|\^/| 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(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( sqrt(c(0.1) * c(x) + c(0.2)))); > end; exact_soln_y := proc(x) return c(20.0)*sqrt(c(0.1)*c(x) + c(0.2))*cosh(sqrt(c(0.1)*c(x) + c(0.2))) - c(20.0)*sinh(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, 0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 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#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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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_g, 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_g, > 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]); > array_tmp4[1] := sinh(array_tmp3[1]); > array_tmp4_g[1] := cosh(array_tmp3[1]); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y_set_initial[1,2]) then # if number 1 > if (1 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1)); > if (2 <= ATS_MAX_TERMS) then # if number 3 > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(1); > array_y_higher[2,1] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre mult CONST - LINEAR $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D1[1] * array_x[2]; > #emit pre add LINEAR - CONST $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre sqrt 2 $eq_no = 1 > array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[2] := att(1,array_tmp4_g,array_tmp3,1); > array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp5[2] := array_tmp4[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y_set_initial[1,3]) then # if number 1 > if (2 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2)); > if (3 <= ATS_MAX_TERMS) then # if number 3 > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(2); > array_y_higher[2,2] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1 > array_tmp3[3] := 0; > array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[3] := att(2,array_tmp4_g,array_tmp3,1); > array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp5[3] := array_tmp4[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y_set_initial[1,4]) then # if number 1 > if (3 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3)); > if (4 <= ATS_MAX_TERMS) then # if number 3 > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(3); > array_y_higher[2,3] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1 > array_tmp3[4] := 0; > array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[4] := att(3,array_tmp4_g,array_tmp3,1); > array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp5[4] := array_tmp4[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y_set_initial[1,5]) then # if number 1 > if (4 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4)); > if (5 <= ATS_MAX_TERMS) then # if number 3 > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(4); > array_y_higher[2,4] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1 > array_tmp3[5] := 0; > array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2; > #emit pre sinh FULL $eq_no = 1 > array_tmp4[5] := att(4,array_tmp4_g,array_tmp3,1); > array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp5[5] := array_tmp4[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y_set_initial[1,6]) then # if number 1 > if (5 <= ATS_MAX_TERMS) then # if number 2 > temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5)); > if (6 <= ATS_MAX_TERMS) then # if number 3 > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > fi;# end if 3; > temporary := c(temporary) / c(glob_h) * c(5); > array_y_higher[2,5] := c(temporary); > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= ATS_MAX_TERMS) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit sqrt LINEAR $eq_no = 1 > array_tmp3[kkk] := 0; > array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2; > #emit sinh FULL $eq_no = 1 > array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1); > array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp5[kkk] := array_tmp4[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1 > if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2 > temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1))); > array_y[kkk + order_d] := c(temporary); > array_y_higher[1,kkk + order_d] := c(temporary); > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := c(temporary) / c(glob_h) * c(adj2); > else > temporary := c(temporary); > fi;# end if 4; > array_y_higher[adj3,term] := c(temporary); > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, 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] := sinh(array_tmp3[1]); array_tmp4_g[1] := cosh(array_tmp3[1]); array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= ATS_MAX_TERMS then temporary := c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1)); if 2 <= ATS_MAX_TERMS then array_y[2] := temporary; array_y_higher[1, 2] := temporary end if; temporary := c(temporary)*c(1)/c(glob_h); array_y_higher[2, 1] := c(temporary) end if end if; kkk := 2; array_tmp1[2] := array_const_0D1[1]*array_x[2]; array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2); array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1); array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1); array_tmp5[2] := array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= ATS_MAX_TERMS then temporary := c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2)); if 3 <= ATS_MAX_TERMS then array_y[3] := temporary; array_y_higher[1, 3] := temporary end if; temporary := c(temporary)*c(2)/c(glob_h); array_y_higher[2, 2] := c(temporary) end if end if; kkk := 3; array_tmp3[3] := 0; array_tmp3[3] := neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1); array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1); array_tmp5[3] := array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= ATS_MAX_TERMS then temporary := c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3)); if 4 <= ATS_MAX_TERMS then array_y[4] := temporary; array_y_higher[1, 4] := temporary end if; temporary := c(temporary)*c(3)/c(glob_h); array_y_higher[2, 3] := c(temporary) end if end if; kkk := 4; array_tmp3[4] := 0; array_tmp3[4] := neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1); array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1); array_tmp5[4] := array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= ATS_MAX_TERMS then temporary := c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4)); if 5 <= ATS_MAX_TERMS then array_y[5] := temporary; array_y_higher[1, 5] := temporary end if; temporary := c(temporary)*c(4)/c(glob_h); array_y_higher[2, 4] := c(temporary) end if end if; kkk := 5; array_tmp3[5] := 0; array_tmp3[5] := neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2); array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1); array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1); array_tmp5[5] := array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= ATS_MAX_TERMS then temporary := c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5)); if 6 <= ATS_MAX_TERMS then array_y[6] := temporary; array_y_higher[1, 6] := temporary end if; temporary := c(temporary)*c(5)/c(glob_h); array_y_higher[2, 5] := c(temporary) end if end if; kkk := 6; while kkk <= ATS_MAX_TERMS do array_tmp3[kkk] := 0; array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/( array_tmp3[1]*glob__2); array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1); array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1); array_tmp5[kkk] := array_tmp4[kkk]; order_d := 1; if kkk + order_d <= ATS_MAX_TERMS then if not array_y_set_initial[1, kkk + order_d] then temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))* c(factorial_3(kkk - 1, kkk + order_d - 1)); array_y[kkk + order_d] := c(temporary); array_y_higher[1, kkk + order_d] := c(temporary); term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1 do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := c(temporary)*c(adj2)/c(glob_h) else temporary := c(temporary) end if; array_y_higher[adj3, term] := c(temporary) end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc # End Function number 12 #END OUTFILE5 # Begin Function number 12 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it; > global > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > glob_no_sing_tests, > glob_ratio_test, > glob_three_term_test, > glob_six_term_test, > glob_log_10, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob__small, > glob_small_float, > glob_smallish_float, > glob_large_float, > glob_larger_float, > glob__m2, > glob__m1, > glob__0, > glob__1, > glob__2, > glob__3, > glob__4, > glob__5, > glob__8, > glob__10, > glob__100, > glob__pi, > glob__0_5, > glob__0_8, > glob__m0_8, > glob__0_25, > glob__0_125, > glob_h, > glob_nxt, > glob_prec, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_estimated_size_answer, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_disp_incr, > glob_diff_rc_fm, > glob_diff_rc_fmm1, > glob_diff_rc_fmm2, > glob_diff_ord_fm, > glob_diff_ord_fmm1, > glob_diff_ord_fmm2, > glob_six_term_ord_save, > glob_guess_error_rc, > glob_guess_error_ord, > glob_least_given_sing, > glob_least_ratio_sing, > glob_least_3_sing, > glob_least_6_sing, > glob_last_good_h, > glob_max_h, > glob_min_h, > glob_display_interval, > glob_abserr, > glob_relerr, > glob_min_pole_est, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_max_hours, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_upper_ratio_limit, > glob_lower_ratio_limit, > glob_max_sec, > glob_orig_start_sec, > glob_normmax, > glob_max_minutes, > glob_next_display, > glob_est_digits, > glob_subiter_method, > glob_html_log, > glob_min_good_digits, > glob_good_digits, > glob_min_apfp_est_good_digits, > glob_apfp_est_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_h_reason, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_type_given_pole, > glob_optimize, > glob_look_poles, > glob_dump_closed_form, > glob_max_iter, > glob_no_eqs, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_start, > glob_iter, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_0D1, > array_const_0D2, > #END CONST > array_y_init, > array_norms, > array_fact_1, > array_1st_rel_error, > array_last_rel_error, > array_est_rel_error, > array_max_est_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_est_digits, > array_y, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > 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_g:= 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_g[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_g); > 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/sinh_sqrtpostcpx.cpx#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = sinh ( 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 := 2.1 + 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,"glob_type_given_pole := 1;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=8;"); > omniout_str(ALWAYS,"glob_max_minutes:=(3.0);"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"glob_max_iter:=10000;"); > omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);"); > omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_h:=c(0.001);"); > omniout_str(ALWAYS,"glob_display_interval:=c(0.01);"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( 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 := 2.1 + 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 ) = sinh ( 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,"2017-11-26T16:25:59-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sinh_sqrt") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = sinh ( 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,"sinh_sqrt diffeq.mxt") > ; > logitem_str(html_log_file,"sinh_sqrt maple results") > ; > logitem_str(html_log_file,"OK") > ; > logend(html_log_file) > ; > ; > fi;# end if 15; > if (glob_html_log) then # if number 15 > fclose(html_log_file); > fi;# end if 15 > ; > ;; > end; > # End Function number 12 > #END OUTFILEMAIN > end; Warning, `h_new` is implicitly declared local to procedure `main` Warning, `ratio` is implicitly declared local to procedure `main` main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new, ratio; global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test, glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED, glob__small, glob_small_float, glob_smallish_float, glob_large_float, glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3, glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5, glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval, glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form, glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1, array_const_0D2, array_y_init, array_norms, array_fact_1, array_1st_rel_error, array_last_rel_error, array_est_rel_error, array_max_est_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, 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_g := 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_g[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_g); 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/sinh_sqrtpostcpx.cpx#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh ( 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 := 2.1 + 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, "glob_type_given_pole := 1;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=8;"); omniout_str(ALWAYS, "glob_max_minutes:=(3.0);"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "glob_max_iter:=10000;"); omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);"); omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_h:=c(0.001);"); omniout_str(ALWAYS, "glob_display_interval:=c(0.01);"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * \ cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( 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,"); 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omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.0001 + 0.004 * I,"); omniout_str(ALWAYS, "0.003 + 0.006 * I,"); omniout_str(ALWAYS, "0.0001 + 0.005 * I,"); omniout_str(ALWAYS, "0.0001 + 0.003 * I,"); omniout_str(ALWAYS, "0.001 + 0.001 * I,"); omniout_str(ALWAYS, "0.001 + 0.003 * I,"); omniout_str(ALWAYS, "0.000 + 0.000 * I ];"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;"); omniout_str(ALWAYS, "it := x_delta[glob_nxt];"); omniout_str(ALWAYS, "return it;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := glob__0; glob_smallish_float := glob__0; glob_large_float := c(0.10*10^101); glob_larger_float := c(0.11*10^101); glob_almost_1 := c(0.99); x_start := 2.1 + 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 ) = sinh ( 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, "2017-11-26T16:25:59-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sinh_sqrt"); logitem_str(html_log_file, "diff ( y , x , 1 ) = si\ nh ( 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, "sinh_sqrt diffeq.mxt"); logitem_str(html_log_file, "sinh_sqrt maple results"); logitem_str(html_log_file, "OK"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc # End Function number 12 > main(); memory used=3.8MB, alloc=40.3MB, time=0.08 ##############ECHO OF PROBLEM################# ##############temp/sinh_sqrtpostcpx.cpx################# diff ( y , x , 1 ) = sinh ( 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 := 2.1 + 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(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * cosh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * sinh( 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 x[1] = 2.1 0.1 h = 0.0001 0.005 y[1] (numeric) = 1.82253049093 0.0684985158039 y[1] (closed_form) = 1.82253049093 0.0684985158039 absolute error = 0 relative error = 0 % Correct digits = 30 Radius of convergence (given) for eq 1 = 4.101 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=30.8MB, alloc=40.3MB, time=0.40 x[1] = 2.1001 0.105 h = 0.0001 0.003 y[1] (numeric) = 1.82255167006 0.0719245109156 y[1] (closed_form) = 1.82255048799 0.0719245674309 absolute error = 1.183e-06 relative error = 6.488e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.101 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1002 0.108 h = 0.001 0.001 y[1] (numeric) = 1.82259036001 0.0739805736261 y[1] (closed_form) = 1.8225887528 0.0739806618945 absolute error = 1.610e-06 relative error = 8.824e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.102 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 x[1] = 2.1012 0.109 h = 0.001 0.003 y[1] (numeric) = 1.82326517352 0.0746758296601 y[1] (closed_form) = 1.82326356709 0.074676012539 absolute error = 1.617e-06 relative error = 8.860e-05 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.103 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=76.4MB, alloc=44.3MB, time=0.98 x[1] = 2.1022 0.112 h = 0.0001 0.004 y[1] (numeric) = 1.82391935845 0.0767415352815 y[1] (closed_form) = 1.82391737596 0.076742005256 absolute error = 2.037e-06 relative error = 0.0001116 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1023 0.116 h = 0.003 0.006 y[1] (numeric) = 1.82394548871 0.0794835040891 y[1] (closed_form) = 1.82394275009 0.0794840185134 absolute error = 2.787e-06 relative error = 0.0001526 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1053 0.122 h = 0.0001 0.005 y[1] (numeric) = 1.82593535004 0.0836278740214 y[1] (closed_form) = 1.82593134979 0.0836301028177 absolute error = 4.579e-06 relative error = 0.0002505 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.107 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=121.8MB, alloc=44.3MB, time=1.54 x[1] = 2.1054 0.127 h = 0.0001 0.003 y[1] (numeric) = 1.82594619604 0.0870566738543 y[1] (closed_form) = 1.82594101405 0.0870589610522 absolute error = 5.664e-06 relative error = 0.0003099 % Correct digits = 6 Radius of convergence (given) for eq 1 = 4.107 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1055 0.13 h = 0.001 0.001 y[1] (numeric) = 1.82597870752 0.0891145047844 y[1] (closed_form) = 1.82597310064 0.0891168244385 absolute error = 6.068e-06 relative error = 0.0003319 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.108 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 x[1] = 2.1065 0.131 h = 0.001 0.003 y[1] (numeric) = 1.82665196501 0.0898123581445 y[1] (closed_form) = 1.82664635907 0.0898147723619 absolute error = 6.104e-06 relative error = 0.0003337 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.109 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=167.3MB, alloc=44.3MB, time=2.12 x[1] = 2.1075 0.134 h = 0.0001 0.004 y[1] (numeric) = 1.8273004413 0.0918817025265 y[1] (closed_form) = 1.82729445997 0.0918844043341 absolute error = 6.563e-06 relative error = 0.0003587 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1076 0.138 h = 0.003 0.006 y[1] (numeric) = 1.82731831903 0.0946259637301 y[1] (closed_form) = 1.827311582 0.0946287112418 absolute error = 7.276e-06 relative error = 0.0003976 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.11 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1106 0.144 h = 0.0001 0.005 y[1] (numeric) = 1.82929729009 0.0987796924952 y[1] (closed_form) = 1.82928929495 0.0987841556612 absolute error = 9.157e-06 relative error = 0.0004998 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.113 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=212.3MB, alloc=44.3MB, time=2.67 x[1] = 2.1107 0.149 h = 0.0001 0.003 y[1] (numeric) = 1.8292978124 0.102211313026 y[1] (closed_form) = 1.8292886362 0.102215836556 absolute error = 1.023e-05 relative error = 0.0005584 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.113 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 x[1] = 2.1108 0.152 h = 0.001 0.001 y[1] (numeric) = 1.82932415142 0.104270921725 y[1] (closed_form) = 1.82931455061 0.10427547841 absolute error = 1.063e-05 relative error = 0.00058 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.114 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1118 0.153 h = 0.001 0.003 y[1] (numeric) = 1.82999585804 0.104971373752 y[1] (closed_form) = 1.82998625832 0.104976024952 absolute error = 1.067e-05 relative error = 0.000582 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.115 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=257.8MB, alloc=44.3MB, time=3.24 x[1] = 2.1128 0.156 h = 0.0001 0.004 y[1] (numeric) = 1.83063863464 0.107044364715 y[1] (closed_form) = 1.8306286602 0.107049303992 absolute error = 1.113e-05 relative error = 0.000607 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.116 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] = 2.1129 0.16 h = 0.003 0.006 y[1] (numeric) = 1.83064826778 0.109790931072 y[1] (closed_form) = 1.83063753811 0.1097959173 absolute error = 1.183e-05 relative error = 0.0006452 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.116 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] = 2.1159 0.166 h = 0.0001 0.005 y[1] (numeric) = 1.83261636975 0.113954032335 y[1] (closed_form) = 1.83260438548 0.113960735462 absolute error = 1.373e-05 relative error = 0.0007478 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.119 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=303.2MB, alloc=44.3MB, time=3.81 x[1] = 2.116 0.171 h = 0.0001 0.003 y[1] (numeric) = 1.83260657828 0.117388489492 y[1] (closed_form) = 1.83259341365 0.117395254933 absolute error = 1.480e-05 relative error = 0.000806 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.12 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] = 2.1161 0.174 h = 0.001 0.001 y[1] (numeric) = 1.83262675094 0.119449885425 y[1] (closed_form) = 1.83261316196 0.119456684716 absolute error = 1.520e-05 relative error = 0.0008274 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.12 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] = 2.1171 0.175 h = 0.001 0.003 y[1] (numeric) = 1.83329691183 0.120152937406 y[1] (closed_form) = 1.8332833241 0.120159831162 absolute error = 1.524e-05 relative error = 0.0008293 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.121 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=348.8MB, alloc=52.3MB, time=4.39 x[1] = 2.1181 0.178 h = 0.0001 0.004 y[1] (numeric) = 1.83393399775 0.122229582664 y[1] (closed_form) = 1.83392003598 0.122236764976 absolute error = 1.570e-05 relative error = 0.0008542 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.122 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] = 2.1182 0.182 h = 0.003 0.006 y[1] (numeric) = 1.83393539435 0.124978466823 y[1] (closed_form) = 1.83392067782 0.124985697324 absolute error = 1.640e-05 relative error = 0.000892 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.122 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] = 2.1212 0.188 h = 0.0001 0.005 y[1] (numeric) = 1.83589264848 0.129150954007 y[1] (closed_form) = 1.83587668087 0.129159902616 absolute error = 1.830e-05 relative error = 0.0009946 % Correct digits = 5 memory used=394.3MB, alloc=52.3MB, time=4.94 Radius of convergence (given) for eq 1 = 4.125 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 x[1] = 2.1213 0.193 h = 0.0001 0.003 y[1] (numeric) = 1.83587255327 0.13258826358 y[1] (closed_form) = 1.83585540601 0.132597276442 absolute error = 1.937e-05 relative error = 0.001052 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1214 0.196 h = 0.001 0.001 y[1] (numeric) = 1.83588656574 0.134651456128 y[1] (closed_form) = 1.83586899441 0.13466050353 absolute error = 1.976e-05 relative error = 0.001074 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.126 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=439.9MB, alloc=52.3MB, time=5.50 x[1] = 2.1224 0.197 h = 0.0001 0.004 y[1] (numeric) = 1.83655518604 0.135357109299 y[1] (closed_form) = 1.83653761612 0.135366251114 absolute error = 1.981e-05 relative error = 0.001076 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.127 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 x[1] = 2.1225 0.201 h = 0.003 0.006 y[1] (numeric) = 1.83654947158 0.138107900548 y[1] (closed_form) = 1.83653114733 0.138117091676 absolute error = 2.050e-05 relative error = 0.001113 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.127 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 x[1] = 2.1255 0.207 h = 0.0001 0.005 y[1] (numeric) = 1.83849729331 0.142288348513 y[1] (closed_form) = 1.83847772098 0.142299258801 absolute error = 2.241e-05 relative error = 0.001215 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.131 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=485.4MB, alloc=52.3MB, time=6.06 x[1] = 2.1256 0.212 h = 0.0001 0.003 y[1] (numeric) = 1.83846830287 0.145728003315 y[1] (closed_form) = 1.83844755151 0.145738979524 absolute error = 2.348e-05 relative error = 0.001273 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.131 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1257 0.215 h = 0.001 0.001 y[1] (numeric) = 1.83847699631 0.147792676499 y[1] (closed_form) = 1.83845582111 0.147803687841 absolute error = 2.387e-05 relative error = 0.001294 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.131 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1267 0.216 h = 0.001 0.003 y[1] (numeric) = 1.83914426364 0.148500551368 y[1] (closed_form) = 1.83912308999 0.148511657079 absolute error = 2.391e-05 relative error = 0.001296 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.132 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 memory used=530.8MB, alloc=52.3MB, time=6.62 x[1] = 2.1277 0.219 h = 0.0001 0.004 y[1] (numeric) = 1.83977074091 0.150583949045 y[1] (closed_form) = 1.83974919448 0.150595344191 absolute error = 2.437e-05 relative error = 0.00132 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.134 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] = 2.1278 0.223 h = 0.003 0.006 y[1] (numeric) = 1.83975680505 0.153337081488 y[1] (closed_form) = 1.83973450473 0.153348527114 absolute error = 2.507e-05 relative error = 0.001358 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.134 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] = 2.1308 0.229 h = 0.0001 0.005 y[1] (numeric) = 1.84169381851 0.157526939969 y[1] (closed_form) = 1.84167027364 0.157540105893 absolute error = 2.698e-05 relative error = 0.001459 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.137 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=576.4MB, alloc=52.3MB, time=7.18 x[1] = 2.1309 0.234 h = 0.0001 0.003 y[1] (numeric) = 1.84165454316 0.16096947632 y[1] (closed_form) = 1.84162982001 0.160982710081 absolute error = 2.804e-05 relative error = 0.001517 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.138 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] = 2.131 0.237 h = 0.001 0.001 y[1] (numeric) = 1.84165708797 0.163035963426 y[1] (closed_form) = 1.84163194127 0.163049233002 absolute error = 2.843e-05 relative error = 0.001538 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.138 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] = 2.132 0.238 h = 0.001 0.003 y[1] (numeric) = 1.84232282427 0.163746441702 y[1] (closed_form) = 1.84229767927 0.163759805594 absolute error = 2.848e-05 relative error = 0.00154 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.139 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=621.9MB, alloc=52.3MB, time=7.73 x[1] = 2.133 0.241 h = 0.0001 0.004 y[1] (numeric) = 1.8429436368 0.165833515255 y[1] (closed_form) = 1.8429181197 0.165847169039 absolute error = 2.894e-05 relative error = 0.001564 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.14 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] = 2.1331 0.245 h = 0.003 0.006 y[1] (numeric) = 1.84292148783 0.168589001161 y[1] (closed_form) = 1.84289521734 0.168602706641 absolute error = 2.963e-05 relative error = 0.001601 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.14 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] = 2.1361 0.251 h = 0.0001 0.005 y[1] (numeric) = 1.84484771447 0.172788282894 y[1] (closed_form) = 1.84482020295 0.172803709775 absolute error = 3.154e-05 relative error = 0.001702 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.144 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=667.4MB, alloc=52.3MB, time=8.29 x[1] = 2.1362 0.256 h = 0.0001 0.003 y[1] (numeric) = 1.8447981646 0.176233716185 y[1] (closed_form) = 1.84476947556 0.176249212806 absolute error = 3.261e-05 relative error = 0.00176 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.144 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 x[1] = 2.1363 0.259 h = 0.001 0.001 y[1] (numeric) = 1.84479456716 0.178302026351 y[1] (closed_form) = 1.84476545488 0.178317559464 absolute error = 3.300e-05 relative error = 0.00178 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.144 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 x[1] = 2.1373 0.26 h = 0.001 0.003 y[1] (numeric) = 1.84545877757 0.179015109119 y[1] (closed_form) = 1.84542966713 0.179030736492 absolute error = 3.304e-05 relative error = 0.001782 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.145 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=713.0MB, alloc=52.3MB, time=8.85 x[1] = 2.1383 0.263 h = 0.0001 0.004 y[1] (numeric) = 1.84607393454 0.181105865846 y[1] (closed_form) = 1.84604445269 0.18112178356 absolute error = 3.350e-05 relative error = 0.001806 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.147 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 x[1] = 2.1384 0.267 h = 0.003 0.006 y[1] (numeric) = 1.8460435809 0.183863717429 y[1] (closed_form) = 1.84601334617 0.183879688048 absolute error = 3.419e-05 relative error = 0.001843 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.147 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 