.001 y[1] (numeric) = 0.144058361641 0.573040349495 y[1] (closed_form) = 0.144065878641 0.573063341978 absolute error = 2.419e-05 relative error = 0.004094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.022 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7461 1.588 h = 0.0001 0.004 y[1] (numeric) = 0.1442853051 0.573606131365 y[1] (closed_form) = 0.144292909838 0.573629000101 absolute error = 2.410e-05 relative error = 0.004074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.023 Order of pole (given) = 0.5 0 NO 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=11624.8MB, alloc=52.3MB, time=143.24 x[1] = -0.746 1.592 h = 0.003 0.006 y[1] (numeric) = 0.143647592617 0.5752089869 y[1] (closed_form) = 0.143654616903 0.575232051377 absolute error = 2.411e-05 relative error = 0.004067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.027 Order of pole (given) = 0.5 0 NO 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=11670.6MB, alloc=52.3MB, time=143.80 x[1] = -0.743 1.598 h = 0.0001 0.005 y[1] (numeric) = 0.143819017205 0.578098914425 y[1] (closed_form) = 0.143826546315 0.578123016245 absolute error = 2.525e-05 relative error = 0.004238 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.033 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7429 1.603 h = 0.0001 0.003 y[1] (numeric) = 0.143008122572 0.580103395571 y[1] (closed_form) = 0.143015444211 0.580126779483 absolute error = 2.450e-05 relative error = 0.004101 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.037 Order of pole (given) = 0.5 0 NO 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=11716.3MB, alloc=52.3MB, time=144.36 x[1] = -0.7428 1.606 h = 0.001 0.001 y[1] (numeric) = 0.142536188854 0.58131334247 y[1] (closed_form) = 0.142543747035 0.581336554673 absolute error = 2.441e-05 relative error = 0.004078 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.04 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 memory used=11762.1MB, alloc=52.3MB, time=144.92 x[1] = -0.7418 1.607 h = 0.001 0.003 y[1] (numeric) = 0.142763214844 0.581881811169 y[1] (closed_form) = 0.14277085988 0.581904899914 absolute error = 2.432e-05 relative error = 0.004059 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.041 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7408 1.61 h = 0.0001 0.004 y[1] (numeric) = 0.142649152315 0.583246045984 y[1] (closed_form) = 0.142656610255 0.583269378902 absolute error = 2.450e-05 relative error = 0.00408 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.044 Order of pole (given) = 0.5 0 NO 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=11807.8MB, alloc=52.3MB, time=145.48 x[1] = -0.7407 1.614 h = 0.003 0.006 y[1] (numeric) = 0.142005329634 0.584855788438 y[1] (closed_form) = 0.14201252769 0.584879092188 absolute error = 2.439e-05 relative error = 0.004052 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.047 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7377 1.62 h = 0.0001 0.005 y[1] (numeric) = 0.14217272713 0.587759941834 y[1] (closed_form) = 0.142180431376 0.587784274854 absolute error = 2.552e-05 relative error = 0.004221 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.054 Order of pole (given) = 0.5 0 NO 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=11853.6MB, alloc=52.3MB, time=146.04 x[1] = -0.7376 1.625 h = 0.0001 0.003 y[1] (numeric) = 0.141354592967 0.589772697855 y[1] (closed_form) = 0.141362087983 0.589796317954 absolute error = 2.478e-05 relative error = 0.004086 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.058 Order of pole (given) = 0.5 0 NO 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=11899.3MB, alloc=52.3MB, time=146.60 x[1] = -0.7375 1.628 h = 0.001 0.001 y[1] (numeric) = 0.140878389873 0.590987671616 y[1] (closed_form) = 0.140886119365 0.591011120023 absolute error = 2.469e-05 relative error = 0.004064 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.06 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] = -0.7365 1.629 h = 0.001 0.003 y[1] (numeric) = 0.141105566243 0.591559242615 y[1] (closed_form) = 0.141113381584 0.591582567919 absolute error = 2.460e-05 relative error = 0.004045 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.062 Order of pole (given) = 0.5 0 NO 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=11944.9MB, alloc=52.3MB, time=147.16 x[1] = -0.7355 1.632 h = 0.0001 0.004 y[1] (numeric) = 0.14098870125 0.592929829397 y[1] (closed_form) = 0.140996331571 0.592953398237 absolute error = 2.477e-05 relative error = 0.004065 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.065 Order of pole (given) = 0.5 0 NO 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=11990.7MB, alloc=52.3MB, time=147.72 x[1] = -0.7354 1.636 h = 0.003 0.006 y[1] (numeric) = 0.140339148339 0.594546218062 y[1] (closed_form) = 0.14034652015 0.594569758964 absolute error = 2.467e-05 relative error = 0.004038 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.068 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7324 1.642 h = 0.0001 0.005 y[1] (numeric) = 0.140502600325 0.597464531946 y[1] (closed_form) = 0.14051047962 0.59748909415 absolute error = 2.580e-05 relative error = 0.004203 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.074 Order of pole (given) = 0.5 0 NO 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=12036.4MB, alloc=52.3MB, time=148.28 x[1] = -0.7323 1.647 h = 0.0001 0.003 y[1] (numeric) = 0.139677302048 0.599485544977 y[1] (closed_form) = 0.139684970411 0.599509399189 absolute error = 2.506e-05 relative error = 0.00407 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.078 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7322 1.65 h = 0.001 0.001 y[1] (numeric) = 0.139196874585 0.600705534176 y[1] (closed_form) = 0.139204775387 0.600729216728 absolute error = 2.497e-05 relative error = 0.004049 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.081 Order of pole (given) = 0.5 0 NO 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=12082.0MB, alloc=52.3MB, time=148.83 x[1] = -0.7312 1.651 h = 0.001 0.003 y[1] (numeric) = 0.139424213116 0.601280189071 y[1] (closed_form) = 0.139432198777 0.601303748875 absolute error = 2.488e-05 relative error = 0.00403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.082 Order of pole (given) = 0.5 0 NO 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=12127.8MB, alloc=52.3MB, time=149.39 x[1] = -0.7302 1.654 h = 0.0001 0.004 y[1] (numeric) = 0.139304587618 0.602657102838 y[1] (closed_form) = 0.139312390303 0.602680905537 absolute error = 2.505e-05 relative error = 0.004049 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.085 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7301 1.658 h = 0.003 0.006 y[1] (numeric) = 0.138649364323 0.604280122977 y[1] (closed_form) = 0.138656909859 0.604303898942 absolute error = 2.494e-05 relative error = 0.004023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.088 Order of pole (given) = 0.5 0 NO 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=12173.6MB, alloc=52.3MB, time=149.95 x[1] = -0.7271 1.664 h = 0.0001 0.005 y[1] (numeric) = 0.138808950823 0.607212532347 y[1] (closed_form) = 0.138817005069 0.607237321748 absolute error = 2.607e-05 relative error = 0.004184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.095 Order of pole (given) = 0.5 0 NO 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=12219.2MB, alloc=52.3MB, time=150.50 x[1] = -0.727 1.669 h = 0.0001 0.003 y[1] (numeric) = 0.137976562688 0.609241784284 y[1] (closed_form) = 0.137984404355 0.609265870565 absolute error = 2.533e-05 relative error = 0.004055 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.099 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7269 1.672 h = 0.001 0.001 y[1] (numeric) = 0.137491955168 0.610466777368 y[1] (closed_form) = 0.137500027264 0.610490692031 absolute error = 2.524e-05 relative error = 0.004033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.102 Order of pole (given) = 0.5 0 NO 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=12264.9MB, alloc=52.3MB, time=151.06 x[1] = -0.7259 1.673 h = 0.001 0.003 y[1] (numeric) = 0.137719467359 0.611044497931 y[1] (closed_form) = 0.137727623341 0.611068290204 absolute error = 2.515e-05 relative error = 0.004015 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.103 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7249 1.676 h = 0.0001 0.004 y[1] (numeric) = 0.137597122577 0.612427713778 y[1] (closed_form) = 0.137605097594 0.6124517483 absolute error = 2.532e-05 relative error = 0.004034 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.106 Order of pole (given) = 0.5 0 NO 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=12310.7MB, alloc=52.3MB, time=151.62 x[1] = -0.7248 1.68 h = 0.003 0.006 y[1] (numeric) = 0.136936287823 0.614057350475 y[1] (closed_form) = 0.136944007042 0.614081359442 absolute error = 2.522e-05 relative error = 0.004008 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.109 Order of pole (given) = 0.5 0 NO 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=12356.5MB, alloc=52.3MB, time=152.18 x[1] = -0.7218 1.686 h = 0.0001 0.005 y[1] (numeric) = 0.137092087344 0.617003790714 y[1] (closed_form) = 0.137100316432 0.617028805351 absolute error = 2.633e-05 relative error = 0.004166 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.116 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7217 1.691 h = 0.0001 0.003 y[1] (numeric) = 0.136252682475 0.619041263231 y[1] (closed_form) = 0.136260697389 0.619065579564 absolute error = 2.560e-05 relative error = 0.004039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.12 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=12402.0MB, alloc=52.3MB, time=152.74 x[1] = -0.7216 1.694 h = 0.001 0.001 y[1] (numeric) = 0.135763938526 0.620271248524 y[1] (closed_form) = 0.135772181889 0.620295393294 absolute error = 2.551e-05 relative error = 0.004018 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.122 Order of pole (given) = 0.5 0 NO 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=12447.7MB, alloc=52.3MB, time=153.30 x[1] = -0.7206 1.695 h = 0.0001 0.004 y[1] (numeric) = 0.135991635606 0.620852016706 y[1] (closed_form) = 0.135999961896 0.620876039445 absolute error = 2.542e-05 relative error = 0.004 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.124 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7205 1.699 h = 0.003 0.006 y[1] (numeric) = 0.135326244641 0.622487044637 y[1] (closed_form) = 0.135334010255 0.622511268936 absolute error = 2.544e-05 relative error = 0.003993 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.127 Order of pole (given) = 0.5 0 NO 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=12493.3MB, alloc=52.3MB, time=153.85 x[1] = -0.7175 1.705 h = 0.0001 0.005 y[1] (numeric) = 0.135478680101 0.625445466872 y[1] (closed_form) = 0.135486956622 0.625470690247 absolute error = 2.655e-05 relative error = 0.004148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.134 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7174 1.71 h = 0.0001 0.003 y[1] (numeric) = 0.134633195546 0.627489918138 y[1] (closed_form) = 0.134641256505 0.627514447291 absolute error = 2.582e-05 relative error = 0.004023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.138 Order of pole (given) = 0.5 0 NO 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=12538.9MB, alloc=52.3MB, time=154.41 x[1] = -0.7173 1.713 h = 0.001 0.001 y[1] (numeric) = 0.134140866252 0.628724142545 y[1] (closed_form) = 0.134149153975 0.628748500169 absolute error = 2.573e-05 relative error = 0.004002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.14 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=12584.6MB, alloc=52.3MB, time=154.97 x[1] = -0.7163 1.714 h = 0.001 0.003 y[1] (numeric) = 0.134368695252 0.629307522077 y[1] (closed_form) = 0.134377065086 0.629331757968 absolute error = 2.564e-05 relative error = 0.003984 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.141 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7153 1.717 h = 0.0001 0.004 y[1] (numeric) = 0.134241323393 0.630702367348 y[1] (closed_form) = 0.134249515929 0.6307268443 absolute error = 2.581e-05 relative error = 0.004003 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.144 Order of pole (given) = 0.5 0 NO 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=12630.3MB, alloc=52.3MB, time=155.52 x[1] = -0.7152 1.721 h = 0.003 0.006 y[1] (numeric) = 0.1335701224 0.63234421043 y[1] (closed_form) = 0.133578061609 0.632368663972 absolute error = 2.571e-05 relative error = 0.003978 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.148 Order of pole (given) = 0.5 0 NO 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=12675.9MB, alloc=52.3MB, time=156.08 x[1] = -0.7122 1.727 h = 0.0001 0.005 y[1] (numeric) = 0.133718913825 0.635316545239 y[1] (closed_form) = 0.133727364983 0.635341990273 absolute error = 2.681e-05 relative error = 0.00413 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.154 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7121 1.732 h = 0.0001 0.003 y[1] (numeric) = 0.132866545891 0.637369183285 y[1] (closed_form) = 0.132874779987 0.637393938811 absolute error = 2.609e-05 relative error = 0.004007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.158 Order of pole (given) = 0.5 0 NO 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=12721.7MB, alloc=52.3MB, time=156.64 x[1] = -0.712 1.735 h = 0.001 0.001 y[1] (numeric) = 0.132370159738 0.638608378388 y[1] (closed_form) = 0.132378618667 0.638632962461 absolute error = 2.600e-05 relative error = 0.003986 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.161 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.711 1.736 h = 0.001 0.003 y[1] (numeric) = 0.13259819403 0.639194772547 y[1] (closed_form) = 0.132606734139 0.639219235247 absolute error = 2.591e-05 relative error = 0.003969 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.162 Order of pole (given) = 0.5 0 NO 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=12767.5MB, alloc=52.3MB, time=157.20 x[1] = -0.71 1.739 h = 0.0001 0.004 y[1] (numeric) = 0.132468217178 0.640595849574 y[1] (closed_form) = 0.132476581912 0.640620552679 absolute error = 2.608e-05 relative error = 0.003987 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.165 Order of pole (given) = 0.5 0 NO 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=12813.3MB, alloc=52.3MB, time=157.76 x[1] = -0.7099 1.743 h = 0.003 0.006 y[1] (numeric) = 0.131791568582 0.642244266335 y[1] (closed_form) = 0.13179968131 0.642268947142 absolute error = 2.598e-05 relative error = 0.003962 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.169 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7069 1.749 h = 0.0001 0.005 y[1] (numeric) = 0.131936790355 0.645230450218 y[1] (closed_form) = 0.131945416013 0.645256115026 absolute error = 2.708e-05 relative error = 0.004111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.175 Order of pole (given) = 0.5 0 NO 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=12859.0MB, alloc=52.3MB, time=158.32 x[1] = -0.7068 1.754 h = 0.0001 0.003 y[1] (numeric) = 0.13107760906 0.647291256156 y[1] (closed_form) = 0.131086016205 0.647316236117 absolute error = 2.636e-05 relative error = 0.003991 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.179 Order of pole (given) = 0.5 0 NO 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=12904.6MB, alloc=52.3MB, time=158.88 x[1] = -0.7067 1.757 h = 0.001 0.001 y[1] (numeric) = 0.130577207814 0.648535409975 y[1] (closed_form) = 0.130585837886 0.648560218569 absolute error = 2.627e-05 relative error = 0.00397 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.182 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7057 1.758 h = 0.001 0.003 y[1] (numeric) = 0.13080545789 0.649124801207 y[1] (closed_form) = 0.130814168226 0.649149488789 absolute error = 2.618e-05 relative error = 0.003953 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.183 Order of pole (given) = 0.5 0 NO 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=12950.3MB, alloc=52.3MB, time=159.43 x[1] = -0.7047 1.761 h = 0.0001 0.004 y[1] (numeric) = 0.130672914575 0.650532085416 y[1] (closed_form) = 0.130681451431 0.650557012745 absolute error = 2.635e-05 relative error = 0.003971 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.186 Order of pole (given) = 0.5 0 NO 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=12996.0MB, alloc=52.3MB, time=159.99 x[1] = -0.7046 1.765 h = 0.003 0.006 y[1] (numeric) = 0.129990873939 0.652187060356 y[1] (closed_form) = 0.129999160097 0.652211966475 absolute error = 2.625e-05 relative error = 0.003947 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.189 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.7016 1.771 h = 0.0001 0.005 y[1] (numeric) = 0.130132599073 0.655187030216 y[1] (closed_form) = 0.130141399086 0.655212912939 absolute error = 2.734e-05 relative error = 0.004092 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.196 Order of pole (given) = 0.5 0 NO 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=13041.6MB, alloc=52.3MB, time=160.55 x[1] = -0.7015 1.776 h = 0.0001 0.003 y[1] (numeric) = 0.129266673393 0.657255984993 y[1] (closed_form) = 0.129275253487 0.657281187476 absolute error = 2.662e-05 relative error = 0.003974 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.2 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] = -0.7014 1.779 h = 0.001 0.001 y[1] (numeric) = 0.128762298196 0.658505085461 y[1] (closed_form) = 0.128771099339 0.658530116675 absolute error = 2.653e-05 relative error = 0.003954 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.203 Order of pole (given) = 0.5 0 NO 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=13087.3MB, alloc=52.3MB, time=161.10 x[1] = -0.7004 1.78 h = 0.001 0.003 y[1] (numeric) = 0.128990774303 0.659097456384 y[1] (closed_form) = 0.128999654809 0.659122366948 absolute error = 2.645e-05 relative error = 0.003938 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.204 Order of pole (given) = 0.5 0 NO 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=13133.0MB, alloc=52.3MB, time=161.67 x[1] = -0.6994 1.783 h = 0.0001 0.004 y[1] (numeric) = 0.128855702402 0.660510923298 y[1] (closed_form) = 0.128864411291 0.660536072948 absolute error = 2.661e-05 relative error = 0.003955 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.207 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6993 1.787 h = 0.003 0.006 y[1] (numeric) = 0.128168324462 0.662172440796 y[1] (closed_form) = 0.128176783952 0.662197570302 absolute error = 2.652e-05 relative error = 0.003931 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.21 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=13178.6MB, alloc=52.3MB, time=162.22 x[1] = -0.6963 1.793 h = 0.0001 0.005 y[1] (numeric) = 0.128306624638 0.665186133943 y[1] (closed_form) = 0.128315598853 0.665212232748 absolute error = 2.760e-05 relative error = 0.004074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.217 Order of pole (given) = 0.5 0 NO 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=13224.4MB, alloc=52.3MB, time=162.78 x[1] = -0.6962 1.798 h = 0.0001 0.003 y[1] (numeric) = 0.12743402253 0.667263218356 y[1] (closed_form) = 0.127442775467 0.667288641475 absolute error = 2.689e-05 relative error = 0.003958 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.221 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6961 1.801 h = 0.001 0.001 y[1] (numeric) = 0.126925713915 0.668517253328 y[1] (closed_form) = 0.126934686045 0.668542505285 absolute error = 2.680e-05 relative error = 0.003938 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.223 Order of pole (given) = 0.5 0 NO 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=13270.0MB, alloc=52.3MB, time=163.34 x[1] = -0.6951 1.802 h = 0.0001 0.004 y[1] (numeric) = 0.127154426067 0.669112586727 y[1] (closed_form) = 0.127163476671 0.669137718396 absolute error = 2.671e-05 relative error = 0.003922 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.225 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.695 1.806 h = 0.003 0.006 y[1] (numeric) = 0.126462713192 0.670779434872 y[1] (closed_form) = 0.12647122179 0.670804772981 absolute error = 2.673e-05 relative error = 0.003916 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.228 Order of pole (given) = 0.5 0 NO 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=13315.7MB, alloc=52.3MB, time=163.90 x[1] = -0.692 1.812 h = 0.0001 0.005 y[1] (numeric) = 0.126597959222 0.673804851019 y[1] (closed_form) = 0.126606983337 0.673831152221 absolute error = 2.781e-05 relative error = 0.004056 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.235 Order of pole (given) = 0.5 0 NO 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=13361.4MB, alloc=52.3MB, time=164.45 x[1] = -0.6919 1.817 h = 0.0001 0.003 y[1] (numeric) = 0.1257195674 0.67588883922 y[1] (closed_form) = 0.125728369047 0.6759144686 absolute error = 2.710e-05 relative error = 0.003942 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.239 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6918 1.82 h = 0.001 0.001 y[1] (numeric) = 0.125207846447 0.677147065658 y[1] (closed_form) = 0.12521686571 0.677172523953 absolute error = 2.701e-05 relative error = 0.003922 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.241 Order of pole (given) = 0.5 0 NO 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=13407.0MB, alloc=52.3MB, time=165.01 x[1] = -0.6908 1.821 h = 0.001 0.003 y[1] (numeric) = 0.125436734608 0.677744938372 y[1] (closed_form) = 0.125445831589 0.67777027668 absolute error = 2.692e-05 relative error = 0.003906 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.243 Order of pole (given) = 0.5 0 NO 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=13452.7MB, alloc=52.3MB, time=165.56 x[1] = -0.6898 1.824 h = 0.0001 0.004 y[1] (numeric) = 0.125296983264 0.679169815983 y[1] (closed_form) = 0.125305912032 0.679195392163 absolute error = 2.709e-05 relative error = 0.003922 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.246 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6897 1.828 h = 0.003 0.006 y[1] (numeric) = 0.124599739287 0.680843403626 y[1] (closed_form) = 0.12460842103 0.680868961606 absolute error = 2.699e-05 relative error = 0.0039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.249 Order of pole (given) = 0.5 0 NO 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=13498.4MB, alloc=52.3MB, time=166.12 x[1] = -0.6867 1.834 h = 0.0001 0.005 y[1] (numeric) = 0.124731691045 0.683882428315 y[1] (closed_form) = 0.124740889076 0.68390894225 absolute error = 2.806e-05 relative error = 0.004037 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.256 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6866 1.839 h = 0.0001 0.003 y[1] (numeric) = 0.123846746845 0.685974510839 y[1] (closed_form) = 0.123855721129 0.686000357413 absolute error = 2.736e-05 relative error = 0.003925 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.26 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=13544.1MB, alloc=52.3MB, time=166.68 x[1] = -0.6865 1.842 h = 0.001 0.001 y[1] (numeric) = 0.12333116646 0.687237649459 y[1] (closed_form) = 0.12334035655 0.687263325069 absolute error = 2.727e-05 relative error = 0.003906 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.262 Order of pole (given) = 0.5 0 NO 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=13589.8MB, alloc=52.3MB, time=167.25 x[1] = -0.6855 1.843 h = 0.001 0.003 y[1] (numeric) = 0.123560308895 0.687838453175 y[1] (closed_form) = 0.12356957584 0.687864009162 absolute error = 2.718e-05 relative error = 0.00389 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.264 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6845 1.846 h = 0.0001 0.004 y[1] (numeric) = 0.123418134129 0.689269444473 y[1] (closed_form) = 0.123427234649 0.689295237666 absolute error = 2.735e-05 relative error = 0.003906 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.267 Order of pole (given) = 0.5 0 NO 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=13635.5MB, alloc=52.3MB, time=167.82 x[1] = -0.6844 1.85 h = 0.003 0.006 y[1] (numeric) = 0.122715705228 0.690949530023 y[1] (closed_form) = 0.122724559988 0.690975306023 absolute error = 2.725e-05 relative error = 0.003884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.27 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=13681.3MB, alloc=52.3MB, time=168.39 x[1] = -0.6814 1.856 h = 0.0001 0.005 y[1] (numeric) = 0.12284443076 0.694002101725 y[1] (closed_form) = 0.122853802532 0.694028826627 absolute error = 2.832e-05 relative error = 0.004018 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.277 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6813 1.861 h = 0.0001 0.003 y[1] (numeric) = 0.121952999348 0.696102258992 y[1] (closed_form) = 0.121962146134 0.696128320943 absolute error = 2.762e-05 relative error = 0.003908 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.281 Order of pole (given) = 0.5 0 NO 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=13727.0MB, alloc=52.3MB, time=168.95 x[1] = -0.6812 1.864 h = 0.001 0.001 y[1] (numeric) = 0.121433598388 0.697370297449 y[1] (closed_form) = 0.121442959195 0.697396188569 absolute error = 2.753e-05 relative error = 0.003889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.283 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6802 1.865 h = 0.001 0.003 y[1] (numeric) = 0.121663004472 0.697974015425 y[1] (closed_form) = 0.121672441284 0.697999787284 absolute error = 2.745e-05 relative error = 0.003874 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.285 Order of pole (given) = 0.5 0 NO 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=13772.7MB, alloc=52.3MB, time=169.51 x[1] = -0.6792 1.868 h = 0.0001 0.004 y[1] (numeric) = 0.121518441777 0.699411096339 y[1] (closed_form) = 0.121527713923 0.699437104736 absolute error = 2.761e-05 relative error = 0.003889 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.288 Order of pole (given) = 0.5 0 NO 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=13818.4MB, alloc=52.3MB, time=170.07 x[1] = -0.6791 1.872 h = 0.003 0.006 y[1] (numeric) = 0.120810879664 0.701097663787 y[1] (closed_form) = 0.120819907308 0.701123655978 absolute error = 2.752e-05 relative error = 0.003867 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.291 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6761 1.878 h = 0.0001 0.005 y[1] (numeric) = 0.120936445812 0.704163721385 y[1] (closed_form) = 0.120945991142 0.704190655513 absolute error = 2.858e-05 relative error = 0.003999 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.298 Order of pole (given) = 0.5 0 NO 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=13864.2MB, alloc=52.3MB, time=170.63 x[1] = -0.676 1.883 h = 0.0001 0.003 y[1] (numeric) = 0.120038591418 0.706271933705 y[1] (closed_form) = 0.120047910563 0.706298209244 absolute error = 2.788e-05 relative error = 0.003891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.302 Order of pole (given) = 0.5 0 NO 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=13910.0MB, alloc=52.3MB, time=171.20 x[1] = -0.6759 1.886 h = 0.001 0.001 y[1] (numeric) = 0.119515408177 0.707544859604 y[1] (closed_form) = 0.119524939581 0.707570964451 absolute error = 2.779e-05 relative error = 0.003873 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.304 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6749 1.887 h = 0.001 0.003 y[1] (numeric) = 0.119745087077 0.708151475259 y[1] (closed_form) = 0.119754693649 0.708177461207 absolute error = 2.770e-05 relative error = 0.003857 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.306 Order of pole (given) = 0.5 0 NO 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=13955.6MB, alloc=52.3MB, time=171.93 x[1] = -0.6739 1.89 h = 0.0001 0.004 y[1] (numeric) = 0.119598171362 0.709594621829 y[1] (closed_form) = 0.119607615002 0.709620843648 absolute error = 2.787e-05 relative error = 0.003873 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.309 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6738 1.894 h = 0.003 0.006 y[1] (numeric) = 0.11888552701 0.711287655089 y[1] (closed_form) = 0.118894727393 0.711313861669 absolute error = 2.777e-05 relative error = 0.003851 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.312 Order of pole (given) = 0.5 0 NO 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=14001.4MB, alloc=52.3MB, time=172.51 x[1] = -0.6708 1.9 h = 0.0001 0.005 y[1] (numeric) = 0.119007999438 0.714367137881 y[1] (closed_form) = 0.119017718137 0.714394279516 absolute error = 2.883e-05 relative error = 0.003981 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.319 Order of pole (given) = 0.5 0 NO 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=14047.2MB, alloc=52.3MB, time=173.10 x[1] = -0.6707 1.905 h = 0.0001 0.003 y[1] (numeric) = 0.118103785373 0.716483385471 y[1] (closed_form) = 0.118113276726 0.716509872829 absolute error = 2.814e-05 relative error = 0.003875 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.323 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6706 1.908 h = 0.001 0.001 y[1] (numeric) = 0.117576857599 0.717761186366 y[1] (closed_form) = 0.117586559472 0.717787503179 absolute error = 2.805e-05 relative error = 0.003856 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.325 Order of pole (given) = 0.5 0 NO 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=14092.8MB, alloc=52.3MB, time=173.69 