x[1] = 2.1414 0.273 h = 0.0001 0.005 y[1] (numeric) = 1.84795904223 0.18807243491 y[1] (closed_form) = 1.84792756999 0.188090127994 absolute error = 3.610e-05 relative error = 0.001944 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.15 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=758.5MB, alloc=52.3MB, time=9.41 x[1] = 2.1415 0.278 h = 0.0001 0.003 y[1] (numeric) = 1.84789922834 0.191520780387 y[1] (closed_form) = 1.84786657936 0.191538545104 absolute error = 3.717e-05 relative error = 0.002001 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1416 0.281 h = 0.001 0.001 y[1] (numeric) = 1.84788949511 0.193590922666 y[1] (closed_form) = 1.84785642319 0.193608724546 absolute error = 3.756e-05 relative error = 0.002021 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.151 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1426 0.282 h = 0.001 0.003 y[1] (numeric) = 1.84855218475 0.194306610958 y[1] (closed_form) = 1.84851911483 0.194324507041 absolute error = 3.760e-05 relative error = 0.002023 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.152 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 memory used=804.1MB, alloc=52.3MB, time=9.97 x[1] = 2.1436 0.285 h = 0.0001 0.004 y[1] (numeric) = 1.8491616954 0.196401058048 y[1] (closed_form) = 1.84912825475 0.196419244914 absolute error = 3.807e-05 relative error = 0.002047 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.153 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 x[1] = 2.1437 0.289 h = 0.003 0.006 y[1] (numeric) = 1.84912314562 0.199161287407 y[1] (closed_form) = 1.8490889526 0.199179528378 absolute error = 3.875e-05 relative error = 0.002084 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.154 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] = 2.1467 0.295 h = 0.0001 0.005 y[1] (numeric) = 1.8510278632 0.203379452891 y[1] (closed_form) = 1.85099243621 0.203399417356 absolute error = 4.067e-05 relative error = 0.002184 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.157 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 memory used=849.7MB, alloc=52.3MB, time=10.54 x[1] = 2.1468 0.3 h = 0.0001 0.003 y[1] (numeric) = 1.85095779592 0.206830725661 y[1] (closed_form) = 1.85092119298 0.206850763635 absolute error = 4.173e-05 relative error = 0.002241 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.158 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 x[1] = 2.1469 0.303 h = 0.001 0.001 y[1] (numeric) = 1.85094193342 0.208902709016 y[1] (closed_form) = 1.85090490783 0.208922784822 absolute error = 4.212e-05 relative error = 0.002261 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.158 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 x[1] = 2.1479 0.304 h = 0.0001 0.004 y[1] (numeric) = 1.85160310742 0.209621003812 y[1] (closed_form) = 1.851566084 0.209641173764 absolute error = 4.216e-05 relative error = 0.002263 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=895.2MB, alloc=52.3MB, time=11.12 x[1] = 2.148 0.308 h = 0.003 0.006 y[1] (numeric) = 1.851557481 0.212383191933 y[1] (closed_form) = 1.85151970569 0.212403417077 absolute error = 4.285e-05 relative error = 0.002299 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.151 0.314 h = 0.0001 0.005 y[1] (numeric) = 1.85345285531 0.216609371943 y[1] (closed_form) = 1.85341384904 0.216631321481 absolute error = 4.476e-05 relative error = 0.002399 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.163 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 x[1] = 2.1511 0.319 h = 0.0001 0.003 y[1] (numeric) = 1.85337393573 0.220063054451 y[1] (closed_form) = 1.85333375419 0.220085079114 absolute error = 4.582e-05 relative error = 0.002455 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.163 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=940.7MB, alloc=52.3MB, time=11.68 x[1] = 2.1512 0.322 h = 0.001 0.001 y[1] (numeric) = 1.85335278055 0.222136556751 y[1] (closed_form) = 1.85331217662 0.222158619819 absolute error = 4.621e-05 relative error = 0.002476 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.164 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1522 0.323 h = 0.001 0.003 y[1] (numeric) = 1.85401262298 0.222857077913 y[1] (closed_form) = 1.85397202135 0.222879235078 absolute error = 4.625e-05 relative error = 0.002477 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.165 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 x[1] = 2.1532 0.326 h = 0.0001 0.004 y[1] (numeric) = 1.8546116077 0.224958343677 y[1] (closed_form) = 1.85457063661 0.224980792433 absolute error = 4.672e-05 relative error = 0.002501 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.166 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=986.3MB, alloc=52.3MB, time=12.24 x[1] = 2.1533 0.33 h = 0.003 0.006 y[1] (numeric) = 1.85455780113 0.227722931937 y[1] (closed_form) = 1.85451607865 0.227745437015 absolute error = 4.741e-05 relative error = 0.002537 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.166 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] = 2.1563 0.336 h = 0.0001 0.005 y[1] (numeric) = 1.85644247184 0.231958582374 y[1] (closed_form) = 1.85639952192 0.231982812806 absolute error = 4.931e-05 relative error = 0.002636 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1564 0.341 h = 0.0001 0.003 y[1] (numeric) = 1.85635331877 0.235415220026 y[1] (closed_form) = 1.85630919441 0.235439527438 absolute error = 5.038e-05 relative error = 0.002692 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.17 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1032.0MB, alloc=52.3MB, time=12.80 x[1] = 2.1565 0.344 h = 0.001 0.001 y[1] (numeric) = 1.8563260465 0.23749057993 y[1] (closed_form) = 1.85628150007 0.237514926406 absolute error = 5.077e-05 relative error = 0.002713 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.171 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] = 2.1575 0.345 h = 0.001 0.003 y[1] (numeric) = 1.85698438282 0.238213709344 y[1] (closed_form) = 1.85693983883 0.238238149856 absolute error = 5.081e-05 relative error = 0.002714 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.172 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] = 2.1585 0.348 h = 0.0001 0.004 y[1] (numeric) = 1.85757774777 0.240318685553 y[1] (closed_form) = 1.85753283502 0.240343418075 absolute error = 5.127e-05 relative error = 0.002737 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.173 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=1077.5MB, alloc=52.3MB, time=13.36 x[1] = 2.1586 0.352 h = 0.003 0.006 y[1] (numeric) = 1.85751576978 0.243085685665 y[1] (closed_form) = 1.85747010619 0.243110475684 absolute error = 5.196e-05 relative error = 0.002774 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.173 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 x[1] = 2.1616 0.358 h = 0.0001 0.005 y[1] (numeric) = 1.85938975862 0.247330818098 y[1] (closed_form) = 1.85934287111 0.247357334396 absolute error = 5.387e-05 relative error = 0.002872 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.177 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 x[1] = 2.1617 0.363 h = 0.0001 0.003 y[1] (numeric) = 1.859290383 0.250790425585 y[1] (closed_form) = 1.85924232189 0.250817020704 absolute error = 5.493e-05 relative error = 0.002928 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1123.1MB, alloc=52.3MB, time=13.91 x[1] = 2.1618 0.366 h = 0.001 0.001 y[1] (numeric) = 1.85925700035 0.252867651807 y[1] (closed_form) = 1.8592085175 0.252894286643 absolute error = 5.532e-05 relative error = 0.002948 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1628 0.367 h = 0.001 0.003 y[1] (numeric) = 1.85991383567 0.253593390306 y[1] (closed_form) = 1.8598653554 0.253620119117 absolute error = 5.536e-05 relative error = 0.002949 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.179 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 x[1] = 2.1638 0.37 h = 0.0001 0.004 y[1] (numeric) = 1.86050159024 0.255702083731 y[1] (closed_form) = 1.86045274191 0.255729104964 absolute error = 5.582e-05 relative error = 0.002973 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.18 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=1168.7MB, alloc=52.3MB, time=14.47 x[1] = 2.1639 0.374 h = 0.003 0.006 y[1] (numeric) = 1.86043144971 0.258471507345 y[1] (closed_form) = 1.86038185109 0.258498587242 absolute error = 5.651e-05 relative error = 0.003009 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.181 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] = 2.1669 0.38 h = 0.0001 0.005 y[1] (numeric) = 1.86229477844 0.262726133103 y[1] (closed_form) = 1.86224395942 0.262754940168 absolute error = 5.842e-05 relative error = 0.003106 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.184 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] = 2.167 0.385 h = 0.0001 0.003 y[1] (numeric) = 1.86218519131 0.266188724971 y[1] (closed_form) = 1.86213319955 0.266217612684 absolute error = 5.948e-05 relative error = 0.003162 % Correct digits = 5 Radius of convergence (given) for eq 1 = 4.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1214.3MB, alloc=52.3MB, time=15.03 x[1] = 2.1671 0.388 h = 0.001 0.001 y[1] (numeric) = 1.86214570506 0.268267826135 y[1] (closed_form) = 1.86209329187 0.268296754214 absolute error = 5.987e-05 relative error = 0.003182 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.185 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1681 0.389 h = 0.001 0.003 y[1] (numeric) = 1.86280104447 0.268996174502 y[1] (closed_form) = 1.86274863402 0.269025196493 absolute error = 5.991e-05 relative error = 0.003183 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.186 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 x[1] = 2.1691 0.392 h = 0.0001 0.004 y[1] (numeric) = 1.8633831981 0.271108591806 y[1] (closed_form) = 1.86333042028 0.271137906623 absolute error = 6.037e-05 relative error = 0.003206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.187 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=1259.9MB, alloc=52.3MB, time=15.59 x[1] = 2.1692 0.396 h = 0.003 0.006 y[1] (numeric) = 1.86330490397 0.273880450454 y[1] (closed_form) = 1.86325137643 0.273909825092 absolute error = 6.106e-05 relative error = 0.003242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.188 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] = 2.1722 0.402 h = 0.0001 0.005 y[1] (numeric) = 1.86515759439 0.278144580628 y[1] (closed_form) = 1.86510284997 0.278175683289 absolute error = 6.296e-05 relative error = 0.003339 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1723 0.407 h = 0.0001 0.003 y[1] (numeric) = 1.86503780693 0.281610171275 y[1] (closed_form) = 1.86498189063 0.281641356397 absolute error = 6.402e-05 relative error = 0.003394 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1305.6MB, alloc=52.3MB, time=16.15 x[1] = 2.1724 0.41 h = 0.001 0.001 y[1] (numeric) = 1.86499222389 0.283691155916 y[1] (closed_form) = 1.86493588651 0.283722382048 absolute error = 6.441e-05 relative error = 0.003415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.192 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1734 0.411 h = 0.0001 0.004 y[1] (numeric) = 1.8656460725 0.284422114883 y[1] (closed_form) = 1.865589738 0.284453434863 absolute error = 6.446e-05 relative error = 0.003415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.194 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] = 2.1735 0.415 h = 0.003 0.006 y[1] (numeric) = 1.86556073802 0.287195981636 y[1] (closed_form) = 1.86550365431 0.28722736249 absolute error = 6.514e-05 relative error = 0.003451 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.194 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=1351.3MB, alloc=52.3MB, time=16.71 x[1] = 2.1765 0.421 h = 0.0001 0.005 y[1] (numeric) = 1.86740417546 0.291468175226 y[1] (closed_form) = 1.86734587788 0.29150128485 absolute error = 6.704e-05 relative error = 0.003547 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.198 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1766 0.426 h = 0.0001 0.003 y[1] (numeric) = 1.86727558093 0.294936237214 y[1] (closed_form) = 1.86721611222 0.29496943086 absolute error = 6.811e-05 relative error = 0.003603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.198 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1767 0.429 h = 0.001 0.001 y[1] (numeric) = 1.86722473293 0.297018777343 y[1] (closed_form) = 1.86716484342 0.297052012553 absolute error = 6.849e-05 relative error = 0.003623 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.199 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=1397.0MB, alloc=52.3MB, time=17.27 x[1] = 2.1777 0.43 h = 0.001 0.003 y[1] (numeric) = 1.86787727127 0.2977519663 y[1] (closed_form) = 1.86781738477 0.297785295303 absolute error = 6.854e-05 relative error = 0.003624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.2 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] = 2.1787 0.433 h = 0.0001 0.004 y[1] (numeric) = 1.8684489835 0.299871263785 y[1] (closed_form) = 1.86838873092 0.299904886352 absolute error = 6.900e-05 relative error = 0.003646 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.201 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] = 2.1788 0.437 h = 0.003 0.006 y[1] (numeric) = 1.86835551219 0.302647586876 y[1] (closed_form) = 1.86829451095 0.302681271405 absolute error = 6.968e-05 relative error = 0.003682 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.202 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=1442.6MB, alloc=52.3MB, time=17.83 x[1] = 2.1818 0.443 h = 0.0001 0.005 y[1] (numeric) = 1.87018835189 0.306929305147 y[1] (closed_form) = 1.87012614029 0.306964719234 absolute error = 7.159e-05 relative error = 0.003777 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1819 0.448 h = 0.0001 0.003 y[1] (numeric) = 1.87004957788 0.310400392446 y[1] (closed_form) = 1.86998619605 0.310435892343 absolute error = 7.265e-05 relative error = 0.003832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.206 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 x[1] = 2.182 0.451 h = 0.001 0.001 y[1] (numeric) = 1.86999264586 0.312484831777 y[1] (closed_form) = 1.86992884356 0.312520373873 absolute error = 7.303e-05 relative error = 0.003852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.206 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=1488.2MB, alloc=52.3MB, time=18.38 x[1] = 2.183 0.452 h = 0.001 0.003 y[1] (numeric) = 1.87064370285 0.313220632625 y[1] (closed_form) = 1.87057990371 0.313256268447 absolute error = 7.308e-05 relative error = 0.003853 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.207 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] = 2.184 0.455 h = 0.0001 0.004 y[1] (numeric) = 1.87120984119 0.315343672564 y[1] (closed_form) = 1.87114567668 0.315379602332 absolute error = 7.354e-05 relative error = 0.003876 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.209 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] = 2.1841 0.459 h = 0.003 0.006 y[1] (numeric) = 1.8711082422 0.318122463131 y[1] (closed_form) = 1.87104332962 0.318158455994 absolute error = 7.422e-05 relative error = 0.003911 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.209 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 memory used=1533.9MB, alloc=52.3MB, time=18.94 x[1] = 2.1871 0.465 h = 0.0001 0.005 y[1] (numeric) = 1.87293050607 0.322413716495 y[1] (closed_form) = 1.87286438664 0.322451439667 absolute error = 7.612e-05 relative error = 0.004006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1872 0.47 h = 0.0001 0.003 y[1] (numeric) = 1.87278156402 0.325887843077 y[1] (closed_form) = 1.87271427527 0.325925653836 absolute error = 7.718e-05 relative error = 0.00406 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1873 0.473 h = 0.001 0.001 y[1] (numeric) = 1.87271855499 0.32797418989 y[1] (closed_form) = 1.87265084611 0.328012043476 absolute error = 7.757e-05 relative error = 0.00408 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.214 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 memory used=1579.4MB, alloc=52.3MB, time=19.50 x[1] = 2.1883 0.474 h = 0.001 0.003 y[1] (numeric) = 1.87336813569 0.328712603218 y[1] (closed_form) = 1.87330043012 0.328750550463 absolute error = 7.761e-05 relative error = 0.004081 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.215 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1893 0.477 h = 0.0001 0.004 y[1] (numeric) = 1.87392870971 0.330839391855 y[1] (closed_form) = 1.87386063947 0.33087763342 absolute error = 7.808e-05 relative error = 0.004103 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.216 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 x[1] = 2.1894 0.481 h = 0.003 0.006 y[1] (numeric) = 1.87381899229 0.33362066097 y[1] (closed_form) = 1.87375017458 0.333658966754 absolute error = 7.876e-05 relative error = 0.004138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.217 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=1625.2MB, alloc=52.3MB, time=20.06 x[1] = 2.1924 0.487 h = 0.0001 0.005 y[1] (numeric) = 1.87563070228 0.337921459602 y[1] (closed_form) = 1.87556068122 0.337961496412 absolute error = 8.066e-05 relative error = 0.004232 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.221 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] = 2.1925 0.492 h = 0.0001 0.003 y[1] (numeric) = 1.87547160373 0.341398639292 y[1] (closed_form) = 1.87540041427 0.341438765448 absolute error = 8.172e-05 relative error = 0.004287 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.221 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] = 2.1926 0.495 h = 0.001 0.001 y[1] (numeric) = 1.87540252472 0.343486901773 y[1] (closed_form) = 1.87533091549 0.343527071381 absolute error = 8.211e-05 relative error = 0.004307 % Correct digits = 4 memory used=1670.8MB, alloc=52.3MB, time=20.62 Radius of convergence (given) for eq 1 = 4.222 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.1936 0.496 h = 0.001 0.003 y[1] (numeric) = 1.87605063421 0.344227928121 y[1] (closed_form) = 1.87597902842 0.34426819132 absolute error = 8.215e-05 relative error = 0.004307 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.223 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 x[1] = 2.1946 0.499 h = 0.0001 0.004 y[1] (numeric) = 1.87660565348 0.346358471594 y[1] (closed_form) = 1.87653368373 0.346399029477 absolute error = 8.261e-05 relative error = 0.004329 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.224 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] = 2.1947 0.503 h = 0.003 0.006 y[1] (numeric) = 1.87648782695 0.349142230207 y[1] (closed_form) = 1.87641511034 0.349182853425 absolute error = 8.329e-05 relative error = 0.004364 % Correct digits = 4 memory used=1716.5MB, alloc=52.3MB, time=21.18 Radius of convergence (given) for eq 1 = 4.225 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] = 2.1977 0.509 h = 0.0001 0.005 y[1] (numeric) = 1.87828900503 0.353452584046 y[1] (closed_form) = 1.87821508858 0.353494938972 absolute error = 8.519e-05 relative error = 0.004458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.228 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] = 2.1978 0.514 h = 0.0001 0.003 y[1] (numeric) = 1.87811976161 0.356932830517 y[1] (closed_form) = 1.87804467769 0.356975276537 absolute error = 8.625e-05 relative error = 0.004512 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.229 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=1762.1MB, alloc=52.3MB, time=21.74 x[1] = 2.1979 0.517 h = 0.001 0.001 y[1] (numeric) = 1.87804461974 0.359023016763 y[1] (closed_form) = 1.8779691164 0.359065506853 absolute error = 8.664e-05 relative error = 0.004531 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.23 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] = 2.1989 0.518 h = 0.0001 0.004 y[1] (numeric) = 1.87869126306 0.359766656624 y[1] (closed_form) = 1.87861576331 0.359809240235 absolute error = 8.668e-05 relative error = 0.004532 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.231 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 x[1] = 2.199 0.522 h = 0.003 0.006 y[1] (numeric) = 1.87856643415 0.362552470297 y[1] (closed_form) = 1.87849018809 0.362595120255 absolute error = 8.736e-05 relative error = 0.004566 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.231 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=1807.8MB, alloc=52.3MB, time=22.30 x[1] = 2.202 0.528 h = 0.0001 0.005 y[1] (numeric) = 1.88035845034 0.36687093162 y[1] (closed_form) = 1.88028100745 0.366915313887 absolute error = 8.926e-05 relative error = 0.004659 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.235 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] = 2.2021 0.533 h = 0.0001 0.003 y[1] (numeric) = 1.88018044718 0.370353708053 y[1] (closed_form) = 1.88010183763 0.370398182917 absolute error = 9.032e-05 relative error = 0.004713 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2022 0.536 h = 0.001 0.001 y[1] (numeric) = 1.88010006928 0.37244548452 y[1] (closed_form) = 1.88002104061 0.372490003987 absolute error = 9.071e-05 relative error = 0.004733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.236 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1853.5MB, alloc=52.3MB, time=22.86 x[1] = 2.2032 0.537 h = 0.001 0.003 y[1] (numeric) = 1.88074542347 0.373191356979 y[1] (closed_form) = 1.88066639851 0.373235969908 absolute error = 9.075e-05 relative error = 0.004733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.237 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2042 0.54 h = 0.0001 0.004 y[1] (numeric) = 1.88129008734 0.375328837387 y[1] (closed_form) = 1.88121069972 0.37537374567 absolute error = 9.121e-05 relative error = 0.004755 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.239 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] = 2.2043 0.544 h = 0.003 0.006 y[1] (numeric) = 1.8811571668 0.37811716078 y[1] (closed_form) = 1.88107703346 0.378162136457 absolute error = 9.189e-05 relative error = 0.004789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.239 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 memory used=1899.1MB, alloc=52.3MB, time=23.42 x[1] = 2.2073 0.55 h = 0.0001 0.005 y[1] (numeric) = 1.88293869192 0.382445195441 y[1] (closed_form) = 1.88285736523 0.382491904044 absolute error = 9.379e-05 relative error = 0.004881 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.243 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 x[1] = 2.2074 0.555 h = 0.0001 0.003 y[1] (numeric) = 1.8827505656 0.385931063838 y[1] (closed_form) = 1.88266807321 0.385977866759 absolute error = 9.484e-05 relative error = 0.004935 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.244 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2075 0.558 h = 0.001 0.001 y[1] (numeric) = 1.8826641381 0.388024778978 y[1] (closed_form) = 1.88258122696 0.38807162711 absolute error = 9.523e-05 relative error = 0.004954 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.244 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1944.7MB, alloc=52.3MB, time=23.98 x[1] = 2.2085 0.559 h = 0.001 0.003 y[1] (numeric) = 1.88330803549 0.388773265797 y[1] (closed_form) = 1.88322512819 0.38882020732 absolute error = 9.527e-05 relative error = 0.004955 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.245 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] = 2.2095 0.562 h = 0.0001 0.004 y[1] (numeric) = 1.88384717209 0.390914518112 y[1] (closed_form) = 1.88376390285 0.390961755333 absolute error = 9.573e-05 relative error = 0.004976 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2096 0.566 h = 0.003 0.006 y[1] (numeric) = 1.8837061694 0.393705361779 y[1] (closed_form) = 1.88362215507 0.393752667482 absolute error = 9.642e-05 relative error = 0.00501 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.247 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=1990.4MB, alloc=52.3MB, time=24.54 x[1] = 2.2126 0.572 h = 0.0001 0.005 y[1] (numeric) = 1.88547722548 0.398042979047 y[1] (closed_form) = 1.88539202129 0.39809201826 absolute error = 9.831e-05 relative error = 0.005102 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.251 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] = 2.2127 0.577 h = 0.0001 0.003 y[1] (numeric) = 1.8852789879 0.40153195265 y[1] (closed_form) = 1.88519261898 0.401581087887 absolute error = 9.937e-05 relative error = 0.005155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.252 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2128 0.58 h = 0.001 0.001 y[1] (numeric) = 1.88518651805 0.403627614297 y[1] (closed_form) = 1.88509973075 0.40367679535 absolute error = 9.975e-05 relative error = 0.005174 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.253 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=2036.0MB, alloc=52.3MB, time=25.10 x[1] = 2.2138 0.581 h = 0.001 0.003 y[1] (numeric) = 1.88582896364 0.404378715832 y[1] (closed_form) = 1.88574218033 0.404427990201 absolute error = 9.980e-05 relative error = 0.005174 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.254 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2148 0.584 h = 0.0001 0.004 y[1] (numeric) = 1.88636258266 0.406523745773 y[1] (closed_form) = 1.8862754381 0.406573316177 absolute error = 0.0001003 relative error = 0.005196 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.255 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2149 0.588 h = 0.003 0.006 y[1] (numeric) = 1.88621350743 0.409317120197 y[1] (closed_form) = 1.88612561842 0.409366760163 absolute error = 0.0001009 relative error = 0.00523 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.256 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 memory used=2081.6MB, alloc=52.3MB, time=25.66 x[1] = 2.2179 0.594 h = 0.0001 0.005 y[1] (numeric) = 1.88797411651 0.413664329109 y[1] (closed_form) = 1.88788504112 0.413715703135 absolute error = 0.0001028 relative error = 0.005321 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.26 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] = 2.218 0.599 h = 0.0001 0.003 y[1] (numeric) = 1.88776577963 0.417156421009 y[1] (closed_form) = 1.8876755405 0.41720789275 absolute error = 0.0001039 relative error = 0.005374 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.26 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] = 2.2181 0.602 h = 0.001 0.001 y[1] (numeric) = 1.88766727473 0.419254036906 y[1] (closed_form) = 1.8875766176 0.419305555061 absolute error = 0.0001043 relative error = 0.005393 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.261 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2127.3MB, alloc=52.3MB, time=26.22 x[1] = 2.2191 0.603 h = 0.001 0.003 y[1] (numeric) = 1.88830827354 0.420007753462 y[1] (closed_form) = 1.88821762054 0.420059364861 absolute error = 0.0001043 relative error = 0.005393 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.262 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 x[1] = 2.2201 0.606 h = 0.0001 0.004 y[1] (numeric) = 1.88883638466 0.422156566643 y[1] (closed_form) = 1.88874537113 0.422208474406 absolute error = 0.0001048 relative error = 0.005414 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.263 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 x[1] = 2.2202 0.61 h = 0.003 0.006 y[1] (numeric) = 1.88867924656 0.424952482186 y[1] (closed_form) = 1.88858748922 0.425004460581 absolute error = 0.0001055 relative error = 0.005448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.264 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=2172.9MB, alloc=52.3MB, time=26.78 x[1] = 2.2232 0.616 h = 0.0001 0.005 y[1] (numeric) = 1.8904294307 0.429309291546 y[1] (closed_form) = 1.89033649045 0.429363004517 absolute error = 0.0001073 relative error = 0.005538 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.268 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 x[1] = 2.2233 0.621 h = 0.0001 0.003 y[1] (numeric) = 1.89021100657 0.432804514681 y[1] (closed_form) = 1.89011690358 0.432858327044 absolute error = 0.0001084 relative error = 0.005591 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2234 0.624 h = 0.001 0.001 y[1] (numeric) = 1.89010647398 0.43490409248 y[1] (closed_form) = 1.89001195336 0.434957951849 absolute error = 0.0001088 relative error = 0.005609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.269 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2218.7MB, alloc=52.3MB, time=27.34 x[1] = 2.2244 0.625 h = 0.0001 0.004 y[1] (numeric) = 1.890746031 0.435660424318 y[1] (closed_form) = 1.89065151464 0.435714376857 absolute error = 0.0001088 relative error = 0.005609 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2245 0.629 h = 0.003 0.006 y[1] (numeric) = 1.89058192995 0.438458439438 y[1] (closed_form) = 1.89048667038 0.438512463581 absolute error = 0.0001095 relative error = 0.005643 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.271 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2275 0.635 h = 0.0001 0.005 y[1] (numeric) = 1.89232304382 0.442823395595 y[1] (closed_form) = 1.89222660433 0.442879154773 absolute error = 0.0001114 relative error = 0.005732 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.275 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2264.4MB, alloc=52.3MB, time=27.91 x[1] = 2.2276 0.64 h = 0.0001 0.003 y[1] (numeric) = 1.89209590912 0.446321204274 y[1] (closed_form) = 1.89199830774 0.446377064288 absolute error = 0.0001125 relative error = 0.005785 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2277 0.643 h = 0.001 0.001 y[1] (numeric) = 