x[1] = -0.6696 1.909 h = 0.0001 0.004 y[1] (numeric) = 0.117806818274 0.718370683279 y[1] (closed_form) = 0.117816594491 0.718396881556 absolute error = 2.796e-05 relative error = 0.003841 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.327 Order of pole (given) = 0.5 0 NO 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=14138.5MB, alloc=52.3MB, time=174.28 x[1] = -0.6695 1.913 h = 0.003 0.006 y[1] (numeric) = 0.117090044959 0.720068984497 y[1] (closed_form) = 0.117099296816 0.720095393305 absolute error = 2.798e-05 relative error = 0.003836 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.33 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] = -0.6665 1.919 h = 0.0001 0.005 y[1] (numeric) = 0.117209747178 0.723159939145 y[1] (closed_form) = 0.117219517936 0.723187277157 absolute error = 2.903e-05 relative error = 0.003963 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.337 Order of pole (given) = 0.5 0 NO 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=14184.2MB, alloc=52.3MB, time=174.87 x[1] = -0.6664 1.924 h = 0.0001 0.003 y[1] (numeric) = 0.11630001354 0.725283012571 y[1] (closed_form) = 0.116309555933 0.725309699966 absolute error = 2.834e-05 relative error = 0.003858 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.341 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6663 1.927 h = 0.001 0.001 y[1] (numeric) = 0.115769834544 0.726564955698 y[1] (closed_form) = 0.115779585976 0.726591472661 absolute error = 2.825e-05 relative error = 0.00384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.344 Order of pole (given) = 0.5 0 NO 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=14229.9MB, alloc=52.3MB, time=175.46 x[1] = -0.6653 1.928 h = 0.001 0.003 y[1] (numeric) = 0.116000010729 0.727176923171 y[1] (closed_form) = 0.1160098358 0.727203321901 absolute error = 2.817e-05 relative error = 0.003825 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.345 Order of pole (given) = 0.5 0 NO 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=14275.7MB, alloc=52.3MB, time=176.06 x[1] = -0.6643 1.931 h = 0.0001 0.004 y[1] (numeric) = 0.115848735988 0.728631266068 y[1] (closed_form) = 0.115858401295 0.728657899442 absolute error = 2.833e-05 relative error = 0.00384 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.348 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6642 1.935 h = 0.003 0.006 y[1] (numeric) = 0.115126691393 0.730336228511 y[1] (closed_form) = 0.115136115723 0.730362848412 absolute error = 2.824e-05 relative error = 0.003819 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.351 Order of pole (given) = 0.5 0 NO 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=14321.5MB, alloc=52.3MB, time=176.64 x[1] = -0.6612 1.941 h = 0.0001 0.005 y[1] (numeric) = 0.115243419758 0.733440497251 y[1] (closed_form) = 0.115253363538 0.733468039627 absolute error = 2.928e-05 relative error = 0.003944 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.358 Order of pole (given) = 0.5 0 NO 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=14367.2MB, alloc=52.3MB, time=177.24 x[1] = -0.6611 1.946 h = 0.0001 0.003 y[1] (numeric) = 0.114327442123 0.735571569634 y[1] (closed_form) = 0.114337156445 0.73559846562 absolute error = 2.860e-05 relative error = 0.003841 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.362 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.661 1.949 h = 0.001 0.001 y[1] (numeric) = 0.113793587559 0.736858364923 y[1] (closed_form) = 0.113803509223 0.736885090636 absolute error = 2.851e-05 relative error = 0.003823 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.365 Order of pole (given) = 0.5 0 NO 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=14413.0MB, alloc=52.3MB, time=177.84 x[1] = -0.66 1.95 h = 0.001 0.003 y[1] (numeric) = 0.114024061863 0.73747318362 y[1] (closed_form) = 0.114034056363 0.737499791462 absolute error = 2.842e-05 relative error = 0.003809 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.366 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.659 1.953 h = 0.0001 0.004 y[1] (numeric) = 0.113870531163 0.738933524669 y[1] (closed_form) = 0.113880367561 0.738960366485 absolute error = 2.859e-05 relative error = 0.003823 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.369 Order of pole (given) = 0.5 0 NO 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=14458.9MB, alloc=52.3MB, time=178.45 x[1] = -0.6589 1.957 h = 0.003 0.006 y[1] (numeric) = 0.113143546378 0.740644907127 y[1] (closed_form) = 0.113153143017 0.740671736386 absolute error = 2.849e-05 relative error = 0.003803 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.372 Order of pole (given) = 0.5 0 NO 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=14504.4MB, alloc=52.3MB, time=179.04 x[1] = -0.6559 1.963 h = 0.0001 0.005 y[1] (numeric) = 0.113257363342 0.743762430427 y[1] (closed_form) = 0.113267479937 0.743790175511 absolute error = 2.953e-05 relative error = 0.003925 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.379 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6558 1.968 h = 0.0001 0.003 y[1] (numeric) = 0.112335202507 0.745901481747 y[1] (closed_form) = 0.112345088586 0.74592858462 absolute error = 2.885e-05 relative error = 0.003824 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.383 Order of pole (given) = 0.5 0 NO 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=14550.1MB, alloc=52.3MB, time=179.64 x[1] = -0.6557 1.971 h = 0.001 0.001 y[1] (numeric) = 0.111797708613 0.747193116636 y[1] (closed_form) = 0.111807800358 0.747220049403 absolute error = 2.876e-05 relative error = 0.003807 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.386 Order of pole (given) = 0.5 0 NO 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=14595.9MB, alloc=52.3MB, time=180.25 x[1] = -0.6547 1.972 h = 0.001 0.003 y[1] (numeric) = 0.112028489443 0.747810770581 y[1] (closed_form) = 0.112038653234 0.747837585839 absolute error = 2.868e-05 relative error = 0.003792 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.387 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6537 1.975 h = 0.0001 0.004 y[1] (numeric) = 0.111872735571 0.749277086273 y[1] (closed_form) = 0.1118827429 0.749304134833 absolute error = 2.884e-05 relative error = 0.003807 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.39 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=14641.6MB, alloc=52.3MB, time=180.85 x[1] = -0.6536 1.979 h = 0.003 0.006 y[1] (numeric) = 0.111140858847 0.750994872422 y[1] (closed_form) = 0.111150627622 0.751021909324 absolute error = 2.875e-05 relative error = 0.003787 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.394 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6506 1.985 h = 0.0001 0.005 y[1] (numeric) = 0.111251825795 0.754125591163 y[1] (closed_form) = 0.111262114992 0.75415353732 absolute error = 2.978e-05 relative error = 0.003907 % Correct digits = 4 memory used=14687.3MB, alloc=52.3MB, time=181.45 Radius of convergence (given) for eq 1 = 2.4 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] = -0.6505 1.99 h = 0.0001 0.003 y[1] (numeric) = 0.110323541712 0.756272601336 y[1] (closed_form) = 0.11033359937 0.756299909414 absolute error = 2.910e-05 relative error = 0.003808 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.404 Order of pole (given) = 0.5 0 NO 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=14733.0MB, alloc=52.3MB, time=182.05 x[1] = -0.6504 1.993 h = 0.001 0.001 y[1] (numeric) = 0.109782444222 0.757569063234 y[1] (closed_form) = 0.109792705891 0.757596201381 absolute error = 2.901e-05 relative error = 0.00379 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.407 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6494 1.994 h = 0.001 0.003 y[1] (numeric) = 0.1100135398 0.758189536604 y[1] (closed_form) = 0.110023872736 0.758216557602 absolute error = 2.893e-05 relative error = 0.003776 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.408 Order of pole (given) = 0.5 0 NO 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=14778.7MB, alloc=52.3MB, time=182.66 x[1] = -0.6484 1.997 h = 0.0001 0.004 y[1] (numeric) = 0.109855595028 0.759661803549 y[1] (closed_form) = 0.109865773118 0.75968905718 absolute error = 2.909e-05 relative error = 0.00379 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.411 Order of pole (given) = 0.5 0 NO 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=14824.4MB, alloc=52.3MB, time=183.26 x[1] = -0.6483 2.001 h = 0.003 0.006 y[1] (numeric) = 0.109118873944 0.761385977024 y[1] (closed_form) = 0.109128814676 0.761413219877 absolute error = 2.900e-05 relative error = 0.00377 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.415 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6453 2.007 h = 0.0001 0.005 y[1] (numeric) = 0.109227051217 0.7645298325 y[1] (closed_form) = 0.1092375128 0.764557978115 absolute error = 3.003e-05 relative error = 0.003888 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.421 Order of pole (given) = 0.5 0 NO 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=14869.9MB, alloc=52.3MB, time=183.84 x[1] = -0.6452 2.012 h = 0.0001 0.003 y[1] (numeric) = 0.108292703011 0.766684781386 y[1] (closed_form) = 0.108302932065 0.766712293009 absolute error = 2.935e-05 relative error = 0.003791 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.426 Order of pole (given) = 0.5 0 NO 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=14915.7MB, alloc=52.3MB, time=184.42 x[1] = -0.6451 2.015 h = 0.001 0.001 y[1] (numeric) = 0.107748037163 0.767986057677 y[1] (closed_form) = 0.107758468594 0.768013399549 absolute error = 2.926e-05 relative error = 0.003773 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.428 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6441 2.016 h = 0.0001 0.004 y[1] (numeric) = 0.107979455536 0.768609334799 y[1] (closed_form) = 0.107989957465 0.768636559884 absolute error = 2.918e-05 relative error = 0.003759 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.43 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=14961.4MB, alloc=52.3MB, time=185.00 x[1] = -0.644 2.02 h = 0.003 0.006 y[1] (numeric) = 0.107238797682 0.770338712222 y[1] (closed_form) = 0.107248791952 0.770366151256 absolute error = 2.920e-05 relative error = 0.003755 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.433 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.641 2.026 h = 0.0001 0.005 y[1] (numeric) = 0.107344465698 0.773493796395 y[1] (closed_form) = 0.107354981235 0.773522132665 absolute error = 3.022e-05 relative error = 0.00387 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.44 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=15007.0MB, alloc=52.3MB, time=185.59 x[1] = -0.6409 2.031 h = 0.0001 0.003 y[1] (numeric) = 0.106404850186 0.775655491202 y[1] (closed_form) = 0.106415132318 0.775683196954 absolute error = 2.955e-05 relative error = 0.003774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.444 Order of pole (given) = 0.5 0 NO 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=15052.8MB, alloc=52.3MB, time=186.17 x[1] = -0.6408 2.034 h = 0.001 0.001 y[1] (numeric) = 0.105857083517 0.7769608595 y[1] (closed_form) = 0.105867566633 0.776988395641 absolute error = 2.946e-05 relative error = 0.003757 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.446 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6398 2.035 h = 0.001 0.003 y[1] (numeric) = 0.106088752904 0.777586541535 y[1] (closed_form) = 0.106099305863 0.77761396119 absolute error = 2.938e-05 relative error = 0.003744 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.448 Order of pole (given) = 0.5 0 NO 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=15098.4MB, alloc=52.3MB, time=186.76 x[1] = -0.6388 2.038 h = 0.0001 0.004 y[1] (numeric) = 0.105926745302 0.779069795333 y[1] (closed_form) = 0.105937146369 0.779097446391 absolute error = 2.954e-05 relative error = 0.003757 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.451 Order of pole (given) = 0.5 0 NO 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=15144.1MB, alloc=52.3MB, time=187.35 x[1] = -0.6387 2.042 h = 0.003 0.006 y[1] (numeric) = 0.105181058771 0.780805754046 y[1] (closed_form) = 0.105191224669 0.780833395937 absolute error = 2.945e-05 relative error = 0.003738 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.454 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6357 2.048 h = 0.0001 0.005 y[1] (numeric) = 0.105284047394 0.783973867497 y[1] (closed_form) = 0.105294734919 0.784002400271 absolute error = 3.047e-05 relative error = 0.003852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.461 Order of pole (given) = 0.5 0 NO 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=15189.8MB, alloc=52.3MB, time=187.92 x[1] = -0.6356 2.053 h = 0.0001 0.003 y[1] (numeric) = 0.104338475876 0.786143464099 y[1] (closed_form) = 0.104348929064 0.786171370362 absolute error = 2.980e-05 relative error = 0.003758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.465 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6355 2.056 h = 0.001 0.001 y[1] (numeric) = 0.103787205287 0.78745362367 y[1] (closed_form) = 0.103797857862 0.787481360512 absolute error = 2.971e-05 relative error = 0.003741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.468 Order of pole (given) = 0.5 0 NO 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=15235.6MB, alloc=52.3MB, time=188.50 x[1] = -0.6345 2.057 h = 0.001 0.003 y[1] (numeric) = 0.104019212165 0.788082080781 y[1] (closed_form) = 0.104029933835 0.788109701497 absolute error = 2.963e-05 relative error = 0.003727 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.469 Order of pole (given) = 0.5 0 NO 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=15281.5MB, alloc=52.3MB, time=189.07 x[1] = -0.6335 2.06 h = 0.0001 0.004 y[1] (numeric) = 0.103855103497 0.78957121997 y[1] (closed_form) = 0.103865674827 0.789599071418 absolute error = 2.979e-05 relative error = 0.003741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.472 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6334 2.064 h = 0.003 0.006 y[1] (numeric) = 0.103104705344 0.791313519538 y[1] (closed_form) = 0.103115042673 0.791341362655 absolute error = 2.970e-05 relative error = 0.003722 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.475 Order of pole (given) = 0.5 0 NO 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=15327.1MB, alloc=52.3MB, time=189.67 x[1] = -0.6304 2.07 h = 0.0001 0.005 y[1] (numeric) = 0.103205072064 0.794494604723 y[1] (closed_form) = 0.103215931345 0.794523332442 absolute error = 3.071e-05 relative error = 0.003833 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.482 Order of pole (given) = 0.5 0 NO 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=15372.8MB, alloc=52.3MB, time=190.24 x[1] = -0.6303 2.075 h = 0.0001 0.003 y[1] (numeric) = 0.102253601393 0.796672082849 y[1] (closed_form) = 0.102264225436 0.796700188021 absolute error = 3.005e-05 relative error = 0.003741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.486 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6302 2.078 h = 0.001 0.001 y[1] (numeric) = 0.10169886076 0.797987021022 y[1] (closed_form) = 0.101709682614 0.798014956969 absolute error = 2.996e-05 relative error = 0.003724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.489 Order of pole (given) = 0.5 0 NO 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=15418.4MB, alloc=52.3MB, time=190.89 x[1] = -0.6292 2.079 h = 0.001 0.003 y[1] (numeric) = 0.101931212691 0.798618237955 y[1] (closed_form) = 0.101942102902 0.798646058136 absolute error = 2.988e-05 relative error = 0.003711 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.49 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] = -0.6282 2.082 h = 0.0001 0.004 y[1] (numeric) = 0.101765033334 0.80011323962 y[1] (closed_form) = 0.101775774736 0.800141289864 absolute error = 3.004e-05 relative error = 0.003724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.493 Order of pole (given) = 0.5 0 NO 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=15464.1MB, alloc=52.3MB, time=191.46 x[1] = -0.6281 2.086 h = 0.003 0.006 y[1] (numeric) = 0.10100996868 0.801861863554 y[1] (closed_form) = 0.101020477239 0.801889906286 absolute error = 2.995e-05 relative error = 0.003705 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.497 Order of pole (given) = 0.5 0 NO 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=15509.7MB, alloc=52.3MB, time=192.04 x[1] = -0.6251 2.092 h = 0.0001 0.005 y[1] (numeric) = 0.101107770039 0.805055863332 y[1] (closed_form) = 0.101118800842 0.805084784458 absolute error = 3.095e-05 relative error = 0.003815 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.503 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.625 2.097 h = 0.0001 0.003 y[1] (numeric) = 0.100150456305 0.807241202682 y[1] (closed_form) = 0.100161250997 0.807269505183 absolute error = 3.029e-05 relative error = 0.003724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.508 Order of pole (given) = 0.5 0 NO 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=15555.5MB, alloc=52.3MB, time=192.61 x[1] = -0.6249 2.1 h = 0.001 0.001 y[1] (numeric) = 0.0995922790484 0.808560906776 y[1] (closed_form) = 0.0996032699943 0.808589040253 absolute error = 3.020e-05 relative error = 0.003707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.51 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=15601.3MB, alloc=52.3MB, time=193.18 x[1] = -0.6239 2.101 h = 0.001 0.003 y[1] (numeric) = 0.0998249834329 0.809194868422 y[1] (closed_form) = 0.0998360420093 0.80922288649 absolute error = 3.012e-05 relative error = 0.003694 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.512 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6229 2.104 h = 0.0001 0.004 y[1] (numeric) = 0.0996567632995 0.810695709774 y[1] (closed_form) = 0.0996676745761 0.810723957236 absolute error = 3.028e-05 relative error = 0.003707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.515 Order of pole (given) = 0.5 0 NO 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=15646.9MB, alloc=52.3MB, time=193.75 x[1] = -0.6228 2.108 h = 0.003 0.006 y[1] (numeric) = 0.098897076662 0.812450641565 y[1] (closed_form) = 0.0989077562439 0.81247888232 absolute error = 3.019e-05 relative error = 0.003689 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.518 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6198 2.114 h = 0.0001 0.005 y[1] (numeric) = 0.0989923682753 0.815657499201 y[1] (closed_form) = 0.0990035703612 0.815686612213 absolute error = 3.119e-05 relative error = 0.003796 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.525 Order of pole (given) = 0.5 0 NO 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=15692.6MB, alloc=52.3MB, time=194.32 x[1] = -0.6197 2.119 h = 0.0001 0.003 y[1] (numeric) = 0.0980292668201 0.81785067945 y[1] (closed_form) = 0.0980402319504 0.817879177718 absolute error = 3.053e-05 relative error = 0.003707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.529 Order of pole (given) = 0.5 0 NO 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=15738.3MB, alloc=52.3MB, time=194.90 x[1] = -0.6196 2.122 h = 0.001 0.001 y[1] (numeric) = 0.0974676859123 0.819175136778 y[1] (closed_form) = 0.0974788457581 0.819203466227 absolute error = 3.045e-05 relative error = 0.003691 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.531 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6186 2.123 h = 0.0001 0.004 y[1] (numeric) = 0.0977007499954 0.819811828167 y[1] (closed_form) = 0.0977119767546 0.819840042566 absolute error = 3.037e-05 relative error = 0.003678 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.533 Order of pole (given) = 0.5 0 NO 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=15784.0MB, alloc=52.3MB, time=195.48 x[1] = -0.6185 2.127 h = 0.003 0.006 y[1] (numeric) = 0.0969373063412 0.821571899168 y[1] (closed_form) = 0.0969480412683 0.821600330361 absolute error = 3.039e-05 relative error = 0.003673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.536 Order of pole (given) = 0.5 0 NO 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=15829.7MB, alloc=52.3MB, time=196.05 x[1] = -0.6155 2.133 h = 0.0001 0.005 y[1] (numeric) = 0.0970303292402 0.824789750284 y[1] (closed_form) = 0.0970415869423 0.824819048508 absolute error = 3.139e-05 relative error = 0.003779 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.543 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6154 2.138 h = 0.0001 0.003 y[1] (numeric) = 0.0960621965931 0.826989595368 y[1] (closed_form) = 0.0960732165892 0.827018282147 absolute error = 3.073e-05 relative error = 0.003691 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.547 Order of pole (given) = 0.5 0 NO 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=15875.5MB, alloc=52.3MB, time=196.64 x[1] = -0.6153 2.141 h = 0.001 0.001 y[1] (numeric) = 0.0954976555899 0.828318093939 y[1] (closed_form) = 0.0955088689896 0.828346612061 absolute error = 3.064e-05 relative error = 0.003675 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.55 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] = -0.6143 2.142 h = 0.001 0.003 y[1] (numeric) = 0.0957310026985 0.82895712752 y[1] (closed_form) = 0.0957422823982 0.828985530891 absolute error = 3.056e-05 relative error = 0.003662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.551 Order of pole (given) = 0.5 0 NO 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=15921.1MB, alloc=52.3MB, time=197.21 x[1] = -0.6133 2.145 h = 0.0001 0.004 y[1] (numeric) = 0.0955589942991 0.83046875146 y[1] (closed_form) = 0.0955701294618 0.830497383 absolute error = 3.072e-05 relative error = 0.003675 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.554 Order of pole (given) = 0.5 0 NO 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=15966.9MB, alloc=52.3MB, time=197.80 x[1] = -0.6132 2.149 h = 0.003 0.006 y[1] (numeric) = 0.0947907490165 0.832235322887 y[1] (closed_form) = 0.0948016545864 0.832263949192 absolute error = 3.063e-05 relative error = 0.003657 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.558 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6102 2.155 h = 0.0001 0.005 y[1] (numeric) = 0.0948813639239 0.835465927996 y[1] (closed_form) = 0.0948927924712 0.835495415324 absolute error = 3.162e-05 relative error = 0.003761 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.564 Order of pole (given) = 0.5 0 NO 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=16012.6MB, alloc=52.3MB, time=198.38 x[1] = -0.6101 2.16 h = 0.0001 0.003 y[1] (numeric) = 0.0939075448375 0.837673576752 y[1] (closed_form) = 0.093918734885 0.837702456441 absolute error = 3.097e-05 relative error = 0.003674 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.569 Order of pole (given) = 0.5 0 NO 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=16058.4MB, alloc=52.3MB, time=198.96 x[1] = -0.61 2.163 h = 0.001 0.001 y[1] (numeric) = 0.0933396605281 0.839006805319 y[1] (closed_form) = 0.0933510424751 0.839035516565 absolute error = 3.089e-05 relative error = 0.003658 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.571 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.609 2.164 h = 0.001 0.003 y[1] (numeric) = 0.0935733805899 0.839648541244 y[1] (closed_form) = 0.0935848281382 0.839677138095 absolute error = 3.080e-05 relative error = 0.003646 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.573 Order of pole (given) = 0.5 0 NO 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=16104.0MB, alloc=52.3MB, time=199.53 x[1] = -0.608 2.167 h = 0.0001 0.004 y[1] (numeric) = 0.0933994147861 0.841165940718 y[1] (closed_form) = 0.0934107192493 0.841194765071 absolute error = 3.096e-05 relative error = 0.003658 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.576 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6079 2.171 h = 0.003 0.006 y[1] (numeric) = 0.0926266718359 0.84293877322 y[1] (closed_form) = 0.0926377478276 0.842967593102 absolute error = 3.087e-05 relative error = 0.003641 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.579 Order of pole (given) = 0.5 0 NO 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=16149.7MB, alloc=52.3MB, time=200.11 x[1] = -0.6049 2.177 h = 0.0001 0.005 y[1] (numeric) = 0.0927149318255 0.846182076721 y[1] (closed_form) = 0.0927265309679 0.846211751685 absolute error = 3.186e-05 relative error = 0.003743 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.586 Order of pole (given) = 0.5 0 NO 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=16195.5MB, alloc=52.3MB, time=200.69 x[1] = -0.6048 2.182 h = 0.0001 0.003 y[1] (numeric) = 0.0917354795841 0.848397508777 y[1] (closed_form) = 0.091746839459 0.848426579866 absolute error = 3.121e-05 relative error = 0.003657 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.59 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] = -0.6047 2.185 h = 0.001 0.001 y[1] (numeric) = 0.0911642837094 0.849735454643 y[1] (closed_form) = 0.0911758339977 0.849764357508 absolute error = 3.113e-05 relative error = 0.003642 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.593 Order of pole (given) = 0.5 0 NO 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=16241.1MB, alloc=52.3MB, time=201.27 x[1] = -0.6037 2.186 h = 0.001 0.003 y[1] (numeric) = 0.0913983835441 0.850379878336 y[1] (closed_form) = 0.0914099987444 0.850408667161 absolute error = 3.104e-05 relative error = 0.00363 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.594 Order of pole (given) = 0.5 0 NO 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=16286.8MB, alloc=52.3MB, time=201.84 x[1] = -0.6027 2.189 h = 0.0001 0.004 y[1] (numeric) = 0.0912224885518 0.851903031041 y[1] (closed_form) = 0.0912339620996 0.851932046702 absolute error = 3.120e-05 relative error = 0.003642 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.597 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.6026 2.193 h = 0.003 0.006 y[1] (numeric) = 0.0904452902265 0.853682108071 y[1] (closed_form) = 0.0904565364148 0.853711120014 absolute error = 3.112e-05 relative error = 0.003624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.6 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=16332.6MB, alloc=52.3MB, time=202.42 x[1] = -0.5996 2.199 h = 0.0001 0.005 y[1] (numeric) = 0.0905312475244 0.85693805476 y[1] (closed_form) = 0.0905430170087 0.856967915908 absolute error = 3.210e-05 relative error = 0.003725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.607 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5995 2.204 h = 0.0001 0.003 y[1] (numeric) = 0.0895462147208 0.859161249737 y[1] (closed_form) = 0.0895577441948 0.859190510737 absolute error = 3.145e-05 relative error = 0.003641 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.611 Order of pole (given) = 0.5 0 NO 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=16378.4MB, alloc=52.3MB, time=202.99 x[1] = -0.5994 2.207 h = 0.001 0.001 y[1] (numeric) = 0.0889717386077 0.860503900208 y[1] (closed_form) = 0.0889834570267 0.860532993207 absolute error = 3.136e-05 relative error = 0.003625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.614 Order of pole (given) = 0.5 0 NO 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=16424.1MB, alloc=52.3MB, time=203.59 x[1] = -0.5984 2.208 h = 0.001 0.003 y[1] (numeric) = 0.0892062248938 0.861150997229 y[1] (closed_form) = 0.0892180075448 0.861179976542 absolute error = 3.128e-05 relative error = 0.003613 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.615 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5974 2.211 h = 0.0001 0.004 y[1] (numeric) = 0.0890284285131 0.862679880988 y[1] (closed_form) = 0.0890400709252 0.862709086474 absolute error = 3.144e-05 relative error = 0.003625 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.618 Order of pole (given) = 0.5 0 NO 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=16469.7MB, alloc=52.3MB, time=204.17 x[1] = -0.5973 2.215 h = 0.003 0.006 y[1] (numeric) = 0.0882468165565 0.864465186003 y[1] (closed_form) = 0.0882582327118 0.864494388506 absolute error = 3.135e-05 relative error = 0.003608 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.622 Order of pole (given) = 0.5 0 NO 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=16515.5MB, alloc=52.3MB, time=204.76 x[1] = -0.5943 2.221 h = 0.0001 0.005 y[1] (numeric) = 0.0883305225606 0.867733721066 y[1] (closed_form) = 0.0883424621302 0.867763766965 absolute error = 3.233e-05 relative error = 0.003707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.628 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5942 2.226 h = 0.0001 0.003 y[1] (numeric) = 0.087339961109 0.869964658584 y[1] (closed_form) = 0.08735165995 0.869994108024 absolute error = 3.169e-05 relative error = 0.003624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.633 Order of pole (given) = 0.5 0 NO 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=16561.2MB, alloc=52.3MB, time=205.32 x[1] = -0.5941 2.229 h = 0.001 0.001 y[1] (numeric) = 0.0867622356786 0.871312000975 y[1] (closed_form) = 0.0867741220135 0.871341282639 absolute error = 3.160e-05 relative error = 0.003609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.635 Order of pole (given) = 0.5 0 NO 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=16606.9MB, alloc=52.3MB, time=205.89 x[1] = -0.5931 2.23 h = 0.0001 0.004 y[1] (numeric) = 0.0869971149576 0.871961757015 y[1] (closed_form) = 0.0870090648535 