1.89198617053 0.448422405186 y[1] (closed_form) = 1.89188815183 0.448478312718 absolute error = 0.0001128 relative error = 0.005804 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.276 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2287 0.644 h = 0.001 0.003 y[1] (numeric) = 1.89262445932 0.449180971252 y[1] (closed_form) = 1.89252644501 0.449236971889 absolute error = 0.0001129 relative error = 0.005803 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.277 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 memory used=2310.2MB, alloc=52.3MB, time=28.47 x[1] = 2.2297 0.647 h = 0.0001 0.004 y[1] (numeric) = 1.8931423022 0.451336773394 y[1] (closed_form) = 1.89304392867 0.451393070995 absolute error = 0.0001133 relative error = 0.005824 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.279 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2298 0.651 h = 0.003 0.006 y[1] (numeric) = 1.89297015635 0.454137348755 y[1] (closed_form) = 1.89287104023 0.454193718962 absolute error = 0.000114 relative error = 0.005858 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.28 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] = 2.2328 0.657 h = 0.0001 0.005 y[1] (numeric) = 1.89470088625 0.458511921394 y[1] (closed_form) = 1.89460059367 0.458570027091 absolute error = 0.0001159 relative error = 0.005946 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.283 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 memory used=2355.9MB, alloc=52.3MB, time=29.03 x[1] = 2.2329 0.662 h = 0.0001 0.003 y[1] (numeric) = 1.89446368678 0.462012885123 y[1] (closed_form) = 1.89436223334 0.462071093304 absolute error = 0.000117 relative error = 0.005999 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.284 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.233 0.665 h = 0.001 0.001 y[1] (numeric) = 1.8943479342 0.464116062016 y[1] (closed_form) = 1.89424606382 0.464174318299 absolute error = 0.0001174 relative error = 0.006017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.285 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 x[1] = 2.234 0.666 h = 0.001 0.003 y[1] (numeric) = 1.89498479044 0.464877243786 y[1] (closed_form) = 1.89488292458 0.464935593097 absolute error = 0.0001174 relative error = 0.006017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.286 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2401.7MB, alloc=52.3MB, time=29.59 x[1] = 2.235 0.669 h = 0.0001 0.004 y[1] (numeric) = 1.89549715321 0.467036844749 y[1] (closed_form) = 1.89539492885 0.467095491331 absolute error = 0.0001179 relative error = 0.006037 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.288 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 x[1] = 2.2351 0.673 h = 0.003 0.006 y[1] (numeric) = 1.89531697236 0.469839990313 y[1] (closed_form) = 1.89521400608 0.469898710545 absolute error = 0.0001185 relative error = 0.006071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.288 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 x[1] = 2.2381 0.679 h = 0.0001 0.005 y[1] (numeric) = 1.89703734038 0.474224187582 y[1] (closed_form) = 1.89693320109 0.474284643725 absolute error = 0.0001204 relative error = 0.006158 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.292 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2447.4MB, alloc=52.3MB, time=30.15 x[1] = 2.2382 0.684 h = 0.0001 0.003 y[1] (numeric) = 1.89679008841 0.477728318862 y[1] (closed_form) = 1.89668478928 0.477788879125 absolute error = 0.0001215 relative error = 0.00621 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.293 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 x[1] = 2.2383 0.687 h = 0.001 0.001 y[1] (numeric) = 1.89666832931 0.479833479125 y[1] (closed_form) = 1.89656261364 0.479894088066 absolute error = 0.0001219 relative error = 0.006229 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.294 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 x[1] = 2.2393 0.688 h = 0.001 0.003 y[1] (numeric) = 1.89730375796 0.480597276726 y[1] (closed_form) = 1.89719804694 0.480657978618 absolute error = 0.0001219 relative error = 0.006228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.295 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2493.1MB, alloc=52.3MB, time=30.71 x[1] = 2.2403 0.691 h = 0.0001 0.004 y[1] (numeric) = 1.89781065039 0.482760681711 y[1] (closed_form) = 1.89770458158 0.482821681174 absolute error = 0.0001224 relative error = 0.006249 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.296 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2404 0.695 h = 0.003 0.006 y[1] (numeric) = 1.89762244444 0.485566407368 y[1] (closed_form) = 1.89751563439 0.485627481515 absolute error = 0.000123 relative error = 0.006282 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.297 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] = 2.2434 0.701 h = 0.0001 0.005 y[1] (numeric) = 1.89933247265 0.489960237187 y[1] (closed_form) = 1.89922449304 0.490023047633 absolute error = 0.0001249 relative error = 0.006369 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.301 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2538.8MB, alloc=52.3MB, time=31.27 x[1] = 2.2435 0.706 h = 0.0001 0.003 y[1] (numeric) = 1.89907518051 0.493467548369 y[1] (closed_form) = 1.89896604211 0.493530464556 absolute error = 0.000126 relative error = 0.006421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.302 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 x[1] = 2.2436 0.709 h = 0.001 0.001 y[1] (numeric) = 1.89894742242 0.495574699295 y[1] (closed_form) = 1.89883786788 0.495637664732 absolute error = 0.0001264 relative error = 0.006439 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.302 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 x[1] = 2.2446 0.71 h = 0.001 0.003 y[1] (numeric) = 1.89958142841 0.496341112812 y[1] (closed_form) = 1.89947187864 0.496404171121 absolute error = 0.0001264 relative error = 0.006438 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.304 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 memory used=2584.4MB, alloc=52.3MB, time=31.83 x[1] = 2.2456 0.713 h = 0.0001 0.004 y[1] (numeric) = 1.90008286028 0.498508326914 y[1] (closed_form) = 1.89997295344 0.498571683087 absolute error = 0.0001269 relative error = 0.006458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.305 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2457 0.717 h = 0.003 0.006 y[1] (numeric) = 1.8998866392 0.50131664243 y[1] (closed_form) = 1.89977599179 0.501380074311 absolute error = 0.0001275 relative error = 0.006491 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.306 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 x[1] = 2.2487 0.723 h = 0.0001 0.005 y[1] (numeric) = 1.90158634967 0.505720112495 y[1] (closed_form) = 1.90147453614 0.505785281031 absolute error = 0.0001294 relative error = 0.006578 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.31 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2630.1MB, alloc=52.3MB, time=32.39 x[1] = 2.2488 0.728 h = 0.0001 0.003 y[1] (numeric) = 1.90131902978 0.509230615775 y[1] (closed_form) = 1.90120605853 0.509295891655 absolute error = 0.0001305 relative error = 0.006629 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.311 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 x[1] = 2.2489 0.731 h = 0.001 0.001 y[1] (numeric) = 1.90118528026 0.511339764567 y[1] (closed_form) = 1.90107189325 0.511405090265 absolute error = 0.0001309 relative error = 0.006647 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.311 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 x[1] = 2.2499 0.732 h = 0.0001 0.004 y[1] (numeric) = 1.9018178685 0.512108794037 y[1] (closed_form) = 1.90170448641 0.512174212528 absolute error = 0.0001309 relative error = 0.006647 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.312 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=2675.7MB, alloc=52.3MB, time=32.95 x[1] = 2.25 0.736 h = 0.003 0.006 y[1] (numeric) = 1.90161472522 0.514919251183 y[1] (closed_form) = 1.90150060318 0.514984746313 absolute error = 0.0001316 relative error = 0.006679 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.313 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] = 2.253 0.742 h = 0.0001 0.005 y[1] (numeric) = 1.90330545725 0.519330902692 y[1] (closed_form) = 1.90319017204 0.519398134798 absolute error = 0.0001335 relative error = 0.006765 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.317 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 x[1] = 2.2531 0.747 h = 0.0001 0.003 y[1] (numeric) = 1.90302947758 0.522844044024 y[1] (closed_form) = 1.90291303554 0.522911384859 absolute error = 0.0001345 relative error = 0.006816 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2721.5MB, alloc=52.3MB, time=33.51 x[1] = 2.2532 0.75 h = 0.001 0.001 y[1] (numeric) = 1.90289055301 0.524954846963 y[1] (closed_form) = 1.90277369555 0.525022238103 absolute error = 0.0001349 relative error = 0.006834 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.319 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] = 2.2542 0.751 h = 0.001 0.003 y[1] (numeric) = 1.90352189366 0.525726111348 y[1] (closed_form) = 1.90340504123 0.525793595213 absolute error = 0.0001349 relative error = 0.006833 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2552 0.754 h = 0.0001 0.004 y[1] (numeric) = 1.90401314529 0.527900361758 y[1] (closed_form) = 1.9038959371 0.527968144019 absolute error = 0.0001354 relative error = 0.006853 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.321 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2767.3MB, alloc=52.3MB, time=34.07 x[1] = 2.2553 0.758 h = 0.0001 0.004 y[1] (numeric) = 1.90380200546 0.530713426779 y[1] (closed_form) = 1.90368405799 0.530781286636 absolute error = 0.0001361 relative error = 0.006885 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.322 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2554 0.762 h = 0.003 0.006 y[1] (numeric) = 1.90358938719 0.533526647212 y[1] (closed_form) = 1.90347070054 0.5335945848 absolute error = 0.0001368 relative error = 0.006918 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.323 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] = 2.2584 0.768 h = 0.0001 0.005 y[1] (numeric) = 1.90526770966 0.537949241939 y[1] (closed_form) = 1.90514786385 0.538018916975 absolute error = 0.0001386 relative error = 0.007003 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.327 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=2812.9MB, alloc=52.3MB, time=34.63 x[1] = 2.2585 0.773 h = 0.0001 0.003 y[1] (numeric) = 1.90497987749 0.541465783837 y[1] (closed_form) = 1.90485887605 0.541535569489 absolute error = 0.0001397 relative error = 0.007053 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.328 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 x[1] = 2.2586 0.776 h = 0.001 0.001 y[1] (numeric) = 1.90483386819 0.543578724686 y[1] (closed_form) = 1.90471245179 0.54364856131 absolute error = 0.0001401 relative error = 0.007071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.329 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2596 0.777 h = 0.001 0.003 y[1] (numeric) = 1.90546346012 0.544353005134 y[1] (closed_form) = 1.9053420489 0.544422934393 absolute error = 0.0001401 relative error = 0.007071 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2858.6MB, alloc=52.3MB, time=35.19 x[1] = 2.2606 0.78 h = 0.0001 0.004 y[1] (numeric) = 1.90594819902 0.546531538888 y[1] (closed_form) = 1.90582643287 0.546601766888 absolute error = 0.0001406 relative error = 0.00709 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.331 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 x[1] = 2.2607 0.784 h = 0.003 0.006 y[1] (numeric) = 1.90572759571 0.549347378491 y[1] (closed_form) = 1.90560509106 0.549417685282 absolute error = 0.0001412 relative error = 0.007122 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.332 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2637 0.79 h = 0.0001 0.005 y[1] (numeric) = 1.90739566704 0.553779636514 y[1] (closed_form) = 1.90727200663 0.553851681011 absolute error = 0.0001431 relative error = 0.007206 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.336 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=2904.3MB, alloc=52.3MB, time=35.75 x[1] = 2.2638 0.795 h = 0.0001 0.003 y[1] (numeric) = 1.9070978446 0.557299407192 y[1] (closed_form) = 1.90697302966 0.557371563866 absolute error = 0.0001442 relative error = 0.007257 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.337 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 x[1] = 2.2639 0.798 h = 0.001 0.001 y[1] (numeric) = 1.9069458667 0.559414367568 y[1] (closed_form) = 1.90682063721 0.559486575764 absolute error = 0.0001446 relative error = 0.007274 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.338 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2649 0.799 h = 0.001 0.003 y[1] (numeric) = 1.90757405571 0.560191264055 y[1] (closed_form) = 1.90744883152 0.560263564805 absolute error = 0.0001446 relative error = 0.007273 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.339 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=2950.0MB, alloc=52.3MB, time=36.31 x[1] = 2.2659 0.802 h = 0.0001 0.004 y[1] (numeric) = 1.90805337341 0.562373626894 y[1] (closed_form) = 1.907927795 0.562446226646 absolute error = 0.0001451 relative error = 0.007292 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.341 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] = 2.266 0.806 h = 0.003 0.006 y[1] (numeric) = 1.9078247952 0.565192095005 y[1] (closed_form) = 1.90769847901 0.565264774533 absolute error = 0.0001457 relative error = 0.007324 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.341 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] = 2.269 0.812 h = 0.0001 0.005 y[1] (numeric) = 1.90948263743 0.569634023117 y[1] (closed_form) = 1.90935516889 0.569708440579 absolute error = 0.0001476 relative error = 0.007408 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.346 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 memory used=2995.8MB, alloc=52.3MB, time=36.87 x[1] = 2.2691 0.817 h = 0.0001 0.003 y[1] (numeric) = 1.90917483742 0.573157034157 y[1] (closed_form) = 1.90904621544 0.573231565341 absolute error = 0.0001487 relative error = 0.007458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.347 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 x[1] = 2.2692 0.82 h = 0.001 0.001 y[1] (numeric) = 1.90901689863 0.575274020891 y[1] (closed_form) = 1.90888786251 0.575348604142 absolute error = 0.000149 relative error = 0.007476 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.347 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 x[1] = 2.2702 0.821 h = 0.001 0.003 y[1] (numeric) = 1.90964368957 0.576053533279 y[1] (closed_form) = 1.90951465888 0.576128209 absolute error = 0.0001491 relative error = 0.007475 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.348 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 memory used=3041.6MB, alloc=52.3MB, time=37.44 x[1] = 2.2712 0.824 h = 0.0001 0.004 y[1] (numeric) = 1.9101175959 0.578239729771 y[1] (closed_form) = 1.9099882117 0.578314704751 absolute error = 0.0001495 relative error = 0.007493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2713 0.828 h = 0.003 0.006 y[1] (numeric) = 1.90988105302 0.581060835541 y[1] (closed_form) = 1.90975093176 0.581135891272 absolute error = 0.0001502 relative error = 0.007525 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.351 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] = 2.2743 0.834 h = 0.0001 0.005 y[1] (numeric) = 1.91152868819 0.585512440316 y[1] (closed_form) = 1.91139741797 0.585589234178 absolute error = 0.0001521 relative error = 0.007608 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.355 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3087.2MB, alloc=52.3MB, time=38.00 x[1] = 2.2744 0.839 h = 0.0001 0.003 y[1] (numeric) = 1.91121092333 0.589038703147 y[1] (closed_form) = 1.91107850078 0.58911561226 absolute error = 0.0001531 relative error = 0.007658 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2745 0.842 h = 0.001 0.001 y[1] (numeric) = 1.9110470314 0.591157722978 y[1] (closed_form) = 1.91091419512 0.591234684697 absolute error = 0.0001535 relative error = 0.007675 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.357 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2755 0.843 h = 0.001 0.003 y[1] (numeric) = 1.91167242911 0.591939851086 y[1] (closed_form) = 1.91153959839 0.592016905191 absolute error = 0.0001536 relative error = 0.007674 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.358 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=3132.9MB, alloc=52.3MB, time=38.57 x[1] = 2.2765 0.846 h = 0.0001 0.004 y[1] (numeric) = 1.91214093391 0.594129885696 y[1] (closed_form) = 1.9120077504 0.594207239308 absolute error = 0.000154 relative error = 0.007692 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.359 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2766 0.85 h = 0.003 0.006 y[1] (numeric) = 1.91189643663 0.596953638152 y[1] (closed_form) = 1.91176251677 0.597031073482 absolute error = 0.0001547 relative error = 0.007724 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.36 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] = 2.2796 0.856 h = 0.0001 0.005 y[1] (numeric) = 1.91353388675 0.601414925946 y[1] (closed_form) = 1.91339882131 0.601494099573 absolute error = 0.0001566 relative error = 0.007806 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.364 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3178.8MB, alloc=52.3MB, time=39.13 x[1] = 2.2797 0.861 h = 0.0001 0.003 y[1] (numeric) = 1.91320616984 0.604944451843 y[1] (closed_form) = 1.9130699532 0.605023742236 absolute error = 0.0001576 relative error = 0.007855 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.365 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 x[1] = 2.2798 0.864 h = 0.001 0.001 y[1] (numeric) = 1.91303633255 0.607065511418 y[1] (closed_form) = 1.9128997026 0.60714485495 absolute error = 0.000158 relative error = 0.007873 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.366 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] = 2.2808 0.865 h = 0.0001 0.004 y[1] (numeric) = 1.91366034184 0.607850255022 y[1] (closed_form) = 1.91352371757 0.607929690855 absolute error = 0.000158 relative error = 0.007871 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.367 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 memory used=3224.5MB, alloc=52.3MB, time=39.69 x[1] = 2.2809 0.869 h = 0.003 0.006 y[1] (numeric) = 1.91340897421 0.610676198162 y[1] (closed_form) = 1.91327161425 0.610755716592 absolute error = 0.0001587 relative error = 0.007903 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.368 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2839 0.875 h = 0.0001 0.005 y[1] (numeric) = 1.91503755954 0.615145704732 y[1] (closed_form) = 1.91489905692 0.615226961616 absolute error = 0.0001606 relative error = 0.007984 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.372 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 x[1] = 2.284 0.88 h = 0.0001 0.003 y[1] (numeric) = 1.91470124748 0.61867792994 y[1] (closed_form) = 1.9145615946 0.618759304896 absolute error = 0.0001616 relative error = 0.008033 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.373 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3270.3MB, alloc=52.3MB, time=40.26 x[1] = 2.2841 0.883 h = 0.001 0.001 y[1] (numeric) = 1.91452627448 0.620800679815 y[1] (closed_form) = 1.91438620865 0.62088210837 absolute error = 0.000162 relative error = 0.00805 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2851 0.884 h = 0.001 0.003 y[1] (numeric) = 1.91514906134 0.62158765808 y[1] (closed_form) = 1.9150090013 0.621669178864 absolute error = 0.0001621 relative error = 0.008049 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2861 0.887 h = 0.0001 0.004 y[1] (numeric) = 1.91560749556 0.623784782 y[1] (closed_form) = 1.91546708404 0.623866602743 absolute error = 0.0001625 relative error = 0.008067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.377 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3316.0MB, alloc=52.3MB, time=40.82 x[1] = 2.2862 0.891 h = 0.003 0.006 y[1] (numeric) = 1.91534819267 0.626613388471 y[1] (closed_form) = 1.91520704616 0.626695292711 absolute error = 0.0001632 relative error = 0.008098 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.378 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] = 2.2892 0.897 h = 0.0001 0.005 y[1] (numeric) = 1.91696663379 0.63109258957 y[1] (closed_form) = 1.91682434797 0.631176232374 absolute error = 0.000165 relative error = 0.008179 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.382 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2893 0.902 h = 0.0001 0.003 y[1] (numeric) = 1.9166203935 0.634628098573 y[1] (closed_form) = 1.91647695857 0.634711860935 absolute error = 0.0001661 relative error = 0.008228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.383 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=3361.9MB, alloc=52.3MB, time=41.40 x[1] = 2.2894 0.905 h = 0.001 0.001 y[1] (numeric) = 1.91643948962 0.636752900407 y[1] (closed_form) = 1.91629564216 0.636836716892 absolute error = 0.0001665 relative error = 0.008245 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.384 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 x[1] = 2.2904 0.906 h = 0.001 0.003 y[1] (numeric) = 1.91706089698 0.637542493699 y[1] (closed_form) = 1.91691705543 0.637626402327 absolute error = 0.0001665 relative error = 0.008243 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.385 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2914 0.909 h = 0.0001 0.004 y[1] (numeric) = 1.91751395781 0.639743468064 y[1] (closed_form) = 1.9173697655 0.639827676877 absolute error = 0.000167 relative error = 0.008261 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.387 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=3407.7MB, alloc=52.3MB, time=41.96 x[1] = 2.2915 0.913 h = 0.003 0.006 y[1] (numeric) = 1.91724673002 0.642574746496 y[1] (closed_form) = 1.91710180345 0.642659039745 absolute error = 0.0001677 relative error = 0.008292 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.388 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2945 0.919 h = 0.0001 0.005 y[1] (numeric) = 1.91885504887 0.647063647862 y[1] (closed_form) = 1.91870898635 0.647149679755 absolute error = 0.0001695 relative error = 0.008372 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.392 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2946 0.924 h = 0.0001 0.003 y[1] (numeric) = 1.9184988933 0.650602451501 y[1] (closed_form) = 1.91835168281 0.650688604422 absolute error = 0.0001706 relative error = 0.00842 % Correct digits = 4 memory used=3453.6MB, alloc=52.3MB, time=42.52 Radius of convergence (given) for eq 1 = 4.393 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] = 2.2947 0.927 h = 0.001 0.001 y[1] (numeric) = 1.91831206642 0.652729311679 y[1] (closed_form) = 1.91816444382 0.65281551924 absolute error = 0.000171 relative error = 0.008437 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.394 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] = 2.2957 0.928 h = 0.001 0.003 y[1] (numeric) = 1.91893209903 0.653521519656 y[1] (closed_form) = 1.91878448246 0.653607819273 absolute error = 0.000171 relative error = 0.008436 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.395 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2967 0.931 h = 0.0001 0.004 y[1] (numeric) = 1.91937979633 0.655726348536 memory used=3499.4MB, alloc=52.3MB, time=43.14 y[1] (closed_form) = 1.91923182971 0.65581294856 absolute error = 0.0001714 relative error = 0.008453 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.396 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 x[1] = 2.2968 0.935 h = 0.003 0.006 y[1] (numeric) = 1.91910465406 0.658560307487 y[1] (closed_form) = 1.91895595393 0.658646992875 absolute error = 0.0001721 relative error = 0.008484 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.397 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.2998 0.941 h = 0.0001 0.005 y[1] (numeric) = 1.92070287256 0.663058914646 y[1] (closed_form) = 1.92055303982 0.663147338727 absolute error = 0.000174 relative error = 0.008563 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.402 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=3545.1MB, alloc=52.3MB, time=43.71 x[1] = 2.2999 0.946 h = 0.0001 0.003 y[1] (numeric) = 1.92033681471 0.666601023606 y[1] (closed_form) = 1.92018583515 0.666689570173 absolute error = 0.000175 relative error = 0.008611 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.403 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3 0.949 h = 0.001 0.001 y[1] (numeric) = 1.92014407271 0.66872994842 y[1] (closed_form) = 1.91999268148 0.668818550138 absolute error = 0.0001754 relative error = 0.008628 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.403 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.301 0.95 h = 0.001 0.003 y[1] (numeric) = 1.92076273531 0.6695247707 y[1] (closed_form) = 1.92061135023 0.669613464386 absolute error = 0.0001755 relative error = 0.008626 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.405 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 memory used=3590.8MB, alloc=52.3MB, time=44.28 x[1] = 2.302 0.953 h = 0.0001 0.004 y[1] (numeric) = 1.92120507895 0.671733458066 y[1] (closed_form) = 1.92105334452 0.671822452373 absolute error = 0.0001759 relative error = 0.008643 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.406 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3021 0.957 h = 0.003 0.006 y[1] (numeric) = 1.92092203266 0.67457010597 y[1] (closed_form) = 1.92076956548 0.674659186559 absolute error = 0.0001766 relative error = 0.008674 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.407 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] = 2.3051 0.963 h = 0.0001 0.005 y[1] (numeric) = 1.9225101727 0.679078424236 y[1] (closed_form) = 1.92235657624 0.679169243539 absolute error = 0.0001784 relative error = 0.008752 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.411 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=3636.7MB, alloc=52.3MB, time=44.85 x[1] = 2.3052 0.968 h = 0.0001 0.003 y[1] (numeric) = 1.9221342256 0.682623849055 y[1] (closed_form) = 1.92197948349 0.682714792283 absolute error = 0.0001795 relative error = 0.0088 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.413 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3053 0.971 h = 0.001 0.001 y[1] (numeric) = 1.92193557641 0.684754844704 y[1] (closed_form) = 1.92178042306 0.68484584359 absolute error = 0.0001799 relative error = 0.008816 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.413 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3063 0.972 h = 0.0001 0.004 y[1] (numeric) = 1.92255287373 0.685552280865 y[1] (closed_form) = 1.92239772664 0.685643371632 absolute error = 0.0001799 relative error = 0.008815 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.415 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 memory used=3682.5MB, alloc=52.3MB, time=45.42 x[1] = 2.3064 0.976 h = 0.003 0.006 y[1] (numeric) = 1.92226300012 0.688391155966 y[1] (closed_form) = 1.92210712096 0.68848233385 absolute error = 0.0001806 relative error = 0.008845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.416 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] = 2.3094 0.982 h = 0.0001 0.005 y[1] (numeric) = 1.92384236671 0.692907717623 y[1] (closed_form) = 1.92368536112 0.693000634255 absolute error = 0.0001824 relative error = 0.008923 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.42 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3095 0.987 h = 0.0001 0.003 y[1] (numeric) = 1.92345787808 0.696455887356 y[1] (closed_form) = 1.92329972784 0.696548929155 absolute error = 0.0001835 relative error = 0.00897 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.421 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=3728.3MB, alloc=52.3MB, time=46.00 x[1] = 2.3096 0.99 h = 0.001 0.001 y[1] (numeric) = 1.92325412577 0.698588600169 y[1] (closed_form) = 1.92309556465 0.698681698062 absolute error = 0.0001839 relative error = 0.008987 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.422 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3106 0.991 h = 0.001 0.003 y[1] (numeric) = 1.92387022053 0.699388269717 y[1] (closed_form) = 1.92371166578 0.699481459415 absolute error = 0.0001839 relative error = 0.008985 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.423 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] = 2.3116 0.994 h = 0.0001 0.004 y[1] (numeric) = 1.9243025824 0.701604083555 y[1] (closed_form) = 1.92414367963 0.701697574262 absolute error = 0.0001844 relative error = 0.009002 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.425 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3774.0MB, alloc=52.3MB, time=47.04 x[1] = 2.3117 0.998 h = 0.003 0.006 y[1] (numeric) = 1.92400482429 0.70444566315 y[1] (closed_form) = 1.92384519016 0.70453924183 absolute error = 0.000185 relative error = 0.009032 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.426 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 x[1] = 2.3147 1.004 h = 0.0001 0.005 y[1] (numeric) = 1.925574153 0.708971945505 y[1] (closed_form) = 1.92541339576 0.7090672629 absolute error = 0.0001869 relative error = 0.009109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.43 