0.871990925347 absolute error = 3.152e-05 relative error = 0.003597 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.637 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.593 2.234 h = 0.003 0.006 y[1] (numeric) = 0.0862119144786 0.873752136224 y[1] (closed_form) = 0.0862233875636 0.873781523703 absolute error = 3.155e-05 relative error = 0.003593 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.64 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=16652.4MB, alloc=52.3MB, time=206.45 x[1] = -0.59 2.24 h = 0.0001 0.005 y[1] (numeric) = 0.0862935741123 0.877031437347 y[1] (closed_form) = 0.0863055707605 0.877061663273 absolute error = 3.252e-05 relative error = 0.00369 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.647 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5899 2.245 h = 0.0001 0.003 y[1] (numeric) = 0.0852982029498 0.879268958042 y[1] (closed_form) = 0.0853099582267 0.879298590646 absolute error = 3.188e-05 relative error = 0.003609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.651 Order of pole (given) = 0.5 0 NO 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=16698.0MB, alloc=52.3MB, time=207.02 x[1] = -0.5898 2.248 h = 0.001 0.001 y[1] (numeric) = 0.0847176493876 0.880620290715 y[1] (closed_form) = 0.0847295909203 0.880649755725 absolute error = 3.179e-05 relative error = 0.003594 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.654 Order of pole (given) = 0.5 0 NO 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=16743.8MB, alloc=52.3MB, time=207.60 x[1] = -0.5888 2.249 h = 0.001 0.003 y[1] (numeric) = 0.0849528406329 0.881272328978 y[1] (closed_form) = 0.0849648451522 0.88130168095 absolute error = 3.171e-05 relative error = 0.003582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.655 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5878 2.252 h = 0.0001 0.004 y[1] (numeric) = 0.0847715111642 0.882811796423 y[1] (closed_form) = 0.0847833780337 0.882841373351 absolute error = 3.187e-05 relative error = 0.003593 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.658 Order of pole (given) = 0.5 0 NO 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=16789.4MB, alloc=52.3MB, time=208.17 x[1] = -0.5877 2.256 h = 0.003 0.006 y[1] (numeric) = 0.0839817220152 0.884608594819 y[1] (closed_form) = 0.0839933646472 0.884638170115 absolute error = 3.178e-05 relative error = 0.003577 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.662 Order of pole (given) = 0.5 0 NO 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=16835.0MB, alloc=52.3MB, time=208.75 x[1] = -0.5847 2.262 h = 0.0001 0.005 y[1] (numeric) = 0.0840612244958 0.88790038395 y[1] (closed_form) = 0.0840733907605 0.887930792 absolute error = 3.275e-05 relative error = 0.003672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.668 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5846 2.267 h = 0.0001 0.003 y[1] (numeric) = 0.0830604197684 0.890145609878 y[1] (closed_form) = 0.0830723439876 0.890175428225 absolute error = 3.211e-05 relative error = 0.003592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.673 Order of pole (given) = 0.5 0 NO 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=16880.7MB, alloc=52.3MB, time=209.33 x[1] = -0.5845 2.27 h = 0.001 0.001 y[1] (numeric) = 0.0824766735236 0.891501611245 y[1] (closed_form) = 0.0824887825788 0.891531262231 absolute error = 3.203e-05 relative error = 0.003577 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.675 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5835 2.271 h = 0.001 0.003 y[1] (numeric) = 0.0827122697471 0.892156282324 y[1] (closed_form) = 0.0827244411344 0.892185820623 absolute error = 3.195e-05 relative error = 0.003566 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.677 Order of pole (given) = 0.5 0 NO 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=16926.4MB, alloc=52.3MB, time=209.90 x[1] = -0.5825 2.274 h = 0.0001 0.004 y[1] (numeric) = 0.0825291164597 0.893701418405 y[1] (closed_form) = 0.0825411515585 0.893731181 absolute error = 3.210e-05 relative error = 0.003577 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.68 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=16972.0MB, alloc=52.3MB, time=210.48 x[1] = -0.5824 2.278 h = 0.003 0.006 y[1] (numeric) = 0.0817350303609 0.895504397963 y[1] (closed_form) = 0.0817468422995 0.895534159627 absolute error = 3.202e-05 relative error = 0.003561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.683 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5794 2.284 h = 0.0001 0.005 y[1] (numeric) = 0.0818124248133 0.898808621389 y[1] (closed_form) = 0.0818247604294 0.898839210177 absolute error = 3.298e-05 relative error = 0.003654 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.69 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=17017.8MB, alloc=52.3MB, time=211.06 x[1] = -0.5793 2.289 h = 0.0001 0.003 y[1] (numeric) = 0.0808062365673 0.901061532183 y[1] (closed_form) = 0.080818329486 0.90109153485 absolute error = 3.235e-05 relative error = 0.003576 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.694 Order of pole (given) = 0.5 0 NO 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=17063.5MB, alloc=52.3MB, time=211.64 x[1] = -0.5792 2.292 h = 0.001 0.001 y[1] (numeric) = 0.080219327443 0.902422189584 y[1] (closed_form) = 0.0802316037944 0.902452025126 absolute error = 3.226e-05 relative error = 0.003561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.697 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5782 2.293 h = 0.001 0.003 y[1] (numeric) = 0.0804553348105 0.903079479539 y[1] (closed_form) = 0.0804676728483 0.903109202745 absolute error = 3.218e-05 relative error = 0.003549 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.698 Order of pole (given) = 0.5 0 NO 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=17109.2MB, alloc=52.3MB, time=212.22 x[1] = -0.5772 2.296 h = 0.0001 0.004 y[1] (numeric) = 0.0802703839785 0.904630262568 y[1] (closed_form) = 0.0802825870716 0.90466020941 absolute error = 3.234e-05 relative error = 0.003561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.701 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5771 2.3 h = 0.003 0.006 y[1] (numeric) = 0.0794720406542 0.906439406771 y[1] (closed_form) = 0.0794840216552 0.906469353372 absolute error = 3.225e-05 relative error = 0.003545 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.705 Order of pole (given) = 0.5 0 NO 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=17154.9MB, alloc=52.3MB, time=212.80 x[1] = -0.5741 2.306 h = 0.0001 0.005 y[1] (numeric) = 0.079547375444 0.909756011161 y[1] (closed_form) = 0.0795598801439 0.909786779316 absolute error = 3.321e-05 relative error = 0.003637 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.711 Order of pole (given) = 0.5 0 NO 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=17200.6MB, alloc=52.3MB, time=213.37 x[1] = -0.574 2.311 h = 0.0001 0.003 y[1] (numeric) = 0.0785358530965 0.912016586469 y[1] (closed_form) = 0.0785481144689 0.912046772049 absolute error = 3.258e-05 relative error = 0.003559 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.716 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5739 2.314 h = 0.001 0.001 y[1] (numeric) = 0.0779458105197 0.913381887256 y[1] (closed_form) = 0.0779582539378 0.913411905951 absolute error = 3.250e-05 relative error = 0.003545 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.718 Order of pole (given) = 0.5 0 NO 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=17246.2MB, alloc=52.3MB, time=213.95 x[1] = -0.5729 2.315 h = 0.001 0.003 y[1] (numeric) = 0.0781822350729 0.914041782274 y[1] (closed_form) = 0.0781947395399 0.914071688982 absolute error = 3.242e-05 relative error = 0.003533 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.72 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=17291.9MB, alloc=52.3MB, time=214.53 x[1] = -0.5719 2.318 h = 0.0001 0.004 y[1] (numeric) = 0.0779955125954 0.915598190689 y[1] (closed_form) = 0.0780078834442 0.915628320376 absolute error = 3.257e-05 relative error = 0.003544 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.723 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5718 2.322 h = 0.003 0.006 y[1] (numeric) = 0.077192951271 0.917413483035 y[1] (closed_form) = 0.0772051010874 0.917443613158 absolute error = 3.249e-05 relative error = 0.003529 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.726 Order of pole (given) = 0.5 0 NO 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=17337.5MB, alloc=52.3MB, time=215.11 x[1] = -0.5688 2.328 h = 0.0001 0.005 y[1] (numeric) = 0.0772662740214 0.920742415437 y[1] (closed_form) = 0.0772789475347 0.920773361605 absolute error = 3.344e-05 relative error = 0.003619 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.733 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5687 2.333 h = 0.0001 0.003 y[1] (numeric) = 0.0762494663727 0.923010634922 y[1] (closed_form) = 0.0762618959498 0.923041002026 absolute error = 3.281e-05 relative error = 0.003543 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.737 Order of pole (given) = 0.5 0 NO 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=17383.2MB, alloc=52.3MB, time=215.70 x[1] = -0.5686 2.336 h = 0.001 0.001 y[1] (numeric) = 0.0756563194016 0.924380566466 y[1] (closed_form) = 0.0756689296531 0.924410766927 absolute error = 3.273e-05 relative error = 0.003529 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.74 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=17428.8MB, alloc=52.3MB, time=216.28 x[1] = -0.5676 2.337 h = 0.0001 0.004 y[1] (numeric) = 0.0758931670605 0.925043052857 y[1] (closed_form) = 0.0759058377318 0.925073141679 absolute error = 3.265e-05 relative error = 0.003517 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.741 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5675 2.341 h = 0.003 0.006 y[1] (numeric) = 0.0750871754897 0.926863354443 y[1] (closed_form) = 0.0750993836261 0.926893664344 absolute error = 3.268e-05 relative error = 0.003514 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.745 Order of pole (given) = 0.5 0 NO 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=17474.5MB, alloc=52.3MB, time=216.86 x[1] = -0.5645 2.347 h = 0.0001 0.005 y[1] (numeric) = 0.0751586579239 0.930202833063 y[1] (closed_form) = 0.0751713898027 0.930233954313 absolute error = 3.362e-05 relative error = 0.003603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.751 Order of pole (given) = 0.5 0 NO 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=17520.2MB, alloc=52.3MB, time=217.44 x[1] = -0.5644 2.352 h = 0.0001 0.003 y[1] (numeric) = 0.074137248752 0.932477553954 y[1] (closed_form) = 0.0741497361457 0.932508099127 absolute error = 3.300e-05 relative error = 0.003528 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.756 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5643 2.355 h = 0.001 0.001 y[1] (numeric) = 0.073541397657 0.933851424883 y[1] (closed_form) = 0.0735540645543 0.933881803609 absolute error = 3.291e-05 relative error = 0.003514 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.758 Order of pole (given) = 0.5 0 NO 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=17565.9MB, alloc=52.3MB, time=218.02 x[1] = -0.5633 2.356 h = 0.001 0.003 y[1] (numeric) = 0.0737785835126 0.934516136108 y[1] (closed_form) = 0.0737913102906 0.934546403486 absolute error = 3.283e-05 relative error = 0.003502 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.76 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] = -0.5623 2.359 h = 0.0001 0.004 y[1] (numeric) = 0.0735885656875 0.93608293471 y[1] (closed_form) = 0.0736011612787 0.936113423864 absolute error = 3.299e-05 relative error = 0.003513 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.763 Order of pole (given) = 0.5 0 NO 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=17611.6MB, alloc=52.3MB, time=218.60 x[1] = -0.5622 2.363 h = 0.003 0.006 y[1] (numeric) = 0.0727781856075 0.937909574292 y[1] (closed_form) = 0.0727905621073 0.937940065123 absolute error = 3.291e-05 relative error = 0.003498 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.766 Order of pole (given) = 0.5 0 NO 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=17657.2MB, alloc=52.3MB, time=219.18 x[1] = -0.5592 2.369 h = 0.0001 0.005 y[1] (numeric) = 0.072847743316 0.941261283939 y[1] (closed_form) = 0.072860643515 0.941292580718 absolute error = 3.385e-05 relative error = 0.003586 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.773 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5591 2.374 h = 0.0001 0.003 y[1] (numeric) = 0.071821138289 0.943543611788 y[1] (closed_form) = 0.0718337934324 0.943574335937 absolute error = 3.323e-05 relative error = 0.003511 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.777 Order of pole (given) = 0.5 0 NO 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=17702.7MB, alloc=52.3MB, time=219.76 x[1] = -0.559 2.377 h = 0.001 0.001 y[1] (numeric) = 0.0712222360616 0.944922090357 y[1] (closed_form) = 0.0712350693662 0.944952648307 absolute error = 3.314e-05 relative error = 0.003497 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.78 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=17748.5MB, alloc=52.3MB, time=220.34 x[1] = -0.558 2.378 h = 0.001 0.003 y[1] (numeric) = 0.0714598558855 0.945589367875 y[1] (closed_form) = 0.0714727484566 0.945619814822 absolute error = 3.306e-05 relative error = 0.003487 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.781 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.557 2.381 h = 0.0001 0.004 y[1] (numeric) = 0.0712681387576 0.947161731175 y[1] (closed_form) = 0.0712809014209 0.947192399245 absolute error = 3.322e-05 relative error = 0.003497 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.784 Order of pole (given) = 0.5 0 NO 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=17794.1MB, alloc=52.3MB, time=220.92 x[1] = -0.5569 2.385 h = 0.003 0.006 y[1] (numeric) = 0.0704536504184 0.948994472245 y[1] (closed_form) = 0.0704661950256 0.949025142637 absolute error = 3.314e-05 relative error = 0.003482 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.788 Order of pole (given) = 0.5 0 NO 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=17839.8MB, alloc=52.3MB, time=221.50 x[1] = -0.5539 2.391 h = 0.0001 0.005 y[1] (numeric) = 0.0705213289827 0.952358361025 y[1] (closed_form) = 0.0705343972251 0.952389832022 absolute error = 3.408e-05 relative error = 0.003568 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.794 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5538 2.396 h = 0.0001 0.003 y[1] (numeric) = 0.0694895751997 0.954648275557 y[1] (closed_form) = 0.0695023978356 0.954679177335 absolute error = 3.346e-05 relative error = 0.003495 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.799 Order of pole (given) = 0.5 0 NO 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=17885.5MB, alloc=52.3MB, time=222.08 x[1] = -0.5537 2.399 h = 0.001 0.001 y[1] (numeric) = 0.0688876498805 0.956031349188 y[1] (closed_form) = 0.0689006493501 0.956062085018 absolute error = 3.337e-05 relative error = 0.003482 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.801 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5527 2.4 h = 0.001 0.003 y[1] (numeric) = 0.0691257092602 0.956701179653 y[1] (closed_form) = 0.06913876739 0.956731804825 absolute error = 3.329e-05 relative error = 0.003471 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.803 Order of pole (given) = 0.5 0 NO 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=17931.2MB, alloc=52.3MB, time=222.66 x[1] = -0.5517 2.403 h = 0.0001 0.004 y[1] (numeric) = 0.0689323173515 0.958279086573 y[1] (closed_form) = 0.0689452468364 0.958309932217 absolute error = 3.345e-05 relative error = 0.003481 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.806 Order of pole (given) = 0.5 0 NO 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=17976.9MB, alloc=52.3MB, time=223.24 x[1] = -0.5516 2.407 h = 0.003 0.006 y[1] (numeric) = 0.06811375814 0.960117912705 y[1] (closed_form) = 0.0681264705959 0.960148761305 absolute error = 3.337e-05 relative error = 0.003466 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.809 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5486 2.413 h = 0.0001 0.005 y[1] (numeric) = 0.0681796024588 0.963493929092 y[1] (closed_form) = 0.0681928384658 0.96352557301 absolute error = 3.430e-05 relative error = 0.003551 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.816 Order of pole (given) = 0.5 0 NO 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=18022.5MB, alloc=52.3MB, time=223.82 x[1] = -0.5485 2.418 h = 0.0001 0.003 y[1] (numeric) = 0.0671427464458 0.965791410057 y[1] (closed_form) = 0.0671557363142 0.965822488134 absolute error = 3.368e-05 relative error = 0.003479 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.82 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=18068.2MB, alloc=52.3MB, time=224.40 x[1] = -0.5484 2.421 h = 0.001 0.001 y[1] (numeric) = 0.0665378257325 0.967179066194 y[1] (closed_form) = 0.0665509911222 0.967209978576 absolute error = 3.360e-05 relative error = 0.003466 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.823 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5474 2.422 h = 0.001 0.003 y[1] (numeric) = 0.066776330145 0.96785143638 y[1] (closed_form) = 0.0667895535961 0.967882238449 absolute error = 3.352e-05 relative error = 0.003455 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.824 Order of pole (given) = 0.5 0 NO 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=18113.9MB, alloc=52.3MB, time=224.98 x[1] = -0.5464 2.425 h = 0.0001 0.004 y[1] (numeric) = 0.0665812876387 0.969434865966 y[1] (closed_form) = 0.0665943836923 0.969465887858 absolute error = 3.367e-05 relative error = 0.003465 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.827 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5463 2.429 h = 0.003 0.006 y[1] (numeric) = 0.0657586944874 0.97127976076 y[1] (closed_form) = 0.0657715745307 0.971310786231 absolute error = 3.359e-05 relative error = 0.003451 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.831 Order of pole (given) = 0.5 0 NO 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=18159.7MB, alloc=52.3MB, time=225.56 x[1] = -0.5433 2.435 h = 0.0001 0.005 y[1] (numeric) = 0.0658227487908 0.974667853593 y[1] (closed_form) = 0.0658361522815 0.974699669149 absolute error = 3.452e-05 relative error = 0.003534 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.837 Order of pole (given) = 0.5 0 NO 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=18205.4MB, alloc=52.3MB, time=226.15 x[1] = -0.5432 2.44 h = 0.0001 0.003 y[1] (numeric) = 0.0647808365111 0.976972880773 y[1] (closed_form) = 0.0647939933499 0.977004133834 absolute error = 3.391e-05 relative error = 0.003463 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.842 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5431 2.443 h = 0.001 0.001 y[1] (numeric) = 0.0641729477651 0.978365106883 y[1] (closed_form) = 0.064186278827 0.978396194506 absolute error = 3.383e-05 relative error = 0.00345 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.844 Order of pole (given) = 0.5 0 NO 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=18251.1MB, alloc=52.3MB, time=226.73 x[1] = -0.5421 2.444 h = 0.0001 0.004 y[1] (numeric) = 0.0644119025795 0.979040003681 y[1] (closed_form) = 0.0644252911117 0.979070981332 absolute error = 3.375e-05 relative error = 0.003439 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.846 Order of pole (given) = 0.5 0 NO 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=18296.7MB, alloc=52.3MB, time=227.32 x[1] = -0.542 2.448 h = 0.003 0.006 y[1] (numeric) = 0.0635860281573 0.98088984308 y[1] (closed_form) = 0.0635989677413 0.980921043373 absolute error = 3.378e-05 relative error = 0.003436 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.849 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.539 2.454 h = 0.0001 0.005 y[1] (numeric) = 0.0636484335617 0.984288269603 y[1] (closed_form) = 0.0636618965502 0.98432025552 absolute error = 3.470e-05 relative error = 0.003518 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.856 Order of pole (given) = 0.5 0 NO 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=18342.4MB, alloc=52.3MB, time=227.90 x[1] = -0.5389 2.459 h = 0.0001 0.003 y[1] (numeric) = 0.0626021158374 0.986599716653 y[1] (closed_form) = 0.062615331707 0.986631142923 absolute error = 3.409e-05 relative error = 0.003448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.86 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] = -0.5388 2.462 h = 0.001 0.001 y[1] (numeric) = 0.0619916397309 0.98799583151 y[1] (closed_form) = 0.0620050287148 0.988027092549 absolute error = 3.401e-05 relative error = 0.003435 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.863 Order of pole (given) = 0.5 0 NO 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=18388.0MB, alloc=52.3MB, time=228.48 x[1] = -0.5378 2.463 h = 0.001 0.003 y[1] (numeric) = 0.0622309565687 0.988672898171 y[1] (closed_form) = 0.0622444025159 0.988704049524 absolute error = 3.393e-05 relative error = 0.003425 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.864 Order of pole (given) = 0.5 0 NO 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=18433.7MB, alloc=52.3MB, time=229.06 x[1] = -0.5368 2.466 h = 0.0001 0.004 y[1] (numeric) = 0.0620328407157 0.99026652981 y[1] (closed_form) = 0.0620461615534 0.990297899799 absolute error = 3.408e-05 relative error = 0.003435 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.867 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5367 2.47 h = 0.003 0.006 y[1] (numeric) = 0.0612027662883 0.992122626381 y[1] (closed_form) = 0.0612158729826 0.992154001092 absolute error = 3.400e-05 relative error = 0.003421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.871 Order of pole (given) = 0.5 0 NO 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=18479.4MB, alloc=52.3MB, time=229.64 x[1] = -0.5337 2.476 h = 0.0001 0.005 y[1] (numeric) = 0.0612634628473 0.995533035614 y[1] (closed_form) = 0.0612770928071 0.995565190818 absolute error = 3.492e-05 relative error = 0.003501 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.878 Order of pole (given) = 0.5 0 NO 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=18525.3MB, alloc=52.3MB, time=230.22 x[1] = -0.5336 2.481 h = 0.0001 0.003 y[1] (numeric) = 0.0602121731613 0.99785199188 y[1] (closed_form) = 0.0602255555224 0.997883590723 absolute error = 3.432e-05 relative error = 0.003433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.882 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5335 2.484 h = 0.001 0.001 y[1] (numeric) = 0.0595987792095 0.999252653776 y[1] (closed_form) = 0.0596123334133 0.999284087647 absolute error = 3.423e-05 relative error = 0.00342 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.885 Order of pole (given) = 0.5 0 NO 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=18571.0MB, alloc=52.3MB, time=230.80 x[1] = -0.5325 2.485 h = 0.001 0.003 y[1] (numeric) = 0.0598385563145 0.999932223019 y[1] (closed_form) = 0.059852166904 0.999963547544 absolute error = 3.415e-05 relative error = 0.003409 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.886 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5315 2.488 h = 0.0001 0.004 y[1] (numeric) = 0.0596388574806 1.00153131834 y[1] (closed_form) = 0.0596523441647 1.00156286086 absolute error = 3.430e-05 relative error = 0.003419 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.889 Order of pole (given) = 0.5 0 NO 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=18616.7MB, alloc=52.3MB, time=231.38 x[1] = -0.5314 2.492 h = 0.003 0.006 y[1] (numeric) = 0.0588048525263 1.00339343724 y[1] (closed_form) = 0.0588181260627 1.00342498507 absolute error = 3.423e-05 relative error = 0.003405 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.893 Order of pole (given) = 0.5 0 NO 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=18662.4MB, alloc=52.3MB, time=231.96 x[1] = -0.5284 2.498 h = 0.0001 0.005 y[1] (numeric) = 0.0588638826295 1.00681577904 y[1] (closed_form) = 0.0588776792748 1.00684810229 absolute error = 3.514e-05 relative error = 0.003485 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.899 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5283 2.503 h = 0.0001 0.003 y[1] (numeric) = 0.0578076653917 1.00914222439 y[1] (closed_form) = 0.0578212139754 1.00917399454 absolute error = 3.454e-05 relative error = 0.003417 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.904 Order of pole (given) = 0.5 0 NO 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=18708.0MB, alloc=52.3MB, time=232.54 x[1] = -0.5282 2.506 h = 0.001 0.001 y[1] (numeric) = 0.0571913800271 1.01054742087 y[1] (closed_form) = 0.0572050991958 1.0105790263 absolute error = 3.445e-05 relative error = 0.003404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.906 Order of pole (given) = 0.5 0 NO 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=18753.9MB, alloc=52.3MB, time=233.12 x[1] = -0.5272 2.507 h = 0.001 0.003 y[1] (numeric) = 0.0574316224724 1.0112294799 y[1] (closed_form) = 0.0574453974563 1.01126097633 absolute error = 3.438e-05 relative error = 0.003394 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.908 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5262 2.51 h = 0.0001 0.004 y[1] (numeric) = 0.0572303635939 1.01283401843 y[1] (closed_form) = 0.0572440158618 1.01286573221 absolute error = 3.453e-05 relative error = 0.003403 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.911 Order of pole (given) = 0.5 0 NO 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=18799.4MB, alloc=52.3MB, time=233.70 x[1] = -0.5261 2.514 h = 0.003 0.006 y[1] (numeric) = 0.0563924633664 1.01470214337 y[1] (closed_form) = 0.0564059034747 1.01473386305 absolute error = 3.445e-05 relative error = 0.00339 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.914 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5231 2.52 h = 0.0001 0.005 y[1] (numeric) = 0.0564498687871 1.01813636794 y[1] (closed_form) = 0.0564638318304 1.018168858 absolute error = 3.536e-05 relative error = 0.003468 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.921 Order of pole (given) = 0.5 0 NO 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=18845.2MB, alloc=52.3MB, time=234.29 x[1] = -0.523 2.525 h = 0.0001 0.003 y[1] (numeric) = 0.0553887678835 1.0204702823 y[1] (closed_form) = 0.055402482419 1.02050222248 absolute error = 3.476e-05 relative error = 0.003401 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.925 Order of pole (given) = 0.5 0 NO 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=18891.0MB, alloc=52.3MB, time=234.86 x[1] = -0.5229 2.528 h = 0.001 0.001 y[1] (numeric) = 0.0547696172252 1.02188000092 y[1] (closed_form) = 0.0547835011017 1.02191177665 absolute error = 3.468e-05 relative error = 0.003388 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.928 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5219 2.529 h = 0.001 0.003 y[1] (numeric) = 0.0550103299855 1.02256453707 y[1] (closed_form) = 0.0550242691137 1.02259620413 absolute error = 3.460e-05 relative error = 0.003379 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.929 Order of pole (given) = 0.5 0 NO 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=18936.5MB, alloc=52.3MB, time=235.42 x[1] = -0.5209 2.532 h = 0.0001 0.004 y[1] (numeric) = 0.0548075336912 1.02417449845 y[1] (closed_form) = 0.0548213512786 1.02420638222 absolute error = 3.475e-05 relative error = 0.003388 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.932 Order of pole (given) = 0.5 0 NO 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=18982.4MB, alloc=52.3MB, time=236.00 x[1] = -0.5208 2.536 h = 0.003 0.006 y[1] (numeric) = 0.0539657730289 1.02604861317 y[1] (closed_form) = 0.0539793794367 1.02608050342 absolute error = 3.467e-05 relative error = 0.003374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.936 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5178 2.542 h = 0.0001 0.005 y[1] (numeric) = 0.0540215949364 1.02949467106 y[1] (closed_form) = 0.0540357240888 1.02952732672 absolute error = 3.558e-05 relative error = 0.003451 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.943 Order of pole (given) = 0.5 0 NO 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=19028.0MB, alloc=52.3MB, time=236.57 x[1] = -0.5177 2.547 h = 0.0001 0.003 y[1] (numeric) = 0.0529556537383 1.03183603438 y[1] (closed_form) = 0.052969533953 1.03186814335 absolute error = 3.498e-05 relative error = 0.003386 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.947 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5176 2.55 h = 0.001 0.001 y[1] (numeric) = 0.0523336635981 1.03325026274 y[1] (closed_form) = 0.052347711923 1.03328220753 absolute error = 3.490e-05 relative error = 0.003373 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.95 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=19073.8MB, alloc=52.3MB, time=237.15 x[1] = -0.5166 2.551 h = 0.0001 0.004 y[1] (numeric) = 0.0525748515518 1.03393726344 y[1] (closed_form) = 0.0525889545718 1.0339690999 absolute error = 3.482e-05 relative error = 0.003363 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.951 Order of pole (given) = 0.5 0 NO 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=19119.5MB, alloc=52.3MB, time=237.74 