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3148 1.009 h = 0.0001 0.003 y[1] (numeric) = 1.9251797994 0.712523450455 y[1] (closed_form) = 1.92501789867 0.712618894428 absolute error = 0.0001879 relative error = 0.009156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.431 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3819.9MB, alloc=52.3MB, time=47.71 x[1] = 2.3149 1.012 h = 0.001 0.001 y[1] (numeric) = 1.92497015463 0.714658245493 y[1] (closed_form) = 1.92480784346 0.714753746057 absolute error = 0.0001883 relative error = 0.009172 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.432 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] = 2.3159 1.013 h = 0.001 0.003 y[1] (numeric) = 1.92558489283 0.715460528089 y[1] (closed_form) = 1.92542258815 0.715556120367 absolute error = 0.0001884 relative error = 0.00917 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.433 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] = 2.3169 1.016 h = 0.0001 0.004 y[1] (numeric) = 1.92601192919 0.717680211337 y[1] (closed_form) = 1.92584927719 0.717776104819 absolute error = 0.0001888 relative error = 0.009187 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.435 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3865.7MB, alloc=52.3MB, time=48.31 x[1] = 2.317 1.02 h = 0.003 0.006 y[1] (numeric) = 1.92570629708 0.72052450347 y[1] (closed_form) = 1.9255429145 0.720620485816 absolute error = 0.0001895 relative error = 0.009217 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.436 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 x[1] = 2.32 1.026 h = 0.0001 0.005 y[1] (numeric) = 1.92726560971 0.725060511241 y[1] (closed_form) = 1.9271011073 0.72515823224 absolute error = 0.0001913 relative error = 0.009293 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3201 1.031 h = 0.0001 0.003 y[1] (numeric) = 1.92686140429 0.728615361512 y[1] (closed_form) = 1.92669575959 0.728713210486 absolute error = 0.0001924 relative error = 0.00934 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.441 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=3911.4MB, alloc=52.3MB, time=48.89 x[1] = 2.3202 1.034 h = 0.001 0.001 y[1] (numeric) = 1.92664587506 0.730752244715 y[1] (closed_form) = 1.92647982036 0.73085015077 absolute error = 0.0001928 relative error = 0.009356 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.442 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3212 1.035 h = 0.001 0.003 y[1] (numeric) = 1.92725926136 0.731557139825 y[1] (closed_form) = 1.92709321326 0.731655137504 absolute error = 0.0001928 relative error = 0.009354 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.443 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3222 1.038 h = 0.0001 0.004 y[1] (numeric) = 1.92768098205 0.733780696071 y[1] (closed_form) = 1.92751458734 0.733878995141 absolute error = 0.0001933 relative error = 0.00937 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.445 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=3957.2MB, alloc=52.3MB, time=49.48 x[1] = 2.3223 1.042 h = 0.003 0.006 y[1] (numeric) = 1.92736748655 0.736627708709 y[1] (closed_form) = 1.92720036202 0.736726097523 absolute error = 0.0001939 relative error = 0.0094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.446 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] = 2.3253 1.048 h = 0.0001 0.005 y[1] (numeric) = 1.92891680485 0.741173446409 y[1] (closed_form) = 1.92874856378 0.741273573786 absolute error = 0.0001958 relative error = 0.009475 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3254 1.053 h = 0.0001 0.003 y[1] (numeric) = 1.92850276081 0.744731651955 y[1] (closed_form) = 1.92833337864 0.744831908688 absolute error = 0.0001968 relative error = 0.009522 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.452 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4002.9MB, alloc=52.3MB, time=50.06 x[1] = 2.3255 1.056 h = 0.001 0.001 y[1] (numeric) = 1.92828135512 0.746870629172 y[1] (closed_form) = 1.9281115634 0.746970943472 absolute error = 0.0001972 relative error = 0.009537 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.453 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 x[1] = 2.3265 1.057 h = 0.001 0.003 y[1] (numeric) = 1.92889339416 0.747678136224 y[1] (closed_form) = 1.92872360915 0.747778542056 absolute error = 0.0001973 relative error = 0.009535 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.454 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] = 2.3275 1.06 h = 0.0001 0.004 y[1] (numeric) = 1.92930980903 0.749905568957 y[1] (closed_form) = 1.92913967811 0.75000627636 absolute error = 0.0001977 relative error = 0.009552 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.455 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4048.6MB, alloc=52.3MB, time=50.65 x[1] = 2.3276 1.064 h = 0.003 0.006 y[1] (numeric) = 1.92898846076 0.752755309948 y[1] (closed_form) = 1.9288176008 0.752856107965 absolute error = 0.0001984 relative error = 0.009581 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.456 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3306 1.07 h = 0.0001 0.005 y[1] (numeric) = 1.93052780643 0.757310781886 y[1] (closed_form) = 1.93035583321 0.757413318349 absolute error = 0.0002002 relative error = 0.009656 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.461 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 x[1] = 2.3307 1.075 h = 0.0001 0.003 y[1] (numeric) = 1.93010393702 0.760872352509 y[1] (closed_form) = 1.92993082389 0.760975019695 absolute error = 0.0002013 relative error = 0.009702 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.462 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4094.4MB, alloc=52.3MB, time=51.24 x[1] = 2.3308 1.078 h = 0.001 0.001 y[1] (numeric) = 1.92987666291 0.763013429501 y[1] (closed_form) = 1.92970314068 0.763116154732 absolute error = 0.0002016 relative error = 0.009718 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.463 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3318 1.079 h = 0.0001 0.004 y[1] (numeric) = 1.93048735931 0.763823547885 y[1] (closed_form) = 1.9303138439 0.763926364557 absolute error = 0.0002017 relative error = 0.009715 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.464 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3319 1.083 h = 0.003 0.006 y[1] (numeric) = 1.93015922749 0.766675550131 y[1] (closed_form) = 1.92998498374 0.766778458211 absolute error = 0.0002024 relative error = 0.009744 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.465 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 memory used=4140.1MB, alloc=52.3MB, time=51.83 x[1] = 2.3349 1.089 h = 0.0001 0.005 y[1] (numeric) = 1.9316898904 0.771239285832 y[1] (closed_form) = 1.93151453619 0.771343932272 absolute error = 0.0002042 relative error = 0.009818 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.47 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.335 1.094 h = 0.0001 0.003 y[1] (numeric) = 1.93125753402 0.774803643914 y[1] (closed_form) = 1.93108104093 0.774908422255 absolute error = 0.0002053 relative error = 0.009864 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.471 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 x[1] = 2.3351 1.097 h = 0.001 0.001 y[1] (numeric) = 1.93102518991 0.776946463091 y[1] (closed_form) = 1.9308482881 0.77705129989 absolute error = 0.0002056 relative error = 0.00988 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.472 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 memory used=4186.0MB, alloc=52.3MB, time=52.44 x[1] = 2.3361 1.098 h = 0.001 0.003 y[1] (numeric) = 1.93163470318 0.777758812787 y[1] (closed_form) = 1.9314578083 0.77786374095 absolute error = 0.0002057 relative error = 0.009878 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.473 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] = 2.3371 1.101 h = 0.0001 0.004 y[1] (numeric) = 1.93204122505 0.779993404785 y[1] (closed_form) = 1.93186398557 0.780098634846 absolute error = 0.0002061 relative error = 0.009894 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.475 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 x[1] = 2.3372 1.105 h = 0.003 0.006 y[1] (numeric) = 1.93170526025 0.782848149835 y[1] (closed_form) = 1.93152729317 0.782953472113 absolute error = 0.0002068 relative error = 0.009922 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.476 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4231.7MB, alloc=52.3MB, time=53.04 x[1] = 2.3402 1.111 h = 0.0001 0.005 y[1] (numeric) = 1.93322599078 0.787421627516 y[1] (closed_form) = 1.93304691648 0.787528687985 absolute error = 0.0002086 relative error = 0.009996 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3403 1.116 h = 0.0001 0.003 y[1] (numeric) = 1.93278383364 0.790989368679 y[1] (closed_form) = 1.93260362168 0.791096562386 absolute error = 0.0002097 relative error = 0.01004 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.481 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3404 1.119 h = 0.001 0.001 y[1] (numeric) = 1.93254563604 0.793134298203 y[1] (closed_form) = 1.9323650158 0.793241550838 absolute error = 0.0002101 relative error = 0.01006 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.482 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=4277.4MB, alloc=52.3MB, time=53.63 x[1] = 2.3414 1.12 h = 0.001 0.003 y[1] (numeric) = 1.9331538152 0.793949258054 y[1] (closed_form) = 1.932973202 0.79405660196 absolute error = 0.0002101 relative error = 0.01005 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.484 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3424 1.123 h = 0.0001 0.004 y[1] (numeric) = 1.93355505934 0.796187736102 y[1] (closed_form) = 1.93337410224 0.796295382068 absolute error = 0.0002106 relative error = 0.01007 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.485 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] = 2.3425 1.127 h = 0.003 0.006 y[1] (numeric) = 1.93321127221 0.79904523142 y[1] (closed_form) = 1.9330295883 0.799152970444 absolute error = 0.0002112 relative error = 0.0101 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.486 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 memory used=4323.1MB, alloc=52.3MB, time=54.24 x[1] = 2.3455 1.133 h = 0.0001 0.005 y[1] (numeric) = 1.93472209193 0.803628454817 y[1] (closed_form) = 1.93453930404 0.803737931837 absolute error = 0.0002131 relative error = 0.01017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.491 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 x[1] = 2.3456 1.138 h = 0.0001 0.003 y[1] (numeric) = 1.93427014736 0.807199588438 y[1] (closed_form) = 1.93408622303 0.807309200019 absolute error = 0.0002141 relative error = 0.01022 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.492 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3457 1.141 h = 0.001 0.001 y[1] (numeric) = 1.93402610436 0.809346633813 y[1] (closed_form) = 1.9338417722 0.809456304785 absolute error = 0.0002145 relative error = 0.01023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.493 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=4368.8MB, alloc=52.3MB, time=54.84 x[1] = 2.3467 1.142 h = 0.001 0.003 y[1] (numeric) = 1.93463295397 0.810164203103 y[1] (closed_form) = 1.93444862896 0.810273965252 absolute error = 0.0002145 relative error = 0.01023 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.494 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 x[1] = 2.3477 1.145 h = 0.0001 0.004 y[1] (numeric) = 1.93502893017 0.81240657032 y[1] (closed_form) = 1.93484426196 0.812516634684 absolute error = 0.000215 relative error = 0.01024 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.496 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3478 1.149 h = 0.003 0.006 y[1] (numeric) = 1.93467733145 0.81526682329 y[1] (closed_form) = 1.93449193722 0.815376981546 absolute error = 0.0002157 relative error = 0.01027 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.497 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=4414.3MB, alloc=52.3MB, time=55.43 x[1] = 2.3508 1.155 h = 0.0001 0.005 y[1] (numeric) = 1.93617826189 0.819859795943 y[1] (closed_form) = 1.9359917669 0.819971691973 absolute error = 0.0002175 relative error = 0.01034 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.501 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3509 1.16 h = 0.0001 0.003 y[1] (numeric) = 1.93571654327 0.823434331253 y[1] (closed_form) = 1.93552891306 0.823546363149 absolute error = 0.0002185 relative error = 0.01039 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.503 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] = 2.351 1.163 h = 0.001 0.001 y[1] (numeric) = 1.93546666296 0.825583497892 y[1] (closed_form) = 1.93527862538 0.825695589637 absolute error = 0.0002189 relative error = 0.0104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.504 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=4460.1MB, alloc=52.3MB, time=56.03 x[1] = 2.352 1.164 h = 0.001 0.003 y[1] (numeric) = 1.93607218754 0.826403675872 y[1] (closed_form) = 1.93588415722 0.8265158587 absolute error = 0.000219 relative error = 0.0104 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.505 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.353 1.167 h = 0.0001 0.004 y[1] (numeric) = 1.93646290562 0.82864993528 y[1] (closed_form) = 1.9362745328 0.828762420471 absolute error = 0.0002194 relative error = 0.01042 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.507 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] = 2.3531 1.171 h = 0.003 0.006 y[1] (numeric) = 1.93610350603 0.831512953171 y[1] (closed_form) = 1.93591440799 0.831625533076 absolute error = 0.0002201 relative error = 0.01044 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.508 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=4505.8MB, alloc=52.3MB, time=56.75 x[1] = 2.3561 1.177 h = 0.0001 0.005 y[1] (numeric) = 1.93759456869 0.836115678425 y[1] (closed_form) = 1.93740437309 0.836229995856 absolute error = 0.0002219 relative error = 0.01052 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.512 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] = 2.3562 1.182 h = 0.0001 0.003 y[1] (numeric) = 1.9371230894 0.839693624504 y[1] (closed_form) = 1.93693175981 0.839808079094 absolute error = 0.000223 relative error = 0.01056 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3563 1.185 h = 0.001 0.001 y[1] (numeric) = 1.9368673799 0.841844917733 y[1] (closed_form) = 1.93667564341 0.841959432624 absolute error = 0.0002233 relative error = 0.01058 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.515 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=4551.5MB, alloc=52.3MB, time=57.54 x[1] = 2.3573 1.186 h = 0.0001 0.004 y[1] (numeric) = 1.93747158397 0.842667703617 y[1] (closed_form) = 1.93727985483 0.842782309496 absolute error = 0.0002234 relative error = 0.01057 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.516 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3574 1.19 h = 0.003 0.006 y[1] (numeric) = 1.93710544518 0.8455330144 y[1] (closed_form) = 1.93691299155 0.845647715744 absolute error = 0.000224 relative error = 0.0106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.517 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3604 1.196 h = 0.0001 0.005 y[1] (numeric) = 1.93858791491 0.850144019701 y[1] (closed_form) = 1.93839436647 0.850260458374 absolute error = 0.0002259 relative error = 0.01067 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.521 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4597.3MB, alloc=52.3MB, time=58.15 x[1] = 2.3605 1.201 h = 0.0001 0.003 y[1] (numeric) = 1.93810800393 0.853724792767 y[1] (closed_form) = 1.93791332256 0.853841369713 absolute error = 0.0002269 relative error = 0.01072 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.523 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3606 1.204 h = 0.001 0.001 y[1] (numeric) = 1.93784725796 0.855877851385 y[1] (closed_form) = 1.93765217007 0.855994489021 absolute error = 0.0002273 relative error = 0.01073 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.524 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] = 2.3616 1.205 h = 0.001 0.003 y[1] (numeric) = 1.9384502979 0.856702865751 y[1] (closed_form) = 1.93825521745 0.856819594297 absolute error = 0.0002273 relative error = 0.01073 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.525 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=4643.1MB, alloc=52.3MB, time=58.74 x[1] = 2.3626 1.208 h = 0.0001 0.004 y[1] (numeric) = 1.93883121144 0.858956312982 y[1] (closed_form) = 1.93863578979 0.859073344158 absolute error = 0.0002278 relative error = 0.01074 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.527 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3627 1.212 h = 0.003 0.006 y[1] (numeric) = 1.9384572918 0.861824402066 y[1] (closed_form) = 1.93826114642 0.86194152947 absolute error = 0.0002285 relative error = 0.01077 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.528 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3657 1.218 h = 0.0001 0.005 y[1] (numeric) = 1.93992993354 0.866445165934 y[1] (closed_form) = 1.93973269653 0.86656403037 absolute error = 0.0002303 relative error = 0.01084 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.532 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4688.8MB, alloc=52.3MB, time=59.32 x[1] = 2.3658 1.223 h = 0.0001 0.003 y[1] (numeric) = 1.93944028676 0.870029366438 y[1] (closed_form) = 1.93924191807 0.870148370411 absolute error = 0.0002313 relative error = 0.01088 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.534 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3659 1.226 h = 0.001 0.001 y[1] (numeric) = 1.93917372669 0.872184561417 y[1] (closed_form) = 1.93897495193 0.872303626522 absolute error = 0.0002317 relative error = 0.0109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.535 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3669 1.227 h = 0.001 0.003 y[1] (numeric) = 1.93977545443 0.873012182186 y[1] (closed_form) = 1.93957668723 0.873131338105 absolute error = 0.0002317 relative error = 0.0109 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.536 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=4734.6MB, alloc=52.3MB, time=59.90 x[1] = 2.3679 1.23 h = 0.0001 0.004 y[1] (numeric) = 1.94015113779 0.875269529855 y[1] (closed_form) = 1.93995203009 0.875388988535 absolute error = 0.0002322 relative error = 0.01091 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.538 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 x[1] = 2.368 1.234 h = 0.003 0.006 y[1] (numeric) = 1.93976944806 0.878140404131 y[1] (closed_form) = 1.93956961742 0.878259959833 absolute error = 0.0002329 relative error = 0.01094 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.539 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.371 1.24 h = 0.0001 0.005 y[1] (numeric) = 1.94123228313 0.882770929361 y[1] (closed_form) = 1.94103136403 0.882892221774 absolute error = 0.0002347 relative error = 0.01101 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.543 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=4780.4MB, alloc=52.3MB, time=60.49 x[1] = 2.3711 1.245 h = 0.0001 0.003 y[1] (numeric) = 1.94073291403 0.886358565969 y[1] (closed_form) = 1.94053086449 0.886479999166 absolute error = 0.0002357 relative error = 0.01105 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.545 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 x[1] = 2.3712 1.248 h = 0.001 0.001 y[1] (numeric) = 1.940460548 0.888515902381 y[1] (closed_form) = 1.94025809286 0.888637397148 absolute error = 0.0002361 relative error = 0.01106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3722 1.249 h = 0.001 0.003 y[1] (numeric) = 1.94106096799 0.889346128669 y[1] (closed_form) = 1.94085852051 0.889467714153 absolute error = 0.0002362 relative error = 0.01106 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.547 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=4826.3MB, alloc=52.3MB, time=61.07 x[1] = 2.3732 1.252 h = 0.0001 0.004 y[1] (numeric) = 1.94143143092 0.89160737944 y[1] (closed_form) = 1.94122864363 0.891729267809 absolute error = 0.0002366 relative error = 0.01108 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.549 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3733 1.256 h = 0.003 0.006 y[1] (numeric) = 1.94104198191 0.894481045724 y[1] (closed_form) = 1.9408384725 0.8946030319 absolute error = 0.0002373 relative error = 0.0111 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.55 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] = 2.3763 1.262 h = 0.0001 0.005 y[1] (numeric) = 1.94249503158 0.899121334925 y[1] (closed_form) = 1.94229043685 0.899245057464 absolute error = 0.0002391 relative error = 0.01117 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.555 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4872.0MB, alloc=52.3MB, time=61.65 x[1] = 2.3764 1.267 h = 0.0001 0.003 y[1] (numeric) = 1.94198595363 0.902712416153 y[1] (closed_form) = 1.94178022973 0.90283628071 absolute error = 0.0002401 relative error = 0.01121 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.556 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3765 1.27 h = 0.001 0.001 y[1] (numeric) = 1.94170778982 0.904871898987 y[1] (closed_form) = 1.94150166078 0.904995825544 absolute error = 0.0002405 relative error = 0.01123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.557 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 x[1] = 2.3775 1.271 h = 0.001 0.003 y[1] (numeric) = 1.94230690646 0.905704729876 y[1] (closed_form) = 1.94210078518 0.905828747053 absolute error = 0.0002406 relative error = 0.01123 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.558 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 memory used=4917.7MB, alloc=52.3MB, time=62.23 x[1] = 2.3785 1.274 h = 0.0001 0.004 y[1] (numeric) = 1.9426721587 0.907969886321 y[1] (closed_form) = 1.9424656983 0.908094206501 absolute error = 0.000241 relative error = 0.01124 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.56 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] = 2.3786 1.278 h = 0.003 0.006 y[1] (numeric) = 1.94227496125 0.910846351312 y[1] (closed_form) = 1.94206777954 0.910970770075 absolute error = 0.0002417 relative error = 0.01127 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.561 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3816 1.284 h = 0.0001 0.005 y[1] (numeric) = 1.94371824672 0.915496406906 y[1] (closed_form) = 1.94350998283 0.91562256166 absolute error = 0.0002435 relative error = 0.01133 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.566 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=4963.5MB, alloc=52.3MB, time=62.82 x[1] = 2.3817 1.289 h = 0.0001 0.003 y[1] (numeric) = 1.94319947342 0.91909094113 y[1] (closed_form) = 1.94299008162 0.91921723912 absolute error = 0.0002445 relative error = 0.01138 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.567 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 x[1] = 2.3818 1.292 h = 0.001 0.001 y[1] (numeric) = 1.94291552 0.921252575284 y[1] (closed_form) = 1.94270572353 0.921378935699 absolute error = 0.0002449 relative error = 0.01139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.568 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3828 1.293 h = 0.0001 0.004 y[1] (numeric) = 1.94351333769 0.922088009823 y[1] (closed_form) = 1.94330354908 0.922214460762 absolute error = 0.000245 relative error = 0.01139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.57 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5009.2MB, alloc=52.3MB, time=63.40 x[1] = 2.3829 1.297 h = 0.003 0.006 y[1] (numeric) = 1.94310944582 0.924966796963 y[1] (closed_form) = 1.94289893665 0.925093347192 absolute error = 0.0002456 relative error = 0.01141 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.571 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] = 2.3859 1.303 h = 0.0001 0.005 y[1] (numeric) = 1.94454422717 0.929625144972 y[1] (closed_form) = 1.9443326385 0.929753430891 absolute error = 0.0002474 relative error = 0.01148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.575 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.386 1.308 h = 0.0001 0.003 y[1] (numeric) = 1.944017078 0.933222542744 y[1] (closed_form) = 1.94380436249 0.93335097295 absolute error = 0.0002485 relative error = 0.01152 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.577 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5055.0MB, alloc=52.3MB, time=63.96 x[1] = 2.3861 1.311 h = 0.001 0.001 y[1] (numeric) = 1.94372812192 0.935385963707 y[1] (closed_form) = 1.94351500214 0.935514456705 absolute error = 0.0002489 relative error = 0.01154 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.578 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3871 1.312 h = 0.001 0.003 y[1] (numeric) = 1.944324794 0.936223623194 y[1] (closed_form) = 1.94411168217 0.936352206633 absolute error = 0.0002489 relative error = 0.01153 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.579 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 x[1] = 2.3881 1.315 h = 0.0001 0.004 y[1] (numeric) = 1.94468032963 0.93849599193 y[1] (closed_form) = 1.94446687997 0.938624878583 absolute error = 0.0002493 relative error = 0.01155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.581 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5100.8MB, alloc=52.3MB, time=64.53 x[1] = 2.3882 1.319 h = 0.003 0.006 y[1] (numeric) = 1.94426870948 0.941377590106 y[1] (closed_form) = 1.94405454003 0.941506576767 absolute error = 0.00025 relative error = 0.01157 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.582 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3912 1.325 h = 0.0001 0.005 y[1] (numeric) = 1.94569376591 0.946045708775 y[1] (closed_form) = 1.94547852006 0.946176430709 absolute error = 0.0002518 relative error = 0.01164 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.587 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3913 1.33 h = 0.0001 0.003 y[1] (numeric) = 1.94515694646 0.949646574905 y[1] (closed_form) = 1.94494057505 0.949777442315 absolute error = 0.0002529 relative error = 0.01168 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.588 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5146.7MB, alloc=52.3MB, time=65.09 x[1] = 2.3914 1.333 h = 0.001 0.001 y[1] (numeric) = 1.94486221596 0.951812156173 y[1] (closed_form) = 1.94464544074 0.951943086792 absolute error = 0.0002532 relative error = 0.0117 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.589 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3924 1.334 h = 0.001 0.003 y[1] (numeric) = 1.94545759719 0.952652417507 y[1] (closed_form) = 1.94524083002 0.952783438469 absolute error = 0.0002533 relative error = 0.01169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.591 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3934 1.337 h = 0.0001 0.004 y[1] (numeric) = 1.94580794987 0.954928698897 y[1] (closed_form) = 1.94559084556 0.955060023172 absolute error = 0.0002537 relative error = 0.01171 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.592 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 memory used=5192.4MB, alloc=52.3MB, time=65.66 x[1] = 2.3935 1.341 h = 0.003 0.006 y[1] (numeric) = 1.94538861226 0.957813114441 y[1] (closed_form) = 1.94517078897 0.957944539473 absolute error = 0.0002544 relative error = 0.01173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.594 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 x[1] = 2.3965 1.347 h = 0.0001 0.005 y[1] (numeric) = 1.94680396479 0.962491005668 y[1] (closed_form) = 1.9465850682 0.962624165531 absolute error = 0.0002562 relative error = 0.0118 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.598 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 x[1] = 2.3966 1.352 h = 0.0001 0.003 y[1] (numeric) = 1.94625748861 0.966095348121 y[1] (closed_form) = 1.94603746774 0.966228654635 absolute error = 0.0002573 relative error = 0.01184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.6 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=5238.1MB, alloc=52.3MB, time=66.22 x[1] = 2.3967 1.355 h = 0.001 0.001 y[1] (numeric) = 1.94595699187 0.968263094349 y[1] (closed_form) = 1.94573656767 0.968396464481 absolute error = 0.0002576 relative error = 0.01185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.601 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.3977 1.356 h = 0.001 0.003 y[1] (numeric) = 1.94655108657 0.969105956488 y[1] (closed_form) = 1.94633067052 0.969239416865 absolute error = 0.0002577 relative error = 0.01185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.602 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 x[1] = 2.3987 1.359 h = 0.0001 0.004 y[1] (numeric) = 1.94689626597 0.971386152758 y[1] (closed_form) = 1.94667551345 0.971519916543 absolute error = 0.0002581 relative error = 0.01186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.604 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5283.9MB, alloc=52.3MB, time=66.79 x[1] = 2.3988 1.363 h = 0.003 0.006 y[1] (numeric) = 1.94646922178 0.974273391929 y[1] (closed_form) = 1.94624775111 0.974407257208 absolute error = 0.0002588 relative error = 0.01189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.605 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 x[1] = 2.4018 1.369 h = 0.0001 0.005 y[1] (numeric) = 1.94787489137 0.978961057433 y[1] (closed_form) = 1.94765235049 0.97909665708 absolute error = 0.0002606 relative error = 0.01195 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.61 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4019 1.374 h = 0.0001 0.003 y[1] (numeric) = 1.94731877203 0.982568884033 y[1] (closed_form) = 1.94709510813 0.98270463149 absolute error = 0.0002616 relative error = 0.012 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.611 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=5329.6MB, alloc=52.3MB, time=67.36 x[1] = 2.402 1.377 h = 0.001 0.001 y[1] (numeric) = 1.94701251726 0.98473879979 y[1] (closed_form) = 1.94678845051 0.984874611269 absolute error = 0.000262 relative error = 0.01201 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.612 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.403 1.378 h = 0.001 0.003 y[1] (numeric) = 1.94760532972 0.98558426166 y[1] (closed_form) = 1.94738127121 0.985720163285 absolute error = 0.0002621 relative error = 0.01201 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.614 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 x[1] = 2.404 1.381 h = 0.0001 0.004 y[1] (numeric) = 1.94794534549 0.987868374951 y[1] (closed_form) = 1.9477209512 0.988004580073 absolute error = 0.0002625 relative error = 0.01202 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.615 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=5375.4MB, alloc=52.3MB, time=67.93 x[1] = 2.4041 1.385 h = 0.003 0.006 y[1] (numeric) = 1.9475106056 0.990758443893 y[1] (closed_form) = 1.94728549399 0.990894751237 absolute error = 0.0002632 relative error = 0.01204 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.617 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] = 2.4071 1.391 h = 0.0001 0.005 y[1] (numeric) = 1.94890661316 0.995455885216 y[1] (closed_form) = 1.94868043439 0.995593926441 absolute error = 0.000265 relative error = 0.01211 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.621 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 x[1] = 2.4072 1.396 h = 0.0001 0.003 y[1] (numeric) = 1.94834086421 0.999067203645 y[1] (closed_form) = 1.94811356371 0.999205393825 absolute error = 0.000266 relative error = 0.01215 % Correct digits = 4 memory used=5421.2MB, alloc=52.3MB, time=68.50 Radius of convergence (given) for eq 1 = 4.623 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4073 1.399 h = 0.001 0.001 y[1] (numeric) = 1.94802885962 1.00123929341 y[1] (closed_form) = 1.94780115674 1.00137754802 absolute error = 0.0002664 relative error = 0.01216 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.624 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] = 2.4083 1.4 h = 0.003 0.006 y[1] (numeric) = 1.94862039411 1.00208735391 y[1] (closed_form) = 1.94839269957 1.00222569856 absolute error = 0.0002664 relative error = 0.01216 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.625 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4113 1.406 h = 0.0001 0.005 y[1] (numeric) = 1.95001001355 1.00679176335 y[1] (closed_form) = 1.94978125405 1.00693184157 absolute error = 0.0002682 relative error = 0.01222 % Correct digits = 4 memory used=5467.0MB, alloc=52.3MB, time=69.08 Radius of convergence (given) for eq 1 = 4.63 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4114 1.411 h = 0.0001 0.003 y[1] (numeric) = 1.94943773658 1.01040573031 y[1] (closed_form) = 1.94920785628 1.01054595824 absolute error = 0.0002693 relative error = 0.01226 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.632 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4115 1.414 h = 0.001 0.001 y[1] (numeric) = 1.94912183644 1.01257946272 y[1] (closed_form) = 1.94889155408 1.01271975532 absolute error = 0.0002697 relative error = 0.01228 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.633 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=5512.7MB, alloc=52.3MB, time=69.65 x[1] = 2.4125 1.415 h = 0.001 0.003 y[1] (numeric) = 1.94971255971 1.01342934218 y[1] (closed_form) = 1.94948228576 1.01356972477 absolute error = 0.0002697 relative error = 0.01227 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.634 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 x[1] = 2.4135 1.418 h = 0.0001 0.004 y[1] (numeric) = 1.95004398048 1.01572020112 y[1] (closed_form) = 1.9498133719 1.01586088732 absolute error = 0.0002701 relative error = 0.01229 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.636 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] = 2.4136 1.422 h = 0.003 0.006 y[1] (numeric) = 1.94959634744 1.01861525328 y[1] (closed_form) = 1.94936502296 1.01875604289 absolute error = 0.0002708 relative error = 0.01231 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.637 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 memory used=5558.5MB, alloc=52.3MB, time=70.22 x[1] = 2.4166 1.428 h = 0.0001 0.005 y[1] (numeric) = 1.9509763401 1.02332944034 y[1] (closed_form) = 1.95074395357 1.02347196288 absolute error = 0.0002726 relative error = 0.01237 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.642 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4167 1.433 h = 0.0001 0.003 y[1] (numeric) = 1.95039445664 1.02694691145 y[1] (closed_form) = 1.9501609506 1.02708958481 absolute error = 0.0002736 relative error = 0.01242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.643 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 x[1] = 2.4168 1.436 h = 0.001 0.001 y[1] (numeric) = 1.95007282065 1.02912282503 y[1] (closed_form) = 1.94983891304 1.02926556346 absolute error = 0.000274 relative error = 0.01243 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.644 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5604.3MB, alloc=52.3MB, time=70.79 x[1] = 2.4178 1.437 h = 0.001 0.003 y[1] (numeric) = 1.95066227307 1.02997530109 y[1] (closed_form) = 1.95042837394 1.0301181294 absolute error = 0.0002741 relative error = 0.01242 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.646 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4188 1.44 h = 0.0001 0.004 y[1] (numeric) = 1.9509885561 1.03227008213 y[1] (closed_form) = 1.95075432302 1.03241321413 absolute error = 0.0002745 relative error = 0.01244 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.648 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4189 1.444 h = 0.003 0.006 y[1] (numeric) = 1.95053325679 1.03516797975 y[1] (closed_form) = 1.95029830866 1.03531121586 absolute error = 0.0002752 relative error = 0.01246 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.649 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5650.1MB, alloc=52.3MB, time=71.37 x[1] = 2.4219 1.45 h = 0.0001 0.005 y[1] (numeric) = 1.95190364326 1.03989194539 y[1] (closed_form) = 1.95166763609 1.04003691388 absolute error = 0.000277 relative error = 0.01252 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.654 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 x[1] = 2.422 1.455 h = 0.0001 0.003 y[1] (numeric) = 1.95131216688 1.04351292794 y[1] (closed_form) = 1.9510750415 1.04365804836 absolute error = 0.000278 relative error = 0.01256 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.655 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] = 2.4221 1.458 h = 0.001 0.001 y[1] (numeric) = 1.95098480327 1.04569102697 y[1] (closed_form) = 1.95074727679 1.04583621284 absolute error = 0.0002784 relative error = 0.01258 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.656 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=5695.8MB, alloc=52.3MB, time=71.94 x[1] = 2.4231 1.459 h = 0.001 0.003 y[1] (numeric) = 1.95157298902 1.04654609844 y[1] (closed_form) = 1.95133547112 1.04669137408 absolute error = 0.0002784 relative error = 0.01257 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.658 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 x[1] = 2.4241 1.462 h = 0.0001 0.004 y[1] (numeric) = 1.95189414387 1.04884480341 y[1] (closed_form) = 1.9516562927 1.04899038281 absolute error = 0.0002789 relative error = 0.01259 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.659 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4242 1.466 h = 0.003 0.006 y[1] (numeric) = 1.95143118922 1.05174555222 y[1] (closed_form) = 1.95119262382 1.05189123642 absolute error = 0.0002795 relative error = 0.01261 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.661 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5741.6MB, alloc=52.3MB, time=72.51 x[1] = 2.4272 1.472 h = 0.0001 0.005 y[1] (numeric) = 1.9527919901 1.05647929734 y[1] (closed_form) = 1.95255236867 1.05662671335 absolute error = 0.0002813 relative error = 0.01267 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.665 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4273 1.477 h = 0.0001 0.003 y[1] (numeric) = 1.95219093441 1.06010379851 y[1] (closed_form) = 1.95195019606 1.06025136754 absolute error = 0.0002824 relative error = 0.01271 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.667 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4274 1.48 h = 0.001 0.001 y[1] (numeric) = 1.95185785139 1.06228408716 y[1] (closed_form) = 1.95161671242 1.06243172203 absolute error = 0.0002827 relative error = 0.01272 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.668 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 memory used=5787.4MB, alloc=52.3MB, time=73.08 x[1] = 2.4284 1.481 h = 0.0001 0.004 y[1] (numeric) = 1.95244477464 1.06314175282 y[1] (closed_form) = 1.95220364435 1.06328947736 absolute error = 0.0002828 relative error = 0.01272 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.669 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4285 1.485 h = 0.003 0.006 y[1] (numeric) = 1.95197520514 1.06604486929 y[1] (closed_form) = 1.95173336139 1.06619269928 absolute error = 0.0002834 relative error = 0.01275 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.671 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4315 1.491 h = 0.0001 0.005 y[1] (numeric) = 1.95332765504 1.07078691902 y[1] (closed_form) = 1.95308475783 1.07093648034 absolute error = 0.0002853 relative error = 0.01281 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.676 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5833.1MB, alloc=52.3MB, time=73.66 x[1] = 2.4316 1.496 h = 0.0001 0.003 y[1] (numeric) = 1.95271832265 1.07441434064 y[1] (closed_form) = 1.95247430963 1.07456405592 absolute error = 0.0002863 relative error = 0.01285 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.677 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] = 2.4317 1.499 h = 0.001 0.001 y[1] (numeric) = 1.95238029698 1.07659644933 y[1] (closed_form) = 1.95213588375 1.07674623078 absolute error = 0.0002867 relative error = 0.01286 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.678 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4327 1.5 h = 0.001 0.003 y[1] (numeric) = 1.95296610596 1.07745633202 y[1] (closed_form) = 1.95272170147 1.07760620305 absolute error = 0.0002867 relative error = 0.01285 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.68 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=5878.8MB, alloc=52.3MB, time=74.23 x[1] = 2.4337 1.503 h = 0.0001 0.004 y[1] (numeric) = 1.95327769708 1.07976228226 y[1] (closed_form) = 1.95303296058 1.07991245716 absolute error = 0.0002871 relative error = 0.01287 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.682 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4338 1.507 h = 0.003 0.006 y[1] (numeric) = 1.95280049251 1.08266826047 y[1] (closed_form) = 1.95255504334 1.08281854145 absolute error = 0.0002878 relative error = 0.01289 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.683 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] = 2.4368 1.513 h = 0.0001 0.005 y[1] (numeric) = 1.95414339501 1.08742009116 y[1] (closed_form) = 1.95389689535 1.08757210287 absolute error = 0.0002896 relative error = 0.01295 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.688 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=5924.5MB, alloc=52.3MB, time=74.80 x[1] = 2.4369 1.518 h = 0.0001 0.003 y[1] (numeric) = 1.95352450851 1.09105104454 y[1] (closed_form) = 1.95327689435 1.09120321128 absolute error = 0.0002906 relative error = 0.01299 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.689 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.437 1.521 h = 0.001 0.001 y[1] (numeric) = 1.95318077868 1.0932353505 y[1] (closed_form) = 1.95293276479 1.09338758377 absolute error = 0.000291 relative error = 0.013 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.69 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] = 2.438 1.522 h = 0.001 0.003 y[1] (numeric) = 1.95376533286 1.0940978251 y[1] (closed_form) = 1.95351732781 1.09425014786 absolute error = 0.000291 relative error = 0.013 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.692 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=5970.3MB, alloc=52.3MB, time=75.37 x[1] = 2.439 1.525 h = 0.0001 0.004 y[1] (numeric) = 1.95407182305 1.09640770414 y[1] (closed_form) = 1.95382348664 1.09656033082 absolute error = 0.0002915 relative error = 0.01301 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.694 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 x[1] = 2.4391 1.529 h = 0.003 0.006 y[1] (numeric) = 1.95358699426 1.09931654947 y[1] (closed_form) = 1.95333794603 1.0994692829 absolute error = 0.0002922 relative error = 0.01303 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.695 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4421 1.535 h = 0.0001 0.005 y[1] (numeric) = 1.95492036977 1.10407816155 y[1] (closed_form) = 1.95467027401 1.10423262508 absolute error = 0.000294 relative error = 0.01309 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.7 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6016.0MB, alloc=52.3MB, time=75.94 x[1] = 2.4422 1.54 h = 0.0001 0.003 y[1] (numeric) = 1.95429194277 1.10771265348 y[1] (closed_form) = 1.95404073381 1.10786727307 absolute error = 0.000295 relative error = 0.01313 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.702 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4423 1.543 h = 0.001 0.001 y[1] (numeric) = 1.95394251699 1.10989916066 y[1] (closed_form) = 1.95369090878 1.11005384714 absolute error = 0.0002954 relative error = 0.01314 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.703 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4433 1.544 h = 0.001 0.003 y[1] (numeric) = 1.95452582047 1.11076422587 y[1] (closed_form) = 1.95427422119 1.11091900175 absolute error = 0.0002954 relative error = 0.01314 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.704 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6061.8MB, alloc=52.3MB, time=76.51 x[1] = 2.4443 1.547 h = 0.0001 0.004 y[1] (numeric) = 1.95482721919 1.11307803522 y[1] (closed_form) = 1.95457528923 1.11323311506 absolute error = 0.0002958 relative error = 0.01315 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.706 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] = 2.4444 1.551 h = 0.003 0.006 y[1] (numeric) = 1.9543347771 1.11598975298 y[1] (closed_form) = 1.95408213616 1.11614494023 absolute error = 0.0002965 relative error = 0.01318 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.707 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4474 1.557 h = 0.0001 0.005 y[1] (numeric) = 1.95565864596 1.12076114672 y[1] (closed_form) = 1.95540496041 1.12091806342 absolute error = 0.0002983 relative error = 0.01323 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.712 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6107.5MB, alloc=52.3MB, time=77.09 x[1] = 2.4475 1.562 h = 0.0001 0.003 y[1] (numeric) = 1.95502069205 1.12439918383 y[1] (closed_form) = 1.95476589462 1.12455625763 absolute error = 0.0002993 relative error = 0.01327 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.714 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4476 1.565 h = 0.001 0.001 y[1] (numeric) = 1.95466557855 1.12658789609 y[1] (closed_form) = 1.95441038235 1.12674503714 absolute error = 0.0002997 relative error = 0.01328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.715 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4486 1.566 h = 0.001 0.003 y[1] (numeric) = 1.95524763539 1.1274555506 y[1] (closed_form) = 1.95499244821 1.12761278094 absolute error = 0.0002997 relative error = 0.01328 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.716 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=6153.3MB, alloc=52.3MB, time=77.67 x[1] = 2.4496 1.569 h = 0.0001 0.004 y[1] (numeric) = 1.9555439521 1.12977329168 y[1] (closed_form) = 1.9552884349 1.12993082603 absolute error = 0.0003002 relative error = 0.01329 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.718 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 x[1] = 2.4497 1.573 h = 0.003 0.006 y[1] (numeric) = 1.95504390761 1.13268788708 y[1] (closed_form) = 1.95478768028 1.13284552948 absolute error = 0.0003008 relative error = 0.01332 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.72 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4527 1.579 h = 0.0001 0.005 y[1] (numeric) = 1.95635829008 1.13746906258 y[1] (closed_form) = 1.95610102106 1.13762843375 absolute error = 0.0003026 relative error = 0.01337 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.724 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6199.0MB, alloc=52.3MB, time=78.24 x[1] = 2.4528 1.584 h = 0.0001 0.003 y[1] (numeric) = 1.95571082285 1.14111065139 y[1] (closed_form) = 1.95545244327 1.14127018068 absolute error = 0.0003037 relative error = 0.01341 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.726 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 x[1] = 2.4529 1.587 h = 0.001 0.001 y[1] (numeric) = 1.95535002983 1.14330157251 y[1] (closed_form) = 1.95509125197 1.14346116941 absolute error = 0.000304 relative error = 0.01342 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.727 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4539 1.588 h = 0.0001 0.004 y[1] (numeric) = 1.95593084409 1.14417181498 y[1] (closed_form) = 1.95567207532 1.14433150106 absolute error = 0.0003041 relative error = 0.01342 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.729 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=6244.9MB, alloc=52.3MB, time=78.81 x[1] = 2.454 1.592 h = 0.003 0.006 y[1] (numeric) = 1.95542423003 1.14708880102 y[1] (closed_form) = 1.95516475191 1.14724859575 absolute error = 0.0003047 relative error = 0.01344 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.73 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.457 1.598 h = 0.0001 0.005 y[1] (numeric) = 1.95673034656 1.15187828363 y[1] (closed_form) = 1.95646982926 1.15203980657 absolute error = 0.0003065 relative error = 0.0135 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.735 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 x[1] = 2.4571 1.603 h = 0.0001 0.003 y[1] (numeric) = 1.95607465906 1.15552282162 y[1] (closed_form) = 1.95581303232 1.15568450357 absolute error = 0.0003076 relative error = 0.01354 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.737 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=6290.8MB, alloc=52.3MB, time=79.37 x[1] = 2.4572 1.606 h = 0.001 0.001 y[1] (numeric) = 1.95570895752 1.15771557951 y[1] (closed_form) = 1.9554469329 1.15787732937 absolute error = 0.0003079 relative error = 0.01355 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.738 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] = 2.4582 1.607 h = 0.001 0.003 y[1] (numeric) = 1.9562886746 1.15858803377 y[1] (closed_form) = 1.95602665916 1.15874987273 absolute error = 0.000308 relative error = 0.01355 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.739 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4592 1.61 h = 0.0001 0.004 y[1] (numeric) = 1.95657551306 1.16091303412 y[1] (closed_form) = 1.95631316883 1.16107517716 absolute error = 0.0003084 relative error = 0.01356 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.741 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 memory used=6336.5MB, alloc=52.3MB, time=79.94 x[1] = 2.4593 1.614 h = 0.003 0.006 y[1] (numeric) = 1.95606131688 1.16383290737 y[1] (closed_form) = 1.9557982641 1.16399515965 absolute error = 0.0003091 relative error = 0.01358 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.742 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4623 1.62 h = 0.0001 0.005 y[1] (numeric) = 1.95735798449 1.16863217175 y[1] (closed_form) = 1.95709389541 1.16879615153 absolute error = 0.0003109 relative error = 0.01364 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.747 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4624 1.625 h = 0.0001 0.003 y[1] (numeric) = 1.95669280889 1.17228027337 y[1] (closed_form) = 1.95642761169 1.17244441315 absolute error = 0.0003119 relative error = 0.01367 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.749 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=6382.3MB, alloc=52.3MB, time=80.50 x[1] = 2.4625 1.628 h = 0.001 0.001 y[1] (numeric) = 1.95632144307 1.17447524704 y[1] (closed_form) = 1.95605584847 1.17463945508 absolute error = 0.0003123 relative error = 0.01369 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.75 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4635 1.629 h = 0.001 0.003 y[1] (numeric) = 1.95689992502 1.17535028672 y[1] (closed_form) = 1.95663433969 1.17551458376 absolute error = 0.0003123 relative error = 0.01368 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.751 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] = 2.4645 1.632 h = 0.0001 0.004 y[1] (numeric) = 1.95718170834 1.17767922256 y[1] (closed_form) = 1.95691579488 1.17784382369 absolute error = 0.0003127 relative error = 0.01369 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.753 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6428.2MB, alloc=52.3MB, time=81.08 x[1] = 2.4646 1.636 h = 0.003 0.006 y[1] (numeric) = 1.9566599409 1.18060198788 y[1] (closed_form) = 1.95639331973 1.18076669887 absolute error = 0.0003134 relative error = 0.01371 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.755 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] = 2.4676 1.642 h = 0.0001 0.005 y[1] (numeric) = 1.95794717961 1.18541103368 y[1] (closed_form) = 1.95767952501 1.18557747145 absolute error = 0.0003152 relative error = 0.01377 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.76 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] = 2.4677 1.647 h = 0.0001 0.003 y[1] (numeric) = 1.95727252949 1.18906270507 y[1] (closed_form) = 1.95700376809 1.18922930381 absolute error = 0.0003162 relative error = 0.01381 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.762 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=6473.9MB, alloc=52.3MB, time=81.65 x[1] = 2.4678 1.65 h = 0.001 0.001 y[1] (numeric) = 1.95689550759 1.19125989809 y[1] (closed_form) = 1.95662634929 1.19142656543 absolute error = 0.0003166 relative error = 0.01382 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.763 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 x[1] = 2.4688 1.651 h = 0.001 0.003 y[1] (numeric) = 1.95747275838 1.19213752177 y[1] (closed_form) = 1.95720360943 1.192304278 absolute error = 0.0003166 relative error = 0.01382 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.764 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4698 1.654 h = 0.0001 0.004 y[1] (numeric) = 1.95774949591 1.1944703942 y[1] (closed_form) = 1.95748001948 1.19463745455 absolute error = 0.0003171 relative error = 0.01383 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.766 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=6519.6MB, alloc=52.3MB, time=82.22 x[1] = 2.4699 1.658 h = 0.003 0.006 y[1] (numeric) = 1.95722016808 1.19739605639 y[1] (closed_form) = 1.95694998481 1.19756322722 absolute error = 0.0003177 relative error = 0.01385 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.767 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4729 1.664 h = 0.0001 0.005 y[1] (numeric) = 1.95849799783 1.20221488312 y[1] (closed_form) = 1.95822678398 1.20238377998 absolute error = 0.0003195 relative error = 0.0139 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.772 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 x[1] = 2.473 1.669 h = 0.0001 0.003 y[1] (numeric) = 1.95781388677 1.20587013027 y[1] (closed_form) = 1.95754156745 1.20603918907 absolute error = 0.0003205 relative error = 0.01394 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.774 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6565.3MB, alloc=52.3MB, time=82.79 x[1] = 2.4731 1.672 h = 0.001 0.001 y[1] (numeric) = 1.95743121699 1.20806954611 y[1] (closed_form) = 1.95715850125 1.20823867384 absolute error = 0.0003209 relative error = 0.01395 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.775 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] = 2.4741 1.673 h = 0.001 0.003 y[1] (numeric) = 1.95800724057 1.20894975235 y[1] (closed_form) = 1.95773453425 1.20911896887 absolute error = 0.0003209 relative error = 0.01395 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.777 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 x[1] = 2.4751 1.676 h = 0.0001 0.004 y[1] (numeric) = 1.95827894162 1.21128656243 y[1] (closed_form) = 1.95800590847 1.21145608308 absolute error = 0.0003214 relative error = 0.01396 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.779 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6611.0MB, alloc=52.3MB, time=83.37 x[1] = 2.4752 1.68 h = 0.003 0.006 y[1] (numeric) = 1.9577420643 1.21421512619 y[1] (closed_form) = 1.95746832516 1.21438475792 absolute error = 0.000322 relative error = 0.01398 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.78 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4782 1.686 h = 0.0001 0.005 y[1] (numeric) = 1.95901050495 1.21904373318 y[1] (closed_form) = 1.95873573807 1.21921509017 absolute error = 0.0003238 relative error = 0.01404 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.785 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4783 1.691 h = 0.0001 0.003 y[1] (numeric) = 1.95831694651 1.22270256198 y[1] (closed_form) = 1.95804107549 1.22287408186 absolute error = 0.0003248 relative error = 0.01407 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.787 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6656.9MB, alloc=52.3MB, time=83.94 x[1] = 2.4784 1.694 h = 0.001 0.001 y[1] (numeric) = 1.95792863704 1.22490420405 y[1] (closed_form) = 1.9576523701 1.22507579318 absolute error = 0.0003252 relative error = 0.01408 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.788 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 x[1] = 2.4794 1.695 h = 0.0001 0.004 y[1] (numeric) = 1.9585034373 1.22578699137 y[1] (closed_form) = 1.95822717985 1.2259586692 absolute error = 0.0003253 relative error = 0.01408 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.789 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 x[1] = 2.4795 1.699 h = 0.003 0.006 y[1] (numeric) = 1.95796003566 1.22871796661 y[1] (closed_form) = 1.95768307299 1.22888975606 absolute error = 0.0003259 relative error = 0.0141 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.791 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6702.6MB, alloc=52.3MB, time=84.52 x[1] = 2.4825 1.705 h = 0.0001 0.005 y[1] (numeric) = 1.95922029383 1.23355487997 y[1] (closed_form) = 1.95894230586 1.23372839404 absolute error = 0.0003277 relative error = 0.01415 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.796 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4826 1.71 h = 0.0001 0.003 y[1] (numeric) = 1.95851857151 1.23721668402 y[1] (closed_form) = 1.95823948052 1.2373903618 absolute error = 0.0003287 relative error = 0.01419 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.798 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4827 1.713 h = 0.001 0.001 y[1] (numeric) = 1.95812538757 1.23942017796 y[1] (closed_form) = 1.95784590107 1.23959392529 absolute error = 0.0003291 relative error = 0.0142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.799 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=6748.2MB, alloc=52.3MB, time=85.09 x[1] = 2.4837 1.714 h = 0.001 0.003 y[1] (numeric) = 1.95869910723 1.2403051713 y[1] (closed_form) = 1.9584196303 1.24047900722 absolute error = 0.0003291 relative error = 0.0142 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.8 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4847 1.717 h = 0.0001 0.004 y[1] (numeric) = 1.95896141434 1.24264925119 y[1] (closed_form) = 1.95868161179 1.24282339127 absolute error = 0.0003296 relative error = 0.01421 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.802 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 x[1] = 2.4848 1.721 h = 0.003 0.006 y[1] (numeric) = 1.95841048342 1.24558313661 y[1] (closed_form) = 1.95812997648 1.24575738888 absolute error = 0.0003302 relative error = 0.01423 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.804 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6794.0MB, alloc=52.3MB, time=85.66 x[1] = 2.4878 1.727 h = 0.0001 0.005 y[1] (numeric) = 1.95966138922 1.25042982886 y[1] (closed_form) = 1.95937985977 1.25060580494 absolute error = 0.000332 relative error = 0.01428 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.809 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] = 2.4879 1.732 h = 0.0001 0.003 y[1] (numeric) = 1.95895024468 1.25409522531 y[1] (closed_form) = 1.95866761354 1.25427136603 absolute error = 0.000333 relative error = 0.01432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.811 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.488 1.735 h = 0.001 0.001 y[1] (numeric) = 1.95855143624 1.2563009517 