x[1] = -0.5165 2.555 h = 0.003 0.006 y[1] (numeric) = 0.0517299501054 1.03581625865 y[1] (closed_form) = 0.0517436171254 1.035848319 absolute error = 3.485e-05 relative error = 0.00336 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.954 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5135 2.561 h = 0.0001 0.005 y[1] (numeric) = 0.0517843013297 1.03927244473 y[1] (closed_form) = 0.0517984909758 1.03930526624 absolute error = 3.576e-05 relative error = 0.003436 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.961 Order of pole (given) = 0.5 0 NO 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=19165.2MB, alloc=52.3MB, time=238.29 x[1] = -0.5134 2.566 h = 0.0001 0.003 y[1] (numeric) = 0.0507141397044 1.04162014688 y[1] (closed_form) = 0.0507280800178 1.04165242442 absolute error = 3.516e-05 relative error = 0.003371 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.966 Order of pole (given) = 0.5 0 NO 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=19210.9MB, alloc=52.3MB, time=238.85 x[1] = -0.5133 2.569 h = 0.001 0.001 y[1] (numeric) = 0.0500896723518 1.04303821376 y[1] (closed_form) = 0.0501037797235 1.04307032733 absolute error = 3.508e-05 relative error = 0.003359 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.968 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5123 2.57 h = 0.001 0.003 y[1] (numeric) = 0.0503312440148 1.04372733162 y[1] (closed_form) = 0.0503454056039 1.04375933714 absolute error = 3.500e-05 relative error = 0.003349 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.97 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 memory used=19256.6MB, alloc=52.3MB, time=239.42 x[1] = -0.5113 2.573 h = 0.0001 0.004 y[1] (numeric) = 0.0501255821185 1.04534731218 y[1] (closed_form) = 0.0501396243238 1.04537953325 absolute error = 3.515e-05 relative error = 0.003358 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.973 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5112 2.577 h = 0.003 0.006 y[1] (numeric) = 0.0492766585238 1.04723248435 y[1] (closed_form) = 0.0492904913464 1.04726471294 absolute error = 3.507e-05 relative error = 0.003345 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.976 Order of pole (given) = 0.5 0 NO 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=19302.3MB, alloc=52.3MB, time=239.98 x[1] = -0.5082 2.583 h = 0.0001 0.005 y[1] (numeric) = 0.0493295018553 1.05070041312 y[1] (closed_form) = 0.0493438570833 1.050733398 absolute error = 3.597e-05 relative error = 0.00342 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.983 Order of pole (given) = 0.5 0 NO 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=19348.0MB, alloc=52.3MB, time=240.53 x[1] = -0.5081 2.588 h = 0.0001 0.003 y[1] (numeric) = 0.0482545795389 1.05305552756 y[1] (closed_form) = 0.0482686850338 1.0530879716 absolute error = 3.538e-05 relative error = 0.003356 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.987 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.508 2.591 h = 0.001 0.001 y[1] (numeric) = 0.0476273200808 1.05447808147 y[1] (closed_form) = 0.0476415914276 1.05451036181 absolute error = 3.529e-05 relative error = 0.003344 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.99 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=19393.6MB, alloc=52.3MB, time=241.09 x[1] = -0.507 2.592 h = 0.001 0.003 y[1] (numeric) = 0.0478693759129 1.05516964084 y[1] (closed_form) = 0.0478837009329 1.05520181346 absolute error = 3.522e-05 relative error = 0.003334 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.991 Order of pole (given) = 0.5 0 NO 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=19439.3MB, alloc=52.3MB, time=241.65 x[1] = -0.506 2.595 h = 0.0001 0.004 y[1] (numeric) = 0.0476622399304 1.05679498693 y[1] (closed_form) = 0.0476764467022 1.05682737447 absolute error = 3.537e-05 relative error = 0.003343 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.994 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5059 2.599 h = 0.003 0.006 y[1] (numeric) = 0.046809553528 1.05868610299 y[1] (closed_form) = 0.0468235518756 1.0587184986 absolute error = 3.529e-05 relative error = 0.00333 % Correct digits = 4 Radius of convergence (given) for eq 1 = 2.998 Order of pole (given) = 0.5 0 NO 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=19485.0MB, alloc=52.3MB, time=242.21 x[1] = -0.5029 2.605 h = 0.0001 0.005 y[1] (numeric) = 0.0468609284707 1.06216572599 y[1] (closed_form) = 0.0468754489878 1.06219887305 absolute error = 3.619e-05 relative error = 0.003404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.005 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5028 2.61 h = 0.0001 0.003 y[1] (numeric) = 0.0457812874122 1.06452823277 y[1] (closed_form) = 0.0457955578107 1.06456084211 absolute error = 3.560e-05 relative error = 0.003341 % Correct digits = 4 memory used=19530.8MB, alloc=52.3MB, time=242.77 Radius of convergence (given) for eq 1 = 3.009 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5027 2.613 h = 0.001 0.001 y[1] (numeric) = 0.04515126081 1.0659552614 y[1] (closed_form) = 0.0451656958669 1.06598770732 absolute error = 3.551e-05 relative error = 0.003328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.012 Order of pole (given) = 0.5 0 NO 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=19576.6MB, alloc=52.3MB, time=243.33 x[1] = -0.5017 2.614 h = 0.001 0.003 y[1] (numeric) = 0.045393805425 1.06664925001 y[1] (closed_form) = 0.0454082936174 1.06668158854 absolute error = 3.544e-05 relative error = 0.003319 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.013 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.5007 2.617 h = 0.0001 0.004 y[1] (numeric) = 0.0451852168521 1.06827994175 y[1] (closed_form) = 0.0451995879184 1.06831249455 absolute error = 3.558e-05 relative error = 0.003328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.016 Order of pole (given) = 0.5 0 NO 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=19622.3MB, alloc=52.3MB, time=243.89 x[1] = -0.5006 2.621 h = 0.003 0.006 y[1] (numeric) = 0.0443288009437 1.07017698558 y[1] (closed_form) = 0.0443429645369 1.070209547 absolute error = 3.551e-05 relative error = 0.003315 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.02 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 memory used=19668.1MB, alloc=52.3MB, time=244.44 x[1] = -0.4976 2.627 h = 0.0001 0.005 y[1] (numeric) = 0.0443787464433 1.07366825466 y[1] (closed_form) = 0.0443934319555 1.07370156274 absolute error = 3.640e-05 relative error = 0.003387 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.026 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4975 2.632 h = 0.0001 0.003 y[1] (numeric) = 0.0432944281111 1.07603813392 y[1] (closed_form) = 0.043308863134 1.07607090735 absolute error = 3.581e-05 relative error = 0.003325 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.031 Order of pole (given) = 0.5 0 NO 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=19713.7MB, alloc=52.3MB, time=245.00 x[1] = -0.4974 2.635 h = 0.001 0.001 y[1] (numeric) = 0.0426616590392 1.07746962498 y[1] (closed_form) = 0.0426762575393 1.07750223527 absolute error = 3.573e-05 relative error = 0.003313 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.033 Order of pole (given) = 0.5 0 NO 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=19759.5MB, alloc=52.3MB, time=245.56 x[1] = -0.4964 2.636 h = 0.001 0.003 y[1] (numeric) = 0.0429046969627 1.07816603067 y[1] (closed_form) = 0.0429193480671 1.0781985339 absolute error = 3.565e-05 relative error = 0.003304 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.035 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4954 2.639 h = 0.0001 0.004 y[1] (numeric) = 0.0426946770155 1.07980204826 y[1] (closed_form) = 0.0427092121029 1.07983476514 absolute error = 3.580e-05 relative error = 0.003313 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.038 Order of pole (given) = 0.5 0 NO 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=19805.1MB, alloc=52.3MB, time=246.12 x[1] = -0.4953 2.643 h = 0.003 0.006 y[1] (numeric) = 0.0418345645217 1.08170500379 y[1] (closed_form) = 0.0418488930798 1.08173772982 absolute error = 3.573e-05 relative error = 0.0033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.041 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4923 2.649 h = 0.0001 0.005 y[1] (numeric) = 0.0418831189764 1.08520787115 y[1] (closed_form) = 0.0418979691887 1.0852413391 absolute error = 3.661e-05 relative error = 0.003371 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.048 Order of pole (given) = 0.5 0 NO 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=19850.8MB, alloc=52.3MB, time=246.68 x[1] = -0.4922 2.654 h = 0.0001 0.003 y[1] (numeric) = 0.0407941643674 1.08758510305 y[1] (closed_form) = 0.0408087637337 1.0876180394 absolute error = 3.603e-05 relative error = 0.00331 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.052 Order of pole (given) = 0.5 0 NO 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=19896.6MB, alloc=52.3MB, time=247.24 x[1] = -0.4921 2.657 h = 0.001 0.001 y[1] (numeric) = 0.0401586772179 1.08902104429 y[1] (closed_form) = 0.0401734388929 1.08905381777 absolute error = 3.594e-05 relative error = 0.003298 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.055 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4911 2.658 h = 0.0001 0.004 y[1] (numeric) = 0.0404022128896 1.089719855 y[1] (closed_form) = 0.0404170266438 1.08975252175 absolute error = 3.587e-05 relative error = 0.003289 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.056 Order of pole (given) = 0.5 0 NO 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=19942.4MB, alloc=52.3MB, time=247.80 x[1] = -0.491 2.662 h = 0.003 0.006 y[1] (numeric) = 0.0395390923291 1.09162762754 y[1] (closed_form) = 0.0395534824392 1.09166051915 absolute error = 3.590e-05 relative error = 0.003287 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.06 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=19988.0MB, alloc=52.3MB, time=248.36 x[1] = -0.488 2.668 h = 0.0001 0.005 y[1] (numeric) = 0.0395863423672 1.09514042432 y[1] (closed_form) = 0.0396012539482 1.0951740538 absolute error = 3.679e-05 relative error = 0.003357 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.067 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4879 2.673 h = 0.0001 0.003 y[1] (numeric) = 0.0384933422164 1.09752391471 y[1] (closed_form) = 0.03850800262 1.09755701519 absolute error = 3.620e-05 relative error = 0.003296 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.071 Order of pole (given) = 0.5 0 NO 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=20033.7MB, alloc=52.3MB, time=248.92 x[1] = -0.4878 2.676 h = 0.001 0.001 y[1] (numeric) = 0.037855481945 1.09896364475 y[1] (closed_form) = 0.0378703036576 1.09899658258 absolute error = 3.612e-05 relative error = 0.003285 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.074 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4868 2.677 h = 0.001 0.003 y[1] (numeric) = 0.0380994210974 1.09966452204 y[1] (closed_form) = 0.0381142944384 1.09969735341 absolute error = 3.604e-05 relative error = 0.003276 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.075 Order of pole (given) = 0.5 0 NO 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=20079.4MB, alloc=52.3MB, time=249.48 x[1] = -0.4858 2.68 h = 0.0001 0.004 y[1] (numeric) = 0.0378867303374 1.1013103811 y[1] (closed_form) = 0.0379014896986 1.10134342497 absolute error = 3.619e-05 relative error = 0.003284 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.078 Order of pole (given) = 0.5 0 NO 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=20125.2MB, alloc=52.3MB, time=250.04 x[1] = -0.4857 2.684 h = 0.003 0.006 y[1] (numeric) = 0.037019755733 1.10322425117 y[1] (closed_form) = 0.0370343102954 1.10325730517 absolute error = 3.612e-05 relative error = 0.003272 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.082 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4827 2.69 h = 0.0001 0.005 y[1] (numeric) = 0.0370656853158 1.10674855857 y[1] (closed_form) = 0.0370807610586 1.10678234579 absolute error = 3.700e-05 relative error = 0.003341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.088 Order of pole (given) = 0.5 0 NO 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=20170.9MB, alloc=52.3MB, time=250.60 x[1] = -0.4826 2.695 h = 0.0001 0.003 y[1] (numeric) = 0.0359681241801 1.10913936531 y[1] (closed_form) = 0.0359829484148 1.10917262653 absolute error = 3.642e-05 relative error = 0.003281 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.093 Order of pole (given) = 0.5 0 NO 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=20216.7MB, alloc=52.3MB, time=251.16 x[1] = -0.4825 2.698 h = 0.001 0.001 y[1] (numeric) = 0.0353275906306 1.1105835231 y[1] (closed_form) = 0.0353425750282 1.11061662195 absolute error = 3.633e-05 relative error = 0.00327 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.095 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4815 2.699 h = 0.001 0.003 y[1] (numeric) = 0.03557203571 1.11128678329 y[1] (closed_form) = 0.0355870712224 1.11131977601 absolute error = 3.626e-05 relative error = 0.003261 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.097 Order of pole (given) = 0.5 0 NO 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=20262.3MB, alloc=52.3MB, time=251.72 x[1] = -0.4805 2.702 h = 0.0001 0.004 y[1] (numeric) = 0.0353579730032 1.11293791252 y[1] (closed_form) = 0.0353728956085 1.11297111711 absolute error = 3.640e-05 relative error = 0.003269 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.1 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] = -0.4804 2.706 h = 0.003 0.006 y[1] (numeric) = 0.0344873941363 1.11485764891 y[1] (closed_form) = 0.0345021128661 1.11489086414 absolute error = 3.633e-05 relative error = 0.003257 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.103 Order of pole (given) = 0.5 0 NO 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=20308.1MB, alloc=52.3MB, time=252.28 x[1] = -0.4774 2.712 h = 0.0001 0.005 y[1] (numeric) = 0.03453204015 1.11839342005 y[1] (closed_form) = 0.0345472797565 1.1184273639 absolute error = 3.721e-05 relative error = 0.003325 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.11 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=20353.8MB, alloc=52.3MB, time=252.83 x[1] = -0.4773 2.717 h = 0.0001 0.003 y[1] (numeric) = 0.0334299577199 1.12079152345 y[1] (closed_form) = 0.033444945501 1.12082494427 absolute error = 3.663e-05 relative error = 0.003266 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.115 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4772 2.72 h = 0.001 0.001 y[1] (numeric) = 0.0327867745042 1.12224009684 