y[1] (closed_form) = 1.95826841008 1.25647716228 absolute error = 0.0003334 relative error = 0.01433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.812 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 memory used=6839.8MB, alloc=52.3MB, time=86.25 x[1] = 2.489 1.736 h = 0.001 0.003 y[1] (numeric) = 1.95912393981 1.25718852337 y[1] (closed_form) = 1.95884092329 1.25736482245 absolute error = 0.0003334 relative error = 0.01432 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.813 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.49 1.739 h = 0.0001 0.004 y[1] (numeric) = 1.95938123691 1.25953654358 y[1] (closed_form) = 1.95909789543 1.25971314681 absolute error = 0.0003339 relative error = 0.01433 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.815 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 x[1] = 2.4901 1.743 h = 0.003 0.006 y[1] (numeric) = 1.95882278755 1.26247334356 y[1] (closed_form) = 1.95853874252 1.26265005956 absolute error = 0.0003345 relative error = 0.01436 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.817 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=6885.6MB, alloc=52.3MB, time=86.82 x[1] = 2.4931 1.749 h = 0.0001 0.005 y[1] (numeric) = 1.96006436058 1.26732981362 y[1] (closed_form) = 1.95977929584 1.26750825261 absolute error = 0.0003363 relative error = 0.01441 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.822 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] = 2.4932 1.754 h = 0.0001 0.003 y[1] (numeric) = 1.95934380735 1.27099880798 y[1] (closed_form) = 1.95905764225 1.27117741252 absolute error = 0.0003373 relative error = 0.01444 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.823 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] = 2.4933 1.757 h = 0.001 0.001 y[1] (numeric) = 1.95893938258 1.27320677001 y[1] (closed_form) = 1.95865282295 1.27338544472 absolute error = 0.0003377 relative error = 0.01446 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.825 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=6931.4MB, alloc=52.3MB, time=87.40 x[1] = 2.4943 1.758 h = 0.001 0.003 y[1] (numeric) = 1.95951067389 1.27409691847 y[1] (closed_form) = 1.95922412398 1.27427568158 absolute error = 0.0003377 relative error = 0.01445 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.826 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4953 1.761 h = 0.0001 0.004 y[1] (numeric) = 1.9597629702 1.27644887975 y[1] (closed_form) = 1.95947609597 1.27662794701 absolute error = 0.0003382 relative error = 0.01446 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.828 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 x[1] = 2.4954 1.765 h = 0.003 0.006 y[1] (numeric) = 1.95919701323 1.2793885986 y[1] (closed_form) = 1.95890943631 1.27956777919 absolute error = 0.0003388 relative error = 0.01448 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.829 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 memory used=6977.2MB, alloc=52.3MB, time=87.97 x[1] = 2.4984 1.771 h = 0.0001 0.005 y[1] (numeric) = 1.96042927303 1.28425484525 y[1] (closed_form) = 1.96014067915 1.28443574799 absolute error = 0.0003406 relative error = 0.01453 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.834 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4985 1.776 h = 0.0001 0.003 y[1] (numeric) = 1.95969932464 1.28792744291 y[1] (closed_form) = 1.95940963175 1.2881085121 absolute error = 0.0003416 relative error = 0.01457 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.836 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.4986 1.779 h = 0.001 0.001 y[1] (numeric) = 1.9592892917 1.29013764368 y[1] (closed_form) = 1.95899920476 1.29031878335 absolute error = 0.000342 relative error = 0.01458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.838 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7023.0MB, alloc=52.3MB, time=88.55 x[1] = 2.4996 1.78 h = 0.001 0.003 y[1] (numeric) = 1.95985937456 1.29103036738 y[1] (closed_form) = 1.95956929742 1.29121159534 absolute error = 0.000342 relative error = 0.01457 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.839 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5006 1.783 h = 0.0001 0.004 y[1] (numeric) = 1.96010667923 1.29338627041 y[1] (closed_form) = 1.95981627841 1.29356780251 absolute error = 0.0003425 relative error = 0.01458 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.841 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5007 1.787 h = 0.003 0.006 y[1] (numeric) = 1.9595332255 1.29632891233 y[1] (closed_form) = 1.95924212285 1.29651055832 absolute error = 0.0003431 relative error = 0.01461 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.842 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 memory used=7068.9MB, alloc=52.3MB, time=89.12 x[1] = 2.5037 1.793 h = 0.0001 0.005 y[1] (numeric) = 1.96075619149 1.30120493418 y[1] (closed_form) = 1.96046407464 1.30138830148 absolute error = 0.0003449 relative error = 0.01466 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.847 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5038 1.798 h = 0.0001 0.003 y[1] (numeric) = 1.96001686145 1.30488114041 y[1] (closed_form) = 1.95972364691 1.30506467503 absolute error = 0.0003459 relative error = 0.01469 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.849 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] = 2.5039 1.801 h = 0.001 0.001 y[1] (numeric) = 1.95960122849 1.30709358295 y[1] (closed_form) = 1.9593076204 1.30727718836 absolute error = 0.0003463 relative error = 0.0147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.851 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7114.7MB, alloc=52.3MB, time=89.70 x[1] = 2.5049 1.802 h = 0.0001 0.004 y[1] (numeric) = 1.96017010667 1.3079888803 y[1] (closed_form) = 1.95987650846 1.3081725739 absolute error = 0.0003463 relative error = 0.0147 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.852 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.505 1.806 h = 0.003 0.006 y[1] (numeric) = 1.95959017372 1.31093395244 y[1] (closed_form) = 1.95929587445 1.31111776044 absolute error = 0.000347 relative error = 0.01472 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.854 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.508 1.812 h = 0.0001 0.005 y[1] (numeric) = 1.96080503898 1.31581827688 y[1] (closed_form) = 1.96050972787 1.31600380546 absolute error = 0.0003488 relative error = 0.01477 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.859 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7160.4MB, alloc=52.3MB, time=90.27 x[1] = 2.5081 1.817 h = 0.0001 0.003 y[1] (numeric) = 1.96005760126 1.31949748182 y[1] (closed_form) = 1.95976119362 1.3196831785 absolute error = 0.0003498 relative error = 0.0148 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.86 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] = 2.5082 1.82 h = 0.001 0.001 y[1] (numeric) = 1.95963712777 1.3217117898 y[1] (closed_form) = 1.95934032698 1.32189755753 absolute error = 0.0003501 relative error = 0.01481 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.862 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 x[1] = 2.5092 1.821 h = 0.001 0.003 y[1] (numeric) = 1.96020494138 1.32260928689 y[1] (closed_form) = 1.95990815053 1.32279514272 absolute error = 0.0003502 relative error = 0.01481 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.863 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=7206.2MB, alloc=52.3MB, time=90.84 x[1] = 2.5102 1.824 h = 0.0001 0.004 y[1] (numeric) = 1.96044293512 1.32497246697 y[1] (closed_form) = 1.96014582177 1.32515862691 absolute error = 0.0003506 relative error = 0.01482 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.865 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5103 1.828 h = 0.003 0.006 y[1] (numeric) = 1.95985552554 1.32792046988 y[1] (closed_form) = 1.95955771195 1.32810674475 absolute error = 0.0003513 relative error = 0.01484 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.867 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] = 2.5133 1.834 h = 0.0001 0.005 y[1] (numeric) = 1.96106113293 1.33281456685 y[1] (closed_form) = 1.96076231023 1.33300256141 absolute error = 0.000353 relative error = 0.01489 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.872 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7252.0MB, alloc=52.3MB, time=91.42 x[1] = 2.5134 1.839 h = 0.0001 0.003 y[1] (numeric) = 1.9603043386 1.33649738999 y[1] (closed_form) = 1.96000442069 1.3366855535 absolute error = 0.0003541 relative error = 0.01492 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.874 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5135 1.842 h = 0.001 0.001 y[1] (numeric) = 1.95987828019 1.33871394529 y[1] (closed_form) = 1.95957796963 1.33890218015 absolute error = 0.0003544 relative error = 0.01493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.875 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5145 1.843 h = 0.001 0.003 y[1] (numeric) = 1.96044489611 1.33961401307 y[1] (closed_form) = 1.96014459556 1.33980233592 absolute error = 0.0003545 relative error = 0.01493 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.876 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 memory used=7297.8MB, alloc=52.3MB, time=92.00 x[1] = 2.5155 1.846 h = 0.0001 0.004 y[1] (numeric) = 1.96067792426 1.34198113656 y[1] (closed_form) = 1.96037730185 1.3421697635 absolute error = 0.0003549 relative error = 0.01494 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.878 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 x[1] = 2.5156 1.85 h = 0.003 0.006 y[1] (numeric) = 1.9600830488 1.34493207415 y[1] (closed_form) = 1.95978172702 1.34512081655 absolute error = 0.0003556 relative error = 0.01496 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.88 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5186 1.856 h = 0.0001 0.005 y[1] (numeric) = 1.96127941751 1.34983594188 y[1] (closed_form) = 1.9609770893 1.35002640307 absolute error = 0.0003573 relative error = 0.01501 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.885 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=7343.6MB, alloc=52.3MB, time=92.57 x[1] = 2.5187 1.861 h = 0.0001 0.003 y[1] (numeric) = 1.96051328003 1.35352238812 y[1] (closed_form) = 1.96020985796 1.3537130191 absolute error = 0.0003583 relative error = 0.01504 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.887 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 x[1] = 2.5188 1.864 h = 0.001 0.001 y[1] (numeric) = 1.96008164483 1.35574119357 y[1] (closed_form) = 1.9597778306 1.35593189619 absolute error = 0.0003587 relative error = 0.01505 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.888 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5198 1.865 h = 0.001 0.003 y[1] (numeric) = 1.96064706675 1.35664383039 y[1] (closed_form) = 1.9603432626 1.3568346209 absolute error = 0.0003587 relative error = 0.01505 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.889 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=7389.4MB, alloc=52.3MB, time=93.15 x[1] = 2.5208 1.868 h = 0.0001 0.004 y[1] (numeric) = 1.96087513836 1.3590148977 y[1] (closed_form) = 1.96057101297 1.35920599227 absolute error = 0.0003592 relative error = 0.01506 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.892 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5209 1.872 h = 0.003 0.006 y[1] (numeric) = 1.96027280781 1.36196877379 y[1] (closed_form) = 1.95996798391 1.36215998434 absolute error = 0.0003598 relative error = 0.01508 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.893 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 x[1] = 2.5239 1.878 h = 0.0001 0.005 y[1] (numeric) = 1.96145995691 1.36688241037 y[1] (closed_form) = 1.96115412927 1.3670753388 absolute error = 0.0003616 relative error = 0.01513 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.898 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7435.1MB, alloc=52.3MB, time=93.72 x[1] = 2.524 1.883 h = 0.0001 0.003 y[1] (numeric) = 1.96068448973 1.37057248451 y[1] (closed_form) = 1.96037756957 1.37076558356 absolute error = 0.0003626 relative error = 0.01516 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.9 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5241 1.886 h = 0.001 0.001 y[1] (numeric) = 1.96024728585 1.37279354286 y[1] (closed_form) = 1.95993997401 1.37298671383 absolute error = 0.000363 relative error = 0.01517 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.901 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5251 1.887 h = 0.001 0.003 y[1] (numeric) = 1.96081151745 1.37369874706 y[1] (closed_form) = 1.96050421576 1.37389200582 absolute error = 0.000363 relative error = 0.01516 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.903 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7480.9MB, alloc=52.3MB, time=94.30 x[1] = 2.5261 1.89 h = 0.0001 0.004 y[1] (numeric) = 1.96103464151 1.37607375853 y[1] (closed_form) = 1.96072701923 1.37626732132 absolute error = 0.0003635 relative error = 0.01517 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.905 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5262 1.894 h = 0.003 0.006 y[1] (numeric) = 1.96042486665 1.37903057684 y[1] (closed_form) = 1.96011654671 1.37922425613 absolute error = 0.0003641 relative error = 0.01519 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.906 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 x[1] = 2.5292 1.9 h = 0.0001 0.005 y[1] (numeric) = 1.96160281514 1.38395398024 y[1] (closed_form) = 1.96129349412 1.38414937647 absolute error = 0.0003659 relative error = 0.01524 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.912 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7526.7MB, alloc=52.3MB, time=94.87 x[1] = 2.5293 1.905 h = 0.0001 0.003 y[1] (numeric) = 1.96081803168 1.38764768695 y[1] (closed_form) = 1.96050761948 1.38784325461 absolute error = 0.0003669 relative error = 0.01527 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.914 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] = 2.5294 1.908 h = 0.001 0.001 y[1] (numeric) = 1.96037526722 1.38987100088 y[1] (closed_form) = 1.96006446383 1.39006664074 absolute error = 0.0003673 relative error = 0.01528 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.915 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5304 1.909 h = 0.0001 0.004 y[1] (numeric) = 1.96093831213 1.39077877077 y[1] (closed_form) = 1.96062751897 1.39097449832 absolute error = 0.0003673 relative error = 0.01528 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.916 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=7572.6MB, alloc=52.3MB, time=95.45 x[1] = 2.5305 1.913 h = 0.003 0.006 y[1] (numeric) = 1.96032210291 1.39373803604 y[1] (closed_form) = 1.96001061288 1.39393388056 absolute error = 0.0003679 relative error = 0.0153 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.918 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] = 2.5335 1.919 h = 0.0001 0.005 y[1] (numeric) = 1.96149203065 1.39866973537 y[1] (closed_form) = 1.96117954183 1.39886729604 absolute error = 0.0003697 relative error = 0.01535 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.923 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] = 2.5336 1.924 h = 0.0001 0.003 y[1] (numeric) = 1.96069919545 1.40236646176 y[1] (closed_form) = 1.96038561659 1.40256419458 absolute error = 0.0003707 relative error = 0.01538 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.925 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=7618.5MB, alloc=52.3MB, time=96.02 x[1] = 2.5337 1.927 h = 0.001 0.001 y[1] (numeric) = 1.96025162417 1.4045916532 y[1] (closed_form) = 1.95993765455 1.40478945847 absolute error = 0.0003711 relative error = 0.01539 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.926 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] = 2.5347 1.928 h = 0.001 0.003 y[1] (numeric) = 1.96081362 1.40550161612 y[1] (closed_form) = 1.96049966066 1.40569950898 absolute error = 0.0003711 relative error = 0.01538 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.928 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] = 2.5357 1.931 h = 0.0001 0.004 y[1] (numeric) = 1.96102751472 1.40788390873 y[1] (closed_form) = 1.96071323594 1.40808210555 absolute error = 0.0003716 relative error = 0.01539 % Correct digits = 4 memory used=7664.2MB, alloc=52.3MB, time=96.60 Radius of convergence (given) for eq 1 = 4.93 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5358 1.935 h = 0.003 0.006 y[1] (numeric) = 1.96040388118 1.41084612306 y[1] (closed_form) = 1.96008890635 1.41104443733 absolute error = 0.0003722 relative error = 0.01541 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.931 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5388 1.941 h = 0.0001 0.005 y[1] (numeric) = 1.96156464343 1.41578758529 y[1] (closed_form) = 1.96124867244 1.41598761475 absolute error = 0.000374 relative error = 0.01546 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.936 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] = 2.5389 1.946 h = 0.0001 0.003 y[1] (numeric) = 1.96076251682 1.41948795279 y[1] (closed_form) = 1.96044545713 1.41968815519 absolute error = 0.000375 relative error = 0.01549 % Correct digits = 4 memory used=7710.1MB, alloc=52.3MB, time=97.18 Radius of convergence (given) for eq 1 = 4.938 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 x[1] = 2.539 1.949 h = 0.001 0.001 y[1] (numeric) = 1.96030939996 1.42171540471 y[1] (closed_form) = 1.95999195 1.42191567982 absolute error = 0.0003753 relative error = 0.0155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.94 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] = 2.54 1.95 h = 0.001 0.003 y[1] (numeric) = 1.96087021585 1.42262793017 y[1] (closed_form) = 1.96055277622 1.42282829277 absolute error = 0.0003754 relative error = 0.0155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.941 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7755.9MB, alloc=52.3MB, time=97.75 x[1] = 2.541 1.953 h = 0.0001 0.004 y[1] (numeric) = 1.9610791886 1.42501416763 y[1] (closed_form) = 1.96076143016 1.42521483415 absolute error = 0.0003758 relative error = 0.0155 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.943 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 x[1] = 2.5411 1.957 h = 0.003 0.006 y[1] (numeric) = 1.96044814143 1.42797933446 y[1] (closed_form) = 1.9601296878 1.42818011893 absolute error = 0.0003765 relative error = 0.01552 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.945 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5441 1.963 h = 0.0001 0.005 y[1] (numeric) = 1.96159975691 1.43293055719 y[1] (closed_form) = 1.96128030973 1.43313305585 absolute error = 0.0003782 relative error = 0.01557 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.95 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=7801.7MB, alloc=52.3MB, time=98.32 x[1] = 2.5442 1.968 h = 0.0001 0.003 y[1] (numeric) = 1.96078835227 1.43663457013 y[1] (closed_form) = 1.96046781773 1.43683724251 absolute error = 0.0003792 relative error = 0.0156 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.952 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5443 1.971 h = 0.001 0.001 y[1] (numeric) = 1.96032969787 1.438864285 y[1] (closed_form) = 1.96000877356 1.43906703037 absolute error = 0.0003796 relative error = 0.01561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.953 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5453 1.972 h = 0.001 0.003 y[1] (numeric) = 1.96088933738 1.43977937127 y[1] (closed_form) = 1.96056842347 1.43998220402 absolute error = 0.0003796 relative error = 0.01561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.955 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7847.5MB, alloc=52.3MB, time=98.90 x[1] = 2.5463 1.975 h = 0.0001 0.004 y[1] (numeric) = 1.96109339705 1.44216955366 y[1] (closed_form) = 1.96077216493 1.44237269028 absolute error = 0.0003801 relative error = 0.01561 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.957 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5464 1.979 h = 0.003 0.006 y[1] (numeric) = 1.96045494694 1.44513767636 y[1] (closed_form) = 1.9601330205 1.44534093141 absolute error = 0.0003807 relative error = 0.01563 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.958 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] = 2.5494 1.985 h = 0.0001 0.005 y[1] (numeric) = 1.96159743428 1.45009865703 y[1] (closed_form) = 1.96127451689 1.45030362529 absolute error = 0.0003825 relative error = 0.01568 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.964 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7893.2MB, alloc=52.3MB, time=99.47 x[1] = 2.5495 1.99 h = 0.0001 0.003 y[1] (numeric) = 1.96077676494 1.45380631964 y[1] (closed_form) = 1.96045276154 1.45401146238 absolute error = 0.0003835 relative error = 0.01571 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.966 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 x[1] = 2.5496 1.993 h = 0.001 0.001 y[1] (numeric) = 1.96031258106 1.45603829988 y[1] (closed_form) = 1.95998818837 1.45624351587 absolute error = 0.0003839 relative error = 0.01572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.967 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5506 1.994 h = 0.001 0.003 y[1] (numeric) = 1.96087104772 1.45695594518 y[1] (closed_form) = 1.9605466655 1.45716124845 absolute error = 0.0003839 relative error = 0.01572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.968 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=7939.0MB, alloc=52.3MB, time=100.04 x[1] = 2.5516 1.997 h = 0.0001 0.004 y[1] (numeric) = 1.96107020314 1.45935007252 y[1] (closed_form) = 1.96074550333 1.45955567961 absolute error = 0.0003843 relative error = 0.01572 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.97 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5517 2.001 h = 0.003 0.006 y[1] (numeric) = 1.96042436078 1.46232115436 y[1] (closed_form) = 1.96009896751 1.46252688034 absolute error = 0.000385 relative error = 0.01574 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.972 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5547 2.007 h = 0.0001 0.005 y[1] (numeric) = 1.96155773853 1.46729189031 y[1] (closed_form) = 1.96123135688 1.4674993285 absolute error = 0.0003867 relative error = 0.01579 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.977 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=7984.7MB, alloc=52.3MB, time=100.62 x[1] = 2.5548 2.012 h = 0.0001 0.003 y[1] (numeric) = 1.96072781782 1.47100320669 y[1] (closed_form) = 1.96040035149 1.47121082012 absolute error = 0.0003877 relative error = 0.01582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.979 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] = 2.5549 2.015 h = 0.001 0.001 y[1] (numeric) = 1.96025811247 1.47323745465 y[1] (closed_form) = 1.95993025735 1.47344514157 absolute error = 0.0003881 relative error = 0.01583 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.981 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 x[1] = 2.5559 2.016 h = 0.0001 0.004 y[1] (numeric) = 1.9608154098 1.4741576572 y[1] (closed_form) = 1.96048756522 1.4743654313 absolute error = 0.0003881 relative error = 0.01582 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.982 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=8030.4MB, alloc=52.3MB, time=101.19 x[1] = 2.556 2.02 h = 0.003 0.006 y[1] (numeric) = 1.96016317764 1.4771312008 y[1] (closed_form) = 1.95983464037 1.47733909425 absolute error = 0.0003888 relative error = 0.01584 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.984 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.559 2.026 h = 0.0001 0.005 y[1] (numeric) = 1.96128861275 1.48211022334 y[1] (closed_form) = 1.96095908933 1.48231982813 absolute error = 0.0003905 relative error = 0.01589 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.989 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 x[1] = 2.5591 2.031 h = 0.0001 0.003 y[1] (numeric) = 1.96045069583 1.48582457798 y[1] (closed_form) = 1.96012008887 1.48603435867 absolute error = 0.0003915 relative error = 0.01592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.991 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=8076.2MB, alloc=52.3MB, time=101.76 x[1] = 2.5592 2.034 h = 0.001 0.001 y[1] (numeric) = 1.95997621715 1.48806071409 y[1] (closed_form) = 1.95964522182 1.48827056849 absolute error = 0.0003919 relative error = 0.01593 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.992 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5602 2.035 h = 0.001 0.003 y[1] (numeric) = 1.96053248032 1.48898310254 y[1] (closed_form) = 1.96020149559 1.48919304403 absolute error = 0.000392 relative error = 0.01592 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.994 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] = 2.5612 2.038 h = 0.0001 0.004 y[1] (numeric) = 1.96072248648 1.49138451215 y[1] (closed_form) = 1.96039118529 1.49159475736 absolute error = 0.0003924 relative error = 0.01593 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.996 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8122.0MB, alloc=52.3MB, time=102.34 x[1] = 2.5613 2.042 h = 0.003 0.006 y[1] (numeric) = 1.9600628819 1.49436102089 y[1] (closed_form) = 1.95973088885 1.49457138588 absolute error = 0.000393 relative error = 0.01595 % Correct digits = 4 Radius of convergence (given) for eq 1 = 4.998 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 x[1] = 2.5643 2.048 h = 0.0001 0.005 y[1] (numeric) = 1.96117924169 1.49934979365 y[1] (closed_form) = 1.96084626502 1.49956186894 absolute error = 0.0003948 relative error = 0.01599 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.003 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] = 2.5644 2.053 h = 0.0001 0.003 y[1] (numeric) = 1.96033209806 1.50306780956 y[1] (closed_form) = 1.9599980392 1.50328006147 absolute error = 0.0003958 relative error = 0.01602 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.005 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=8167.8MB, alloc=52.3MB, time=102.91 x[1] = 2.5645 2.056 h = 0.001 0.001 y[1] (numeric) = 1.95985211279 1.50530621764 y[1] (closed_form) = 1.95951766603 1.50551854354 absolute error = 0.0003962 relative error = 0.01603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.006 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 x[1] = 2.5655 2.057 h = 0.001 0.003 y[1] (numeric) = 1.96040721311 1.50623116003 y[1] (closed_form) = 1.96007277702 1.5064435729 absolute error = 0.0003962 relative error = 0.01603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.007 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] = 2.5665 2.06 h = 0.0001 0.004 y[1] (numeric) = 1.9605923401 1.50863651438 y[1] (closed_form) = 1.96025758815 1.5088492309 absolute error = 0.0003966 relative error = 0.01603 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.01 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8213.5MB, alloc=52.3MB, time=103.48 x[1] = 2.5666 2.064 h = 0.003 0.006 y[1] (numeric) = 1.95992537369 1.51161599125 y[1] (closed_form) = 1.95958993074 1.511828828 absolute error = 0.0003973 relative error = 0.01605 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.011 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5696 2.07 h = 0.0001 0.005 y[1] (numeric) = 1.9610326764 1.51661451122 y[1] (closed_form) = 1.96069625237 1.51682905722 absolute error = 0.000399 relative error = 0.0161 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.017 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5697 2.075 h = 0.0001 0.003 y[1] (numeric) = 1.96017631931 1.52033619218 y[1] (closed_form) = 1.95983881443 1.52055091552 absolute error = 0.0004 relative error = 0.01613 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.019 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8259.4MB, alloc=52.3MB, time=104.06 x[1] = 2.5698 2.078 h = 0.001 0.001 y[1] (numeric) = 1.95969083542 1.5225768744 y[1] (closed_form) = 1.95935294313 1.52279167196 absolute error = 0.0004004 relative error = 0.01613 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.02 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5708 2.079 h = 0.001 0.003 y[1] (numeric) = 1.96024477634 1.52350436889 y[1] (closed_form) = 1.95990689477 1.52371925333 absolute error = 0.0004004 relative error = 0.01613 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.021 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 x[1] = 2.5718 2.082 h = 0.0001 0.004 y[1] (numeric) = 1.96042503285 1.52591366775 y[1] (closed_form) = 1.96008683604 1.52612885577 absolute error = 0.0004009 relative error = 0.01614 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.024 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8305.1MB, alloc=52.3MB, time=104.64 x[1] = 2.5719 2.086 h = 0.003 0.006 y[1] (numeric) = 1.95975071521 1.52889611567 y[1] (closed_form) = 1.95941182825 1.52911142437 absolute error = 0.0004015 relative error = 0.01615 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.025 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5749 2.092 h = 0.0001 0.005 y[1] (numeric) = 1.96084897902 1.53390437971 y[1] (closed_form) = 1.96050911349 1.5341213966 absolute error = 0.0004032 relative error = 0.0162 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.031 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 x[1] = 2.575 2.097 h = 0.0001 0.003 y[1] (numeric) = 1.95998342169 1.5376297294 y[1] (closed_form) = 1.95964247665 1.53784692433 absolute error = 0.0004042 relative error = 0.01623 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.033 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=8350.9MB, alloc=52.3MB, time=105.22 x[1] = 2.5751 2.1 h = 0.001 0.001 y[1] (numeric) = 1.95949244714 1.53987268783 y[1] (closed_form) = 1.95915111518 1.54008995722 absolute error = 0.0004046 relative error = 0.01624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.034 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] = 2.5761 2.101 h = 0.001 0.003 y[1] (numeric) = 1.96004523205 1.54080273259 y[1] (closed_form) = 1.95970391088 1.54102008875 absolute error = 0.0004047 relative error = 0.01623 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.035 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] = 2.5771 2.104 h = 0.0001 0.004 y[1] (numeric) = 1.96022062675 1.54321597566 y[1] (closed_form) = 1.95987899093 1.54343363533 absolute error = 0.0004051 relative error = 0.01624 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.038 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=8396.8MB, alloc=52.3MB, time=105.80 x[1] = 2.5772 2.108 h = 0.003 0.006 y[1] (numeric) = 1.95953896846 1.54620139748 y[1] (closed_form) = 1.95919664335 1.54641917826 absolute error = 0.0004057 relative error = 0.01626 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.039 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 x[1] = 2.5802 2.114 h = 0.0001 0.005 y[1] (numeric) = 1.96062821143 1.55121940234 y[1] (closed_form) = 1.96028491024 1.55143889023 absolute error = 0.0004075 relative error = 0.0163 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.045 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 x[1] = 2.5803 2.119 h = 0.0001 0.003 y[1] (numeric) = 1.95975346705 1.55494842432 y[1] (closed_form) = 1.95940908769 1.55516809094 absolute error = 0.0004085 relative error = 0.01633 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.047 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 memory used=8442.5MB, alloc=52.3MB, time=106.38 x[1] = 2.5804 2.122 h = 0.001 0.001 y[1] (numeric) = 1.95925700979 1.55719366099 y[1] (closed_form) = 1.958912244 1.55741340231 absolute error = 0.0004088 relative error = 0.01634 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.048 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 x[1] = 2.5814 2.123 h = 0.0001 0.004 y[1] (numeric) = 1.95980864208 1.55812625413 y[1] (closed_form) = 1.95946388713 1.55834608212 absolute error = 0.0004089 relative error = 0.01633 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.049 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5815 2.127 h = 0.003 0.006 y[1] (numeric) = 1.95912063813 1.56111415068 y[1] (closed_form) = 1.95877519469 1.56133410019 absolute error = 0.0004095 relative error = 0.01635 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.051 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8488.2MB, alloc=52.3MB, time=106.95 x[1] = 2.5845 2.133 h = 0.0001 0.005 y[1] (numeric) = 1.96020201469 1.56614043027 y[1] (closed_form) = 1.9598555973 1.56636208597 absolute error = 0.0004113 relative error = 0.01639 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.056 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 x[1] = 2.5846 2.138 h = 0.0001 0.003 y[1] (numeric) = 1.95931932914 1.56987250678 y[1] (closed_form) = 1.95897183472 1.57009434182 absolute error = 0.0004123 relative error = 0.01642 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.059 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5847 2.141 h = 0.001 0.001 y[1] (numeric) = 1.95881813171 1.57211964086 y[1] (closed_form) = 1.95847025129 1.57234155081 absolute error = 0.0004126 relative error = 0.01643 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.06 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=8533.9MB, alloc=52.3MB, time=107.52 x[1] = 2.5857 2.142 h = 0.001 0.003 y[1] (numeric) = 1.95936874422 1.5730544124 y[1] (closed_form) = 1.95902087469 1.57327640892 absolute error = 0.0004127 relative error = 0.01642 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.061 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5867 2.145 h = 0.0001 0.004 y[1] (numeric) = 1.95953506816 1.57547493608 y[1] (closed_form) = 1.95918688509 1.57569723597 absolute error = 0.0004131 relative error = 0.01643 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.063 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 x[1] = 2.5868 2.149 h = 0.003 0.006 y[1] (numeric) = 1.95883974321 1.57846581173 y[1] (closed_form) = 1.95849087245 1.57868823353 absolute error = 0.0004137 relative error = 0.01645 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.065 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=8579.7MB, alloc=52.3MB, time=108.09 x[1] = 2.5898 2.155 h = 0.0001 0.005 y[1] (numeric) = 1.95991213232 1.58350182599 y[1] (closed_form) = 1.95956229008 1.58372595289 absolute error = 0.0004155 relative error = 0.01649 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.071 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 x[1] = 2.5899 2.16 h = 0.0001 0.003 y[1] (numeric) = 1.95902028415 1.58723758129 y[1] (closed_form) = 1.95866936622 1.5874618882 absolute error = 0.0004165 relative error = 0.01652 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.073 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.59 2.163 h = 0.001 0.001 y[1] (numeric) = 1.95851361872 1.58948699729 y[1] (closed_form) = 1.95816231526 1.58971137932 absolute error = 0.0004168 relative error = 0.01653 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.074 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=8625.5MB, alloc=52.3MB, time=108.65 x[1] = 2.591 2.164 h = 0.001 0.003 y[1] (numeric) = 1.95906308484 1.59042431375 y[1] (closed_form) = 1.95871179234 1.59064878225 absolute error = 0.0004169 relative error = 0.01652 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.075 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 x[1] = 2.592 2.167 h = 0.0001 0.004 y[1] (numeric) = 1.95922457153 1.59284878058 y[1] (closed_form) = 1.95887296608 1.59307355236 absolute error = 0.0004173 relative error = 0.01653 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.078 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] = 2.5921 2.171 h = 0.003 0.006 y[1] (numeric) = 1.95852193603 1.59584263788 y[1] (closed_form) = 1.95816964376 1.596067532 absolute error = 0.000418 relative error = 0.01654 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.079 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 memory used=8671.3MB, alloc=52.3MB, time=109.22 x[1] = 2.5951 2.177 h = 0.0001 0.005 y[1] (numeric) = 1.9595853555 1.60088838326 y[1] (closed_form) = 1.95923209418 1.60111498135 absolute error = 0.0004197 relative error = 0.01659 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.085 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] = 2.5952 2.182 h = 0.0001 0.003 y[1] (numeric) = 1.9586843578 1.6046278206 y[1] (closed_form) = 1.95833002213 1.60485459936 absolute error = 0.0004207 relative error = 0.01662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.087 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5953 2.185 h = 0.001 0.001 y[1] (numeric) = 1.95817223225 1.60687952035 y[1] (closed_form) = 1.95781751155 1.60710637446 absolute error = 0.0004211 relative error = 0.01662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.088 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=8717.1MB, alloc=52.3MB, time=109.79 x[1] = 2.5963 2.186 h = 0.001 0.003 y[1] (numeric) = 1.9587205553 1.60781937981 y[1] (closed_form) = 1.95836584559 1.60804632029 absolute error = 0.0004211 relative error = 0.01662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.09 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5973 2.189 h = 0.0001 0.004 y[1] (numeric) = 1.95887721325 1.61024778927 y[1] (closed_form) = 1.95852219118 1.61047503294 absolute error = 0.0004215 relative error = 0.01662 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.092 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.5974 2.193 h = 0.003 0.006 y[1] (numeric) = 1.95816727769 1.61324463074 y[1] (closed_form) = 1.95781156967 1.61347199715 absolute error = 0.0004222 relative error = 0.01664 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.094 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8762.9MB, alloc=52.3MB, time=110.36 x[1] = 2.6004 2.199 h = 0.0001 0.005 y[1] (numeric) = 1.9592217452 1.61830010354 y[1] (closed_form) = 1.95886507054 1.6185291728 absolute error = 0.0004239 relative error = 0.01668 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.099 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] = 2.6005 2.204 h = 0.0001 0.003 y[1] (numeric) = 1.95831161105 1.62204322608 y[1] (closed_form) = 1.95795386339 1.62227247664 absolute error = 0.0004249 relative error = 0.01671 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.101 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6006 2.207 h = 0.001 0.001 y[1] (numeric) = 1.95779403326 1.62429721135 y[1] (closed_form) = 1.95743590104 1.62452653748 absolute error = 0.0004253 relative error = 0.01672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.103 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=8808.7MB, alloc=52.3MB, time=110.95 x[1] = 2.6016 2.208 h = 0.001 0.003 y[1] (numeric) = 1.95834121649 1.62523961189 y[1] (closed_form) = 1.95798309534 1.62546902429 absolute error = 0.0004253 relative error = 0.01671 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.104 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6026 2.211 h = 0.0001 0.004 y[1] (numeric) = 1.95849305417 1.6276719634 y[1] (closed_form) = 1.95813462125 1.62790167889 absolute error = 0.0004257 relative error = 0.01672 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.106 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 x[1] = 2.6027 2.215 h = 0.003 0.006 y[1] (numeric) = 1.95777582902 1.63067179146 y[1] (closed_form) = 1.95741671099 1.63090163009 absolute error = 0.0004264 relative error = 0.01673 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.108 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=8854.4MB, alloc=52.3MB, time=111.51 x[1] = 2.6057 2.221 h = 0.0001 0.005 y[1] (numeric) = 1.95882136216 1.63573698788 y[1] (closed_form) = 1.9584612799 1.63596852822 absolute error = 0.0004281 relative error = 0.01678 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.113 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 x[1] = 2.6058 2.226 h = 0.0001 0.003 y[1] (numeric) = 1.9579021046 1.63948379867 y[1] (closed_form) = 1.95754095067 1.63971552095 absolute error = 0.0004291 relative error = 0.0168 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.116 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] = 2.6059 2.229 h = 0.001 0.001 y[1] (numeric) = 1.95737908241 1.64174007116 y[1] (closed_form) = 1.95701754442 1.64197186923 absolute error = 0.0004295 relative error = 0.01681 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.117 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=8900.1MB, alloc=52.3MB, time=112.07 x[1] = 2.6069 2.23 h = 0.0001 0.004 y[1] (numeric) = 1.95792512909 1.64268501085 y[1] (closed_form) = 1.95756360221 1.64291689507 absolute error = 0.0004295 relative error = 0.01681 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.118 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.607 2.234 h = 0.003 0.006 y[1] (numeric) = 1.95720160199 1.64568732485 y[1] (closed_form) = 1.95683939079 1.64591933258 absolute error = 0.0004301 relative error = 0.01682 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.12 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] = 2.61 2.24 h = 0.0001 0.005 y[1] (numeric) = 1.95823934296 1.65076078178 y[1] (closed_form) = 1.95787616961 1.65099449026 absolute error = 0.0004319 relative error = 0.01686 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.125 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=8946.0MB, alloc=52.3MB, time=112.63 x[1] = 2.6101 2.245 h = 0.0001 0.003 y[1] (numeric) = 1.95731219872 1.65451066118 y[1] (closed_form) = 1.95694795483 1.65474455215 absolute error = 0.0004329 relative error = 0.01689 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.128 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6102 2.248 h = 0.001 0.001 y[1] (numeric) = 1.95678446918 1.65676883904 y[1] (closed_form) = 1.95641984164 1.65700280598 absolute error = 0.0004332 relative error = 0.0169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.129 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6112 2.249 h = 0.001 0.003 y[1] (numeric) = 1.9573295099 1.65771594928 y[1] (closed_form) = 1.95696489353 1.65795000229 absolute error = 0.0004333 relative error = 0.01689 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.13 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=8991.7MB, alloc=52.3MB, time=113.19 x[1] = 2.6122 2.252 h = 0.0001 0.004 y[1] (numeric) = 1.95747235367 1.6601555771 y[1] (closed_form) = 1.9571074266 1.66038993303 absolute error = 0.0004337 relative error = 0.0169 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.133 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] = 2.6123 2.256 h = 0.003 0.006 y[1] (numeric) = 1.95674155639 1.66316088212 y[1] (closed_form) = 1.95637594581 1.66339536193 absolute error = 0.0004343 relative error = 0.01691 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.134 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] = 2.6153 2.262 h = 0.0001 0.005 y[1] (numeric) = 1.95777039551 1.66824405555 y[1] (closed_form) = 1.95740382514 1.66848023493 absolute error = 0.0004361 relative error = 0.01695 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.14 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=9037.5MB, alloc=52.3MB, time=113.76 x[1] = 2.6154 2.267 h = 0.0001 0.003 y[1] (numeric) = 1.95683415201 1.67199762873 y[1] (closed_form) = 1.95646651244 1.67223399122 absolute error = 0.0004371 relative error = 0.01698 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.142 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] = 2.6155 2.27 h = 0.001 0.001 y[1] (numeric) = 1.9563009926 1.67425809693 y[1] (closed_form) = 1.95593296987 1.67449453559 absolute error = 0.0004374 relative error = 0.01699 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.144 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 x[1] = 2.6165 2.271 h = 0.001 0.003 y[1] (numeric) = 1.95684490276 1.6752077427 y[1] (closed_form) = 1.95647689125 1.67544426733 absolute error = 0.0004375 relative error = 0.01698 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.145 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9083.3MB, alloc=52.3MB, time=114.32 x[1] = 2.6175 2.274 h = 0.0001 0.004 y[1] (numeric) = 1.95698295029 1.6776513107 y[1] (closed_form) = 1.95661462866 1.67788813815 absolute error = 0.0004379 relative error = 0.01699 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.147 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 x[1] = 2.6176 2.278 h = 0.003 0.006 y[1] (numeric) = 1.95624489316 1.68065960891 y[1] (closed_form) = 1.95587588888 1.68089656061 absolute error = 0.0004385 relative error = 0.017 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.149 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6206 2.284 h = 0.0001 0.005 y[1] (numeric) = 1.95726484773 1.68575249473 y[1] (closed_form) = 1.95689488601 1.68599114483 absolute error = 0.0004403 relative error = 0.01704 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.154 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 memory used=9129.1MB, alloc=52.3MB, time=114.88 x[1] = 2.6207 2.289 h = 0.0001 0.003 y[1] (numeric) = 1.95631951792 1.68950976445 y[1] (closed_form) = 1.95594848833 1.68974859825 absolute error = 0.0004413 relative error = 0.01707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.157 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] = 2.6208 2.292 h = 0.001 0.001 y[1] (numeric) = 1.95578093644 1.69177252452 y[1] (closed_form) = 1.95540952418 1.6920114347 absolute error = 0.0004416 relative error = 0.01708 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.158 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 x[1] = 2.6218 2.293 h = 0.001 0.003 y[1] (numeric) = 1.95632371921 1.69272470384 y[1] (closed_form) = 1.95595231821 1.69296369988 absolute error = 0.0004417 relative error = 0.01707 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.159 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9174.9MB, alloc=52.3MB, time=115.44 x[1] = 2.6228 2.296 h = 0.0001 0.004 y[1] (numeric) = 1.95645697882 1.69517221123 y[1] (closed_form) = 1.95608526828 1.69541150998 absolute error = 0.0004421 relative error = 0.01708 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.162 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 x[1] = 2.6229 2.3 h = 0.003 0.006 y[1] (numeric) = 1.9557116722 1.69818350472 y[1] (closed_form) = 1.95533927987 1.6984229281 absolute error = 0.0004427 relative error = 0.01709 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.163 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 x[1] = 2.6259 2.306 h = 0.0001 0.005 y[1] (numeric) = 1.95672275943 1.70328609874 y[1] (closed_form) = 1.95634941199 1.70352721933 absolute error = 0.0004444 relative error = 0.01713 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.169 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 memory used=9220.7MB, alloc=52.3MB, time=116.01 x[1] = 2.626 2.311 h = 0.0001 0.003 y[1] (numeric) = 1.95576835621 1.70704706765 y[1] (closed_form) = 1.95539394224 1.70728837253 absolute error = 0.0004454 relative error = 0.01716 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.171 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] = 2.6261 2.314 h = 0.001 0.001 y[1] (numeric) = 1.95522436043 1.70931212107 y[1] (closed_form) = 1.95484956426 1.70955350253 absolute error = 0.0004458 relative error = 0.01717 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.173 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 x[1] = 2.6271 2.315 h = 0.001 0.003 y[1] (numeric) = 1.95576601895 1.71026683194 y[1] (closed_form) = 1.9553912341 1.71050829915 absolute error = 0.0004458 relative error = 0.01716 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.174 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9266.5MB, alloc=52.3MB, time=116.57 x[1] = 2.6281 2.318 h = 0.0001 0.004 y[1] (numeric) = 1.95589449893 1.71271827786 y[1] (closed_form) = 1.9555194051 1.71296004767 absolute error = 0.0004463 relative error = 0.01717 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.176 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6282 2.322 h = 0.003 0.006 y[1] (numeric) = 1.95514195315 1.71573256867 y[1] (closed_form) = 1.95476617839 1.71597446347 absolute error = 0.0004469 relative error = 0.01718 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.178 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6312 2.328 h = 0.0001 0.005 y[1] (numeric) = 1.95614419014 1.72084486658 y[1] (closed_form) = 1.95576746258 1.7210884574 absolute error = 0.0004486 relative error = 0.01722 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.183 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=9312.2MB, alloc=52.3MB, time=117.13 x[1] = 2.6313 2.333 h = 0.0001 0.003 y[1] (numeric) = 1.9551807264 1.72460953724 y[1] (closed_form) = 1.95480293364 1.72485331292 absolute error = 0.0004496 relative error = 0.01725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.186 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 x[1] = 2.6314 2.336 h = 0.001 0.001 y[1] (numeric) = 1.95463132406 1.72687688542 y[1] (closed_form) = 1.9542531496 1.72712073787 absolute error = 0.00045 relative error = 0.01725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.187 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 x[1] = 2.6324 2.337 h = 0.0001 0.004 y[1] (numeric) = 1.95517186145 1.72783412583 y[1] (closed_form) = 1.95479369835 1.72807806393 absolute error = 0.00045 relative error = 0.01725 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.189 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=9357.8MB, alloc=52.3MB, time=117.69 x[1] = 2.6325 2.341 h = 0.003 0.006 y[1] (numeric) = 1.95441305692 1.73085091211 y[1] (closed_form) = 1.95403421366 1.73109497553 absolute error = 0.0004507 relative error = 0.01726 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.19 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6355 2.347 h = 0.0001 0.005 y[1] (numeric) = 1.95540757401 1.73597145413 y[1] (closed_form) = 1.95502777996 1.73621721257 absolute error = 0.0004524 relative error = 0.0173 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.196 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 x[1] = 2.6356 2.352 h = 0.0001 0.003 y[1] (numeric) = 1.95443627743 1.73973920537 y[1] (closed_form) = 1.9540554193 1.73998514918 absolute error = 0.0004534 relative error = 0.01733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.198 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9403.6MB, alloc=52.3MB, time=118.26 x[1] = 2.6357 2.355 h = 0.001 0.001 y[1] (numeric) = 1.95388220014 1.74200846562 y[1] (closed_form) = 1.95350096072 1.74225448636 absolute error = 0.0004537 relative error = 0.01733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.2 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] = 2.6367 2.356 h = 0.001 0.003 y[1] (numeric) = 1.95442174487 1.74296786845 y[1] (closed_form) = 1.95404051686 1.74321397475 absolute error = 0.0004538 relative error = 0.01733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.201 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] = 2.6377 2.359 h = 0.0001 0.004 y[1] (numeric) = 1.95454130607 1.74542658392 y[1] (closed_form) = 1.95415977014 1.74567299262 absolute error = 0.0004542 relative error = 0.01733 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.203 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=9449.4MB, alloc=52.3MB, time=118.82 x[1] = 2.6378 2.363 h = 0.003 0.006 y[1] (numeric) = 1.95377528155 1.74844637122 y[1] (closed_form) = 1.95339306626 1.74869290557 absolute error = 0.0004548 relative error = 0.01735 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.205 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6408 2.369 h = 0.0001 0.005 y[1] (numeric) = 1.95476098002 1.75357660908 y[1] (closed_form) = 1.95437781622 1.75382483722 absolute error = 0.0004565 relative error = 0.01739 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.21 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6409 2.374 h = 0.0001 0.003 y[1] (numeric) = 1.95378064675 1.75734806671 y[1] (closed_form) = 1.95339642021 1.75759648076 absolute error = 0.0004575 relative error = 0.01741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.213 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9495.2MB, alloc=52.3MB, time=119.38 x[1] = 2.641 2.377 h = 0.001 0.001 y[1] (numeric) = 1.95322117724 1.75961962428 y[1] (closed_form) = 1.95283656989 1.75986811547 absolute error = 0.0004579 relative error = 0.01742 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.214 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] = 2.642 2.378 h = 0.001 0.003 y[1] (numeric) = 1.9537596066 1.76058155292 y[1] (closed_form) = 1.9533750107 1.76083012956 absolute error = 0.0004579 relative error = 0.01741 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.216 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 x[1] = 2.643 2.381 h = 0.0001 0.004 y[1] (numeric) = 1.95387441164 1.7630442043 y[1] (closed_form) = 1.95348950838 1.76329308322 absolute error = 0.0004584 relative error = 0.01742 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.218 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=9540.9MB, alloc=52.3MB, time=119.94 x[1] = 2.6431 2.385 h = 0.003 0.006 y[1] (numeric) = 1.95310117732 1.7660669944 y[1] (closed_form) = 1.95271559556 1.76631599931 absolute error = 0.000459 relative error = 0.01743 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.22 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6461 2.391 h = 0.0001 0.005 y[1] (numeric) = 1.95407807399 1.7712069235 y[1] (closed_form) = 1.95369154599 1.77145762097 absolute error = 0.0004607 relative error = 0.01747 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.225 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] = 2.6462 2.396 h = 0.0001 0.003 y[1] (numeric) = 1.95308871681 1.77498208979 y[1] (closed_form) = 1.95270112739 1.77523297372 absolute error = 0.0004617 relative error = 0.0175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.228 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=9586.7MB, alloc=52.3MB, time=120.50 x[1] = 2.6463 2.399 h = 0.001 0.001 y[1] (numeric) = 1.95252386277 1.77725594594 y[1] (closed_form) = 1.95213589301 1.77750690718 absolute error = 0.0004621 relative error = 0.0175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.229 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 x[1] = 2.6473 2.4 h = 0.001 0.003 y[1] (numeric) = 1.95306117979 1.77822039834 y[1] (closed_form) = 1.95267322154 1.77847144493 absolute error = 0.0004621 relative error = 0.0175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.23 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] = 2.6483 2.403 h = 0.0001 0.004 y[1] (numeric) = 1.9531712368 1.78068698459 y[1] (closed_form) = 1.95278297175 1.78093833333 absolute error = 0.0004625 relative error = 0.0175 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.233 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9632.4MB, alloc=52.3MB, time=121.06 x[1] = 2.6484 2.407 h = 0.003 0.006 y[1] (numeric) = 1.95239080291 1.78371277921 y[1] (closed_form) = 1.9520018602 1.78396425429 absolute error = 0.0004632 relative error = 0.01751 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.235 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] = 2.6514 2.413 h = 0.0001 0.005 y[1] (numeric) = 1.95335891449 1.78886239488 y[1] (closed_form) = 1.95296902779 1.78911556128 absolute error = 0.0004649 relative error = 0.01755 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.24 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6515 2.418 h = 0.0001 0.003 y[1] (numeric) = 1.95236054614 1.792641272 y[1] (closed_form) = 1.95196959934 1.79289462539 absolute error = 0.0004659 relative error = 0.01758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.242 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 memory used=9678.1MB, alloc=52.3MB, time=121.62 x[1] = 2.6516 2.421 h = 0.001 0.001 y[1] (numeric) = 1.95179031522 1.79491742792 y[1] (closed_form) = 1.95139898857 1.7951708588 absolute error = 0.0004662 relative error = 0.01758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.244 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6526 2.422 h = 0.001 0.003 y[1] (numeric) = 1.95232652292 1.79588440202 y[1] (closed_form) = 1.95193520783 1.79613791815 absolute error = 0.0004663 relative error = 0.01758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.245 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] = 2.6536 2.425 h = 0.0001 0.004 y[1] (numeric) = 1.95243183999 1.79835492203 y[1] (closed_form) = 1.95204021864 1.79860874018 absolute error = 0.0004667 relative error = 0.01758 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.248 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9724.0MB, alloc=52.3MB, time=122.18 x[1] = 2.6537 2.429 h = 0.003 0.006 y[1] (numeric) = 1.9516442167 1.80138372283 y[1] (closed_form) = 1.95125191855 1.80163766764 absolute error = 0.0004673 relative error = 0.0176 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.249 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 x[1] = 2.6567 2.435 h = 0.0001 0.005 y[1] (numeric) = 1.95260355982 1.80654302031 y[1] (closed_form) = 1.9522103199 1.80679865519 absolute error = 0.000469 relative error = 0.01763 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.255 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6568 2.44 h = 0.0001 0.003 y[1] (numeric) = 1.95159619299 1.81032561034 y[1] (closed_form) = 1.9512018943 1.81058143274 absolute error = 0.00047 relative error = 0.01766 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.257 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=9769.8MB, alloc=52.3MB, time=122.74 x[1] = 2.6569 2.443 h = 0.001 0.001 y[1] (numeric) = 1.95102059283 1.81260406717 y[1] (closed_form) = 1.95062591477 1.81285996723 absolute error = 0.0004704 relative error = 0.01766 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.259 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6579 2.444 h = 0.0001 0.004 y[1] (numeric) = 1.9515556942 1.8135735609 y[1] (closed_form) = 1.95116102774 1.8138295461 absolute error = 0.0004704 relative error = 0.01766 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.26 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] = 2.658 2.448 h = 0.003 0.006 y[1] (numeric) = 1.95076185477 1.81660486508 y[1] (closed_form) = 1.95036651228 1.81686097725 absolute error = 0.0004711 relative error = 0.01767 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.262 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=9815.6MB, alloc=52.3MB, time=123.30 x[1] = 2.661 2.454 h = 0.0001 0.005 y[1] (numeric) = 1.95171354827 1.82177238825 y[1] (closed_form) = 1.95131726593 1.82203018944 absolute error = 0.0004728 relative error = 0.01771 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.268 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 x[1] = 2.6611 2.459 h = 0.0001 0.003 y[1] (numeric) = 1.95069840173 1.82555806885 y[1] (closed_form) = 1.95030106175 1.82581605801 absolute error = 0.0004737 relative error = 0.01773 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.27 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6612 