y[1] (closed_form) = 0.0328019213137 1.12227335556 absolute error = 3.655e-05 relative error = 0.003255 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.117 Order of pole (given) = 0.5 0 NO 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=20399.5MB, alloc=52.3MB, time=253.39 x[1] = -0.4762 2.721 h = 0.001 0.003 y[1] (numeric) = 0.0330317297127 1.12294572815 y[1] (closed_form) = 0.0330469271294 1.12297888107 absolute error = 3.647e-05 relative error = 0.003246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.119 Order of pole (given) = 0.5 0 NO 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=20445.4MB, alloc=52.3MB, time=253.95 x[1] = -0.4752 2.724 h = 0.0001 0.004 y[1] (numeric) = 0.0328163152424 1.12460210821 y[1] (closed_form) = 0.0328314008126 1.12463547239 absolute error = 3.662e-05 relative error = 0.003254 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.122 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4751 2.728 h = 0.003 0.006 y[1] (numeric) = 0.0319421636228 1.12652769501 y[1] (closed_form) = 0.0319570462338 1.12656107033 absolute error = 3.654e-05 relative error = 0.003242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.125 Order of pole (given) = 0.5 0 NO 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=20491.0MB, alloc=52.3MB, time=254.51 x[1] = -0.4721 2.734 h = 0.0001 0.005 y[1] (numeric) = 0.031985562446 1.13007488334 y[1] (closed_form) = 0.0320009656174 1.13010898271 absolute error = 3.742e-05 relative error = 0.00331 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.132 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.472 2.739 h = 0.0001 0.003 y[1] (numeric) = 0.0308789979706 1.13248026374 y[1] (closed_form) = 0.0308941490123 1.13251384302 absolute error = 3.684e-05 relative error = 0.003252 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.136 Order of pole (given) = 0.5 0 NO 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=20536.7MB, alloc=52.3MB, time=255.06 x[1] = -0.4719 2.742 h = 0.001 0.001 y[1] (numeric) = 0.0302331884366 1.13393324061 y[1] (closed_form) = 0.0302484973839 1.13396665807 absolute error = 3.676e-05 relative error = 0.00324 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.139 Order of pole (given) = 0.5 0 NO 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=20582.5MB, alloc=52.3MB, time=255.62 x[1] = -0.4709 2.743 h = 0.001 0.003 y[1] (numeric) = 0.0304786578972 1.13464123136 y[1] (closed_form) = 0.0304940169499 1.13467454335 absolute error = 3.668e-05 relative error = 0.003232 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.14 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] = -0.4699 2.746 h = 0.0001 0.004 y[1] (numeric) = 0.0302619115913 1.13630284304 y[1] (closed_form) = 0.030277159846 1.13633636566 absolute error = 3.683e-05 relative error = 0.00324 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.144 Order of pole (given) = 0.5 0 NO 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=20628.1MB, alloc=52.3MB, time=256.18 x[1] = -0.4698 2.75 h = 0.003 0.006 y[1] (numeric) = 0.0293842183789 1.13823426438 y[1] (closed_form) = 0.0293992645837 1.13826779864 absolute error = 3.676e-05 relative error = 0.003228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.147 Order of pole (given) = 0.5 0 NO 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=20673.9MB, alloc=52.3MB, time=256.74 x[1] = -0.4668 2.756 h = 0.0001 0.005 y[1] (numeric) = 0.0294264058922 1.14179282365 y[1] (closed_form) = 0.0294419723288 1.14182707743 absolute error = 3.762e-05 relative error = 0.003294 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.154 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4667 2.761 h = 0.0001 0.003 y[1] (numeric) = 0.0283153981866 1.14420546148 y[1] (closed_form) = 0.0283307122019 1.14423919809 absolute error = 3.705e-05 relative error = 0.003237 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.158 Order of pole (given) = 0.5 0 NO 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=20719.8MB, alloc=52.3MB, time=257.30 x[1] = -0.4666 2.764 h = 0.001 0.001 y[1] (numeric) = 0.0276669854231 1.14566282973 y[1] (closed_form) = 0.0276824562325 1.14569640481 absolute error = 3.697e-05 relative error = 0.003226 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.161 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4656 2.765 h = 0.0001 0.004 y[1] (numeric) = 0.0279129731814 1.14637316834 y[1] (closed_form) = 0.0279284936001 1.14640663827 absolute error = 3.689e-05 relative error = 0.003217 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.162 Order of pole (given) = 0.5 0 NO 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=20765.4MB, alloc=52.3MB, time=257.86 x[1] = -0.4655 2.769 h = 0.003 0.006 y[1] (numeric) = 0.0270323974886 1.14830934399 y[1] (closed_form) = 0.0270475060687 1.14834303949 absolute error = 3.693e-05 relative error = 0.003215 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.166 Order of pole (given) = 0.5 0 NO 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=20811.1MB, alloc=52.3MB, time=258.41 x[1] = -0.4625 2.775 h = 0.0001 0.005 y[1] (numeric) = 0.027073435999 1.15187764032 y[1] (closed_form) = 0.0270890645717 1.15191205149 absolute error = 3.779e-05 relative error = 0.00328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.172 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4624 2.78 h = 0.0001 0.003 y[1] (numeric) = 0.0259585483314 1.15429645715 y[1] (closed_form) = 0.0259739242073 1.15433035364 absolute error = 3.722e-05 relative error = 0.003224 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.177 Order of pole (given) = 0.5 0 NO 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=20856.8MB, alloc=52.3MB, time=258.97 x[1] = -0.4623 2.783 h = 0.001 0.001 y[1] (numeric) = 0.025307860974 1.15575756508 y[1] (closed_form) = 0.025323392693 1.15579130026 absolute error = 3.714e-05 relative error = 0.003213 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.18 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=20902.6MB, alloc=52.3MB, time=259.53 x[1] = -0.4613 2.784 h = 0.001 0.003 y[1] (numeric) = 0.0255542702654 1.15646992168 y[1] (closed_form) = 0.0255698511675 1.15650355198 absolute error = 3.706e-05 relative error = 0.003204 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.181 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4603 2.787 h = 0.0001 0.004 y[1] (numeric) = 0.0253350361243 1.1581412021 y[1] (closed_form) = 0.0253505081554 1.15817504191 absolute error = 3.721e-05 relative error = 0.003212 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.184 Order of pole (given) = 0.5 0 NO 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=20948.3MB, alloc=52.3MB, time=260.09 x[1] = -0.4602 2.791 h = 0.003 0.006 y[1] (numeric) = 0.0244507655353 1.16008339675 y[1] (closed_form) = 0.0244660371848 1.16011724909 absolute error = 3.714e-05 relative error = 0.0032 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.188 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4572 2.797 h = 0.0001 0.005 y[1] (numeric) = 0.0244906587496 1.16366297922 y[1] (closed_form) = 0.024506450041 1.16369754279 absolute error = 3.800e-05 relative error = 0.003265 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.194 Order of pole (given) = 0.5 0 NO 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=20993.9MB, alloc=52.3MB, time=260.64 x[1] = -0.4571 2.802 h = 0.0001 0.003 y[1] (numeric) = 0.0233713991795 1.16608901762 y[1] (closed_form) = 0.0233869375053 1.16612306938 absolute error = 3.743e-05 relative error = 0.003209 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.199 Order of pole (given) = 0.5 0 NO 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=21039.7MB, alloc=52.3MB, time=261.20 x[1] = -0.457 2.805 h = 0.001 0.001 y[1] (numeric) = 0.022718151023 1.16755449481 y[1] (closed_form) = 0.0227338441012 1.16758838554 absolute error = 3.735e-05 relative error = 0.003198 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.201 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.456 2.806 h = 0.001 0.003 y[1] (numeric) = 0.0229650860745 1.16826917801 y[1] (closed_form) = 0.0229808278503 1.16830296419 absolute error = 3.727e-05 relative error = 0.00319 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.203 Order of pole (given) = 0.5 0 NO 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=21085.3MB, alloc=52.3MB, time=261.76 x[1] = -0.455 2.809 h = 0.0001 0.004 y[1] (numeric) = 0.0227445759625 1.16994563593 y[1] (closed_form) = 0.0227602098825 1.169979631 absolute error = 3.742e-05 relative error = 0.003198 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.206 Order of pole (given) = 0.5 0 NO 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=21131.0MB, alloc=52.3MB, time=262.32 x[1] = -0.4549 2.813 h = 0.003 0.006 y[1] (numeric) = 0.0218568512271 1.17189362033 y[1] (closed_form) = 0.0218722856555 1.1719276284 absolute error = 3.735e-05 relative error = 0.003186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.209 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4519 2.819 h = 0.0001 0.005 y[1] (numeric) = 0.0218956336486 1.17548444355 y[1] (closed_form) = 0.021911587357 1.17551915846 absolute error = 3.821e-05 relative error = 0.00325 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.216 Order of pole (given) = 0.5 0 NO 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=21176.9MB, alloc=52.3MB, time=262.88 x[1] = -0.4518 2.824 h = 0.0001 0.003 y[1] (numeric) = 0.0207720397886 1.17791768409 y[1] (closed_form) = 0.0207877402744 1.17795189003 absolute error = 3.764e-05 relative error = 0.003195 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.221 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4517 2.827 h = 0.001 0.001 y[1] (numeric) = 0.0201162532034 1.17938751856 y[1] (closed_form) = 0.0201321073618 1.17942156375 absolute error = 3.756e-05 relative error = 0.003184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.223 Order of pole (given) = 0.5 0 NO 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=21222.6MB, alloc=52.3MB, time=263.44 x[1] = -0.4507 2.828 h = 0.001 0.003 y[1] (numeric) = 0.0203637178466 1.18010451705 y[1] (closed_form) = 0.0203796202225 1.18013845801 absolute error = 3.748e-05 relative error = 0.003176 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.225 Order of pole (given) = 0.5 0 NO 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=21268.3MB, alloc=52.3MB, time=263.99 x[1] = -0.4497 2.831 h = 0.0001 0.004 y[1] (numeric) = 0.0201419507472 1.18178613368 y[1] (closed_form) = 0.0201577462713 1.18182028291 absolute error = 3.763e-05 relative error = 0.003183 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.228 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4496 2.835 h = 0.003 0.006 y[1] (numeric) = 0.0192508017267 1.18373989212 y[1] (closed_form) = 0.0192663986426 1.18377405483 absolute error = 3.755e-05 relative error = 0.003172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.231 Order of pole (given) = 0.5 0 NO 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=21314.0MB, alloc=52.3MB, time=264.55 x[1] = -0.4466 2.841 h = 0.0001 0.005 y[1] (numeric) = 0.0192885073957 1.18734191106 y[1] (closed_form) = 0.0193046232187 1.18737677624 absolute error = 3.841e-05 relative error = 0.003234 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.238 Order of pole (given) = 0.5 0 NO 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=21359.8MB, alloc=52.3MB, time=265.11 x[1] = -0.4465 2.846 h = 0.0001 0.003 y[1] (numeric) = 0.0181606164517 1.18978233435 y[1] (closed_form) = 0.0181764788067 1.18981669338 absolute error = 3.784e-05 relative error = 0.00318 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.242 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4464 2.849 h = 0.001 0.001 y[1] (numeric) = 0.017502313565 1.19125651415 y[1] (closed_form) = 0.0175183285236 1.19129071272 absolute error = 3.776e-05 relative error = 0.00317 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.245 Order of pole (given) = 0.5 0 NO 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=21405.7MB, alloc=52.3MB, time=265.67 x[1] = -0.4454 2.85 h = 0.001 0.003 y[1] (numeric) = 0.0177503115603 1.19197581671 y[1] (closed_form) = 0.0177663742617 1.19200991135 absolute error = 3.769e-05 relative error = 0.003161 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.246 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = -0.4444 2.853 h = 0.0001 0.004 y[1] (numeric) = 0.0175273062233 1.19366257336 y[1] (closed_form) = 0.0175432630656 1.19369687569 absolute error = 3.783e-05 relative error = 0.003169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.25 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=21451.3MB, alloc=52.3MB, time=266.23 x[1] = -0.4443 2.857 h = 0.003 0.006 y[1] (numeric) = 0.0166327624562 1.19562209021 y[1] (closed_form) = 0.0166485215672 1.19565640646 absolute error = 3.776e-05 relative error = 0.003158 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.253 Order of pole (given) = 0.5 0 NO 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=21497.0MB, alloc=52.3MB, time=266.79 x[1] = -0.4413 2.863 h = 0.0001 0.005 y[1] (numeric) = 0.0166694249584 1.19923526009 y[1] (closed_form) = 0.0166857025932 1.1992702745 absolute error = 3.861e-05 relative error = 0.003219 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.26 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] = -0.4412 2.868 h = 0.0001 0.003 y[1] (numeric) = 0.0155372737361 1.20168284681 y[1] (closed_form) = 0.0155532976687 1.20171735787 absolute error = 3.805e-05 relative error = 0.003166 % Correct digits = 4 Radius of convergence (given) for eq 1 = 3.264 Order of pole (given) = 0.5 0 NO 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=21542.7MB, alloc=52.3MB, time=267.34 x[1] = -0.4411 2.871 h = 0.001 0.001 y[1] (numeric) = 0.0148764764364 1.20316136004 y[1] (closed_form) = 0.0148926519141 1.20319571092 absolute error = 3.797e-05 relative error = 0.003155 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.267 Order of pole (given) = 0.5 0 NO 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=21588.4MB, alloc=52.3MB, time=267.90 x[1] = -0.4401 2.872 h = 0.001 0.003 y[1] (numeric) = 0.015125011474 1.20388295552 y[1] (closed_form) = 0.0151412342252 1.20391720279 absolute error = 3.790e-05 relative error = 0.003147 % Correct digits = 5 Radius of convergence (given) for eq 1 = 3.268 Order of pole (given) = 0.5 0 NO 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! Maximum Time Reached before Solution Completed! diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 754 Total Elapsed Time = 4 Minutes 28 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 4 Minutes 28 Seconds > quit memory used=21621.0MB, alloc=52.3MB, time=268.28