2.462 h = 0.001 0.001 y[1] (numeric) = 1.95011815858 1.82783844325 y[1] (closed_form) = 1.94972043964 1.82809651022 absolute error = 0.0004741 relative error = 0.01774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.271 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9861.4MB, alloc=52.3MB, time=123.86 x[1] = 2.6622 2.463 h = 0.001 0.003 y[1] (numeric) = 1.95065228005 1.828810091 y[1] (closed_form) = 1.95025457275 1.82906824303 absolute error = 0.0004741 relative error = 0.01773 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.273 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6632 2.466 h = 0.0001 0.004 y[1] (numeric) = 1.95074875173 1.83128787148 y[1] (closed_form) = 1.95035073921 1.8315463253 absolute error = 0.0004746 relative error = 0.01774 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.275 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6633 2.47 h = 0.003 0.006 y[1] (numeric) = 1.94994774181 1.83432218485 y[1] (closed_form) = 1.94954905405 1.83458076593 absolute error = 0.0004752 relative error = 0.01775 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.277 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 memory used=9907.2MB, alloc=52.3MB, time=124.42 x[1] = 2.6663 2.476 h = 0.0001 0.005 y[1] (numeric) = 1.95089069756 1.83949938091 y[1] (closed_form) = 1.95049107215 1.83975964974 absolute error = 0.0004769 relative error = 0.01779 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.283 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] = 2.6664 2.481 h = 0.0001 0.003 y[1] (numeric) = 1.94986657604 1.84328877819 y[1] (closed_form) = 1.94946589431 1.84354923549 absolute error = 0.0004779 relative error = 0.01781 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.285 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 x[1] = 2.6665 2.484 h = 0.001 0.001 y[1] (numeric) = 1.94928097778 1.84557145555 y[1] (closed_form) = 1.94887991757 1.84583199083 absolute error = 0.0004783 relative error = 0.01782 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.286 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=9952.9MB, alloc=52.3MB, time=124.98 x[1] = 2.6675 2.485 h = 0.001 0.003 y[1] (numeric) = 1.94981399844 1.84654561909 y[1] (closed_form) = 1.94941294992 1.84680623932 absolute error = 0.0004783 relative error = 0.01781 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.288 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 x[1] = 2.6685 2.488 h = 0.0001 0.004 y[1] (numeric) = 1.94990575309 1.84902733001 y[1] (closed_form) = 1.94950439988 1.84928825189 absolute error = 0.0004787 relative error = 0.01782 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.29 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6686 2.492 h = 0.003 0.006 y[1] (numeric) = 1.94909758272 1.85206465398 y[1] (closed_form) = 1.94869555513 1.85232570342 absolute error = 0.0004793 relative error = 0.01783 % Correct digits = 4 memory used=9998.7MB, alloc=52.3MB, time=125.54 Radius of convergence (given) for eq 1 = 5.292 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6716 2.498 h = 0.0001 0.005 y[1] (numeric) = 1.95003181705 1.85725151788 y[1] (closed_form) = 1.94962885399 1.85751425381 absolute error = 0.0004811 relative error = 0.01786 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.298 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 x[1] = 2.6717 2.503 h = 0.0001 0.003 y[1] (numeric) = 1.94899873315 1.86104463368 y[1] (closed_form) = 1.94859471508 1.86130755856 absolute error = 0.000482 relative error = 0.01789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.3 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10044.4MB, alloc=52.3MB, time=126.10 x[1] = 2.6718 2.506 h = 0.001 0.001 y[1] (numeric) = 1.94840778735 1.86332961497 y[1] (closed_form) = 1.94800339127 1.863592618 absolute error = 0.0004824 relative error = 0.01789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.301 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6728 2.507 h = 0.001 0.003 y[1] (numeric) = 1.94893971011 1.86430629219 y[1] (closed_form) = 1.94853532576 1.86456938007 absolute error = 0.0004824 relative error = 0.01789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.303 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6738 2.51 h = 0.0001 0.004 y[1] (numeric) = 1.94902675566 1.86679193226 y[1] (closed_form) = 1.94862206717 1.86705532165 absolute error = 0.0004829 relative error = 0.01789 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.305 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10090.1MB, alloc=52.3MB, time=126.66 x[1] = 2.6739 2.514 h = 0.003 0.006 y[1] (numeric) = 1.9482114349 1.86983226819 y[1] (closed_form) = 1.94780607288 1.87009578544 absolute error = 0.0004835 relative error = 0.01791 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.307 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6769 2.52 h = 0.0001 0.005 y[1] (numeric) = 1.94913696404 1.87502879483 y[1] (closed_form) = 1.94873066871 1.87529399728 absolute error = 0.0004852 relative error = 0.01794 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.313 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] = 2.677 2.525 h = 0.0001 0.003 y[1] (numeric) = 1.9480949303 1.87882563086 y[1] (closed_form) = 1.94768758127 1.87909102275 absolute error = 0.0004862 relative error = 0.01796 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.315 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10135.8MB, alloc=52.3MB, time=127.22 x[1] = 2.6771 2.528 h = 0.001 0.001 y[1] (numeric) = 1.9474986445 1.88111291701 y[1] (closed_form) = 1.94709091795 1.8813783872 absolute error = 0.0004865 relative error = 0.01797 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.317 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 x[1] = 2.6781 2.529 h = 0.001 0.003 y[1] (numeric) = 1.94802947225 1.8820921058 y[1] (closed_form) = 1.94762175747 1.88235766074 absolute error = 0.0004866 relative error = 0.01796 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.318 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6791 2.532 h = 0.0001 0.004 y[1] (numeric) = 1.94811181658 1.88458167367 y[1] (closed_form) = 1.94770379819 1.88484752998 absolute error = 0.000487 relative error = 0.01797 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.32 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10181.6MB, alloc=52.3MB, time=127.79 x[1] = 2.6792 2.536 h = 0.003 0.006 y[1] (numeric) = 1.94728935547 1.88762502286 y[1] (closed_form) = 1.94688066439 1.88789100733 absolute error = 0.0004876 relative error = 0.01798 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.322 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6822 2.542 h = 0.0001 0.005 y[1] (numeric) = 1.94820619555 1.89283120704 y[1] (closed_form) = 1.9477965733 1.8930988754 absolute error = 0.0004893 relative error = 0.01801 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.328 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 x[1] = 2.6823 2.547 h = 0.0001 0.003 y[1] (numeric) = 1.94715522448 1.89663176493 y[1] (closed_form) = 1.94674454985 1.89689962321 absolute error = 0.0004903 relative error = 0.01804 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.33 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10227.4MB, alloc=52.3MB, time=128.36 x[1] = 2.6824 2.55 h = 0.001 0.001 y[1] (numeric) = 1.9465536062 1.8989213568 y[1] (closed_form) = 1.94614255452 1.89918929354 absolute error = 0.0004907 relative error = 0.01804 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.332 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6834 2.551 h = 0.0001 0.004 y[1] (numeric) = 1.9470833418 1.89990305505 y[1] (closed_form) = 1.94667230193 1.90017107643 absolute error = 0.0004907 relative error = 0.01804 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.333 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6835 2.555 h = 0.003 0.006 y[1] (numeric) = 1.94625470657 1.902948914 y[1] (closed_form) = 1.94584299476 1.90321706382 absolute error = 0.0004913 relative error = 0.01805 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.335 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10273.0MB, alloc=52.3MB, time=128.92 x[1] = 2.6865 2.561 h = 0.0001 0.005 y[1] (numeric) = 1.94716396528 1.90816330359 y[1] (closed_form) = 1.94675132416 1.90843313621 absolute error = 0.000493 relative error = 0.01809 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.341 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] = 2.6866 2.566 h = 0.0001 0.003 y[1] (numeric) = 1.94610526688 1.91196696013 y[1] (closed_form) = 1.94569157449 1.91223698307 absolute error = 0.000494 relative error = 0.01811 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.343 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6867 2.569 h = 0.001 0.001 y[1] (numeric) = 1.94549903708 1.91425847395 y[1] (closed_form) = 1.94508496806 1.91452857549 absolute error = 0.0004944 relative error = 0.01811 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.345 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=10318.7MB, alloc=52.3MB, time=129.48 x[1] = 2.6877 2.57 h = 0.001 0.003 y[1] (numeric) = 1.94602780502 1.91524231758 y[1] (closed_form) = 1.94561374784 1.91551250367 absolute error = 0.0004944 relative error = 0.01811 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.346 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] = 2.6887 2.573 h = 0.0001 0.004 y[1] (numeric) = 1.94610137558 1.91773913469 y[1] (closed_form) = 1.9456870158 1.91800962189 absolute error = 0.0004948 relative error = 0.01811 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.348 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] = 2.6888 2.577 h = 0.003 0.006 y[1] (numeric) = 1.9452656186 1.92078800925 y[1] (closed_form) = 1.94485058768 1.92105862515 absolute error = 0.0004955 relative error = 0.01812 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.35 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10364.4MB, alloc=52.3MB, time=130.04 x[1] = 2.6918 2.583 h = 0.0001 0.005 y[1] (numeric) = 1.94616621805 1.92601204666 y[1] (closed_form) = 1.94575025994 1.92628434405 absolute error = 0.0004972 relative error = 0.01816 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.356 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6919 2.588 h = 0.0001 0.003 y[1] (numeric) = 1.94509860547 1.92981942802 y[1] (closed_form) = 1.94468159739 1.93009191618 absolute error = 0.0004981 relative error = 0.01818 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.358 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 x[1] = 2.692 2.591 h = 0.001 0.001 y[1] (numeric) = 1.94448705711 1.93211324914 y[1] (closed_form) = 1.94406967286 1.93238581604 absolute error = 0.0004985 relative error = 0.01819 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.36 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10410.2MB, alloc=52.3MB, time=130.60 x[1] = 2.693 2.592 h = 0.001 0.003 y[1] (numeric) = 1.94501473818 1.93309959827 y[1] (closed_form) = 1.94459736582 1.93337224962 absolute error = 0.0004985 relative error = 0.01818 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.361 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.694 2.595 h = 0.0001 0.004 y[1] (numeric) = 1.94508362986 1.93560033921 y[1] (closed_form) = 1.94466595544 1.93587329151 absolute error = 0.000499 relative error = 0.01818 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.364 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6941 2.599 h = 0.003 0.006 y[1] (numeric) = 1.94424076103 1.93865223044 y[1] (closed_form) = 1.9438224163 1.93892531172 absolute error = 0.0004996 relative error = 0.0182 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.366 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 memory used=10455.9MB, alloc=52.3MB, time=131.16 x[1] = 2.6971 2.605 h = 0.0001 0.005 y[1] (numeric) = 1.94513271708 1.94388591023 y[1] (closed_form) = 1.94471344724 1.94416067168 absolute error = 0.0005013 relative error = 0.01823 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.371 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6972 2.61 h = 0.0001 0.003 y[1] (numeric) = 1.9440562027 1.9476970178 y[1] (closed_form) = 1.94363588421 1.94797197046 absolute error = 0.0005023 relative error = 0.01825 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.374 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6973 2.613 h = 0.001 0.001 y[1] (numeric) = 1.94343934321 1.94999314692 y[1] (closed_form) = 1.94301864903 1.95026817847 absolute error = 0.0005026 relative error = 0.01826 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.375 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10501.7MB, alloc=52.3MB, time=131.72 x[1] = 2.6983 2.614 h = 0.001 0.003 y[1] (numeric) = 1.94396594021 1.95098199942 y[1] (closed_form) = 1.94354525795 1.95125711532 absolute error = 0.0005027 relative error = 0.01825 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.377 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.6993 2.617 h = 0.0001 0.004 y[1] (numeric) = 1.94403016075 1.95348666266 y[1] (closed_form) = 1.94360917695 1.95376207936 absolute error = 0.0005031 relative error = 0.01825 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.379 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] = 2.6994 2.621 h = 0.003 0.006 y[1] (numeric) = 1.94318018996 1.95654157159 y[1] (closed_form) = 1.9427585367 1.95681711753 absolute error = 0.0005037 relative error = 0.01827 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.381 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=10547.4MB, alloc=52.3MB, time=132.28 x[1] = 2.7024 2.627 h = 0.0001 0.005 y[1] (numeric) = 1.94406351834 1.96178488824 y[1] (closed_form) = 1.94364094205 1.96206211302 absolute error = 0.0005054 relative error = 0.0183 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.386 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 x[1] = 2.7025 2.632 h = 0.0001 0.003 y[1] (numeric) = 1.94297811452 1.96559972331 y[1] (closed_form) = 1.94255449088 1.96587713973 absolute error = 0.0005064 relative error = 0.01832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.389 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7026 2.635 h = 0.001 0.001 y[1] (numeric) = 1.94235595131 1.96789816111 y[1] (closed_form) = 1.94193195245 1.96817565657 absolute error = 0.0005067 relative error = 0.01833 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.391 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10593.1MB, alloc=52.3MB, time=132.84 x[1] = 2.7036 2.636 h = 0.001 0.003 y[1] (numeric) = 1.942881467 1.96888951481 y[1] (closed_form) = 1.9424574801 1.96916709451 absolute error = 0.0005068 relative error = 0.01832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.392 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7046 2.639 h = 0.0001 0.004 y[1] (numeric) = 1.94294102408 1.9713980988 y[1] (closed_form) = 1.94251673616 1.97167597915 absolute error = 0.0005072 relative error = 0.01832 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.394 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] = 2.7047 2.643 h = 0.003 0.006 y[1] (numeric) = 1.94208396122 1.97445602637 y[1] (closed_form) = 1.94165900467 1.97473403622 absolute error = 0.0005078 relative error = 0.01834 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.396 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=10638.9MB, alloc=52.3MB, time=133.40 x[1] = 2.7077 2.649 h = 0.0001 0.005 y[1] (numeric) = 1.94295867757 1.97970897428 y[1] (closed_form) = 1.94253280005 1.97998866164 absolute error = 0.0005095 relative error = 0.01837 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.402 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 x[1] = 2.7078 2.654 h = 0.0001 0.003 y[1] (numeric) = 1.94186439661 1.98352753807 y[1] (closed_form) = 1.94143747304 1.98380741749 absolute error = 0.0005105 relative error = 0.01839 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.404 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 x[1] = 2.7079 2.657 h = 0.001 0.001 y[1] (numeric) = 1.94123693708 1.98582828517 y[1] (closed_form) = 1.94080963876 1.98610824375 absolute error = 0.0005108 relative error = 0.0184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.406 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=10684.6MB, alloc=52.3MB, time=133.97 x[1] = 2.7089 2.658 h = 0.0001 0.004 y[1] (numeric) = 1.9417613742 1.98682213789 y[1] (closed_form) = 1.94133408788 1.98710218062 absolute error = 0.0005109 relative error = 0.01839 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.407 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] = 2.709 2.662 h = 0.003 0.006 y[1] (numeric) = 1.94089817856 1.98988258018 y[1] (closed_form) = 1.94047022438 1.99016275266 absolute error = 0.0005115 relative error = 0.0184 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.409 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.712 2.668 h = 0.0001 0.005 y[1] (numeric) = 1.94176537978 1.99514371147 y[1] (closed_form) = 1.94133650641 1.99542556034 absolute error = 0.0005132 relative error = 0.01843 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.415 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 memory used=10730.5MB, alloc=52.3MB, time=134.53 x[1] = 2.7121 2.673 h = 0.0001 0.003 y[1] (numeric) = 1.94066342306 1.99896538018 y[1] (closed_form) = 1.94023350474 1.99924742147 absolute error = 0.0005142 relative error = 0.01846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.417 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7122 2.676 h = 0.001 0.001 y[1] (numeric) = 1.94003138301 2.00126805253 y[1] (closed_form) = 1.93960109036 2.0015501731 absolute error = 0.0005145 relative error = 0.01846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.419 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7132 2.677 h = 0.001 0.003 y[1] (numeric) = 1.94055486418 2.00226404179 y[1] (closed_form) = 1.94012458355 2.00254624642 absolute error = 0.0005146 relative error = 0.01845 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.42 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=10776.3MB, alloc=52.3MB, time=135.09 x[1] = 2.7142 2.68 h = 0.0001 0.004 y[1] (numeric) = 1.9406057173 2.00477986177 y[1] (closed_form) = 1.94017513662 2.00506236675 absolute error = 0.000515 relative error = 0.01846 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.423 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] = 2.7143 2.684 h = 0.003 0.006 y[1] (numeric) = 1.93973544789 2.00784332442 y[1] (closed_form) = 1.93930420012 2.00812595939 absolute error = 0.0005156 relative error = 0.01847 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.425 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7173 2.69 h = 0.0001 0.005 y[1] (numeric) = 1.94059406598 2.01311407653 y[1] (closed_form) = 1.94016190106 2.01339838654 absolute error = 0.0005173 relative error = 0.0185 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.43 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=10822.0MB, alloc=52.3MB, time=135.65 x[1] = 2.7174 2.695 h = 0.0001 0.003 y[1] (numeric) = 1.93948325489 2.01693947614 y[1] (closed_form) = 1.93905004632 2.01722397896 absolute error = 0.0005183 relative error = 0.01852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.433 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] = 2.7175 2.698 h = 0.001 0.001 y[1] (numeric) = 1.93884593221 2.01924445889 y[1] (closed_form) = 1.93841234976 2.01952904113 absolute error = 0.0005186 relative error = 0.01853 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.435 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7185 2.699 h = 0.001 0.003 y[1] (numeric) = 1.93936833985 2.02024294315 y[1] (closed_form) = 1.93893476948 2.02052760935 absolute error = 0.0005187 relative error = 0.01852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.436 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=10867.8MB, alloc=52.3MB, time=136.21 x[1] = 2.7195 2.702 h = 0.0001 0.004 y[1] (numeric) = 1.93941455129 2.02276267929 y[1] (closed_form) = 1.93898068138 2.02304764567 absolute error = 0.0005191 relative error = 0.01852 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.438 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7196 2.706 h = 0.003 0.006 y[1] (numeric) = 1.93853721782 2.02582916305 y[1] (closed_form) = 1.93810268166 2.02611425967 absolute error = 0.0005197 relative error = 0.01854 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.44 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7226 2.712 h = 0.0001 0.005 y[1] (numeric) = 1.93938726815 2.03110953016 y[1] (closed_form) = 1.93895181684 2.03139630045 absolute error = 0.0005214 relative error = 0.01857 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.446 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 memory used=10913.5MB, alloc=52.3MB, time=136.77 x[1] = 2.7227 2.717 h = 0.0001 0.003 y[1] (numeric) = 1.93826761488 2.03493866164 y[1] (closed_form) = 1.93783112121 2.03522562513 absolute error = 0.0005224 relative error = 0.01859 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.448 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 x[1] = 2.7228 2.72 h = 0.001 0.001 y[1] (numeric) = 1.93762501686 2.03724595525 y[1] (closed_form) = 1.93718814979 2.0375329983 absolute error = 0.0005227 relative error = 0.01859 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.45 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7238 2.721 h = 0.001 0.003 y[1] (numeric) = 1.93814635366 2.03824693233 y[1] (closed_form) = 1.93770949869 2.03853405923 absolute error = 0.0005228 relative error = 0.01859 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.451 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=10959.3MB, alloc=52.3MB, time=137.33 x[1] = 2.7248 2.724 h = 0.0001 0.004 y[1] (numeric) = 1.93818793093 2.0407705829 y[1] (closed_form) = 1.93775077694 2.04105800983 absolute error = 0.0005232 relative error = 0.01859 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.454 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] = 2.7249 2.728 h = 0.003 0.006 y[1] (numeric) = 1.93730354315 2.04384008847 y[1] (closed_form) = 1.93686572373 2.04412764586 absolute error = 0.0005238 relative error = 0.0186 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.456 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7279 2.734 h = 0.0001 0.005 y[1] (numeric) = 1.93814504096 2.04913006468 y[1] (closed_form) = 1.93770630839 2.04941929438 absolute error = 0.0005255 relative error = 0.01863 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.461 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=11005.1MB, alloc=52.3MB, time=137.90 x[1] = 2.728 2.739 h = 0.0001 0.003 y[1] (numeric) = 1.93701655764 2.05296292892 y[1] (closed_form) = 1.936576784 2.05325235221 absolute error = 0.0005265 relative error = 0.01865 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.464 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7281 2.742 h = 0.001 0.001 y[1] (numeric) = 1.93636869159 2.05527253384 y[1] (closed_form) = 1.93592854501 2.0555620368 absolute error = 0.0005268 relative error = 0.01866 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.466 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] = 2.7291 2.743 h = 0.001 0.003 y[1] (numeric) = 1.93688896019 2.05627600152 y[1] (closed_form) = 1.93644882575 2.05656558823 absolute error = 0.0005269 relative error = 0.01865 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.467 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11050.9MB, alloc=52.3MB, time=138.46 x[1] = 2.7301 2.746 h = 0.0001 0.004 y[1] (numeric) = 1.93692591078 2.05880356477 y[1] (closed_form) = 1.93648547782 2.05909345134 absolute error = 0.0005273 relative error = 0.01865 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.469 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 x[1] = 2.7302 2.75 h = 0.003 0.006 y[1] (numeric) = 1.93603447837 2.06187609277 y[1] (closed_form) = 1.93559338081 2.06216611004 absolute error = 0.0005279 relative error = 0.01867 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.471 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 x[1] = 2.7332 2.756 h = 0.0001 0.005 y[1] (numeric) = 1.93686743883 2.06717567211 y[1] (closed_form) = 1.9364254301 2.06746736033 absolute error = 0.0005296 relative error = 0.0187 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.477 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11096.6MB, alloc=52.3MB, time=139.02 x[1] = 2.7333 2.761 h = 0.0001 0.003 y[1] (numeric) = 1.93573013756 2.07101226993 y[1] (closed_form) = 1.93528708904 2.0713041521 absolute error = 0.0005306 relative error = 0.01872 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.48 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7334 2.764 h = 0.001 0.001 y[1] (numeric) = 1.93507701073 2.07332418653 y[1] (closed_form) = 1.93463358975 2.07361614849 absolute error = 0.0005309 relative error = 0.01872 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.481 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7344 2.765 h = 0.0001 0.004 y[1] (numeric) = 1.93559621374 2.07433014261 y[1] (closed_form) = 1.93515280492 2.07462218822 absolute error = 0.0005309 relative error = 0.01871 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.483 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11142.3MB, alloc=52.3MB, time=139.58 x[1] = 2.7345 2.769 h = 0.003 0.006 y[1] (numeric) = 1.93469868924 2.0774051889 y[1] (closed_form) = 1.93425461658 2.07769736543 absolute error = 0.0005316 relative error = 0.01873 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.485 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] = 2.7375 2.775 h = 0.0001 0.005 y[1] (numeric) = 1.93552419879 2.08271292802 y[1] (closed_form) = 1.93507921666 2.08300677433 absolute error = 0.0005332 relative error = 0.01876 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.49 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] = 2.7376 2.78 h = 0.0001 0.003 y[1] (numeric) = 1.93437927248 2.08655263532 y[1] (closed_form) = 1.93393325167 2.08684667591 absolute error = 0.0005342 relative error = 0.01878 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.493 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=11188.1MB, alloc=52.3MB, time=140.14 x[1] = 2.7377 2.783 h = 0.001 0.001 y[1] (numeric) = 1.93372159561 2.08886647945 y[1] (closed_form) = 1.93327520273 2.08916059994 absolute error = 0.0005346 relative error = 0.01878 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.495 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7387 2.784 h = 0.001 0.003 y[1] (numeric) = 1.93423985386 2.08987456304 y[1] (closed_form) = 1.93379347318 2.0901687671 absolute error = 0.0005346 relative error = 0.01877 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.496 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7397 2.787 h = 0.0001 0.004 y[1] (numeric) = 1.93426816849 2.09240934714 y[1] (closed_form) = 1.93382149023 2.09270385074 absolute error = 0.000535 relative error = 0.01878 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.498 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11233.7MB, alloc=52.3MB, time=140.71 x[1] = 2.7398 2.791 h = 0.003 0.006 y[1] (numeric) = 1.93336361737 2.095487417 y[1] (closed_form) = 1.93291627604 2.09578205172 absolute error = 0.0005357 relative error = 0.01879 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.5 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] = 2.7428 2.797 h = 0.0001 0.005 y[1] (numeric) = 1.93418061756 2.10080474814 y[1] (closed_form) = 1.93373236872 2.10110105125 absolute error = 0.0005373 relative error = 0.01882 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.506 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 x[1] = 2.7429 2.802 h = 0.0001 0.003 y[1] (numeric) = 1.93302689568 2.10464819045 y[1] (closed_form) = 1.93257760944 2.1049446882 absolute error = 0.0005383 relative error = 0.01884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.509 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11279.6MB, alloc=52.3MB, time=141.27 x[1] = 2.743 2.805 h = 0.001 0.001 y[1] (numeric) = 1.93236397147 2.10696434693 y[1] (closed_form) = 1.93191431361 2.10726092469 absolute error = 0.0005387 relative error = 0.01884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.51 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.744 2.806 h = 0.001 0.003 y[1] (numeric) = 1.93288116897 2.10797491482 y[1] (closed_form) = 1.93243152334 2.10827157605 absolute error = 0.0005387 relative error = 0.01884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.512 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] = 2.745 2.809 h = 0.0001 0.004 y[1] (numeric) = 1.93290487811 2.11051360643 y[1] (closed_form) = 1.93245493541 2.11081056703 absolute error = 0.0005391 relative error = 0.01884 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.514 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11325.4MB, alloc=52.3MB, time=141.83 x[1] = 2.7451 2.813 h = 0.003 0.006 y[1] (numeric) = 1.93199330991 2.11359470029 y[1] (closed_form) = 1.93154270496 2.11389179222 absolute error = 0.0005397 relative error = 0.01885 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.516 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7481 2.819 h = 0.0001 0.005 y[1] (numeric) = 1.93280181562 2.11892161728 y[1] (closed_form) = 1.93235030508 2.11922037622 absolute error = 0.0005414 relative error = 0.01888 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.522 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 x[1] = 2.7482 2.824 h = 0.0001 0.003 y[1] (numeric) = 1.93163931014 2.1227687952 y[1] (closed_form) = 1.93118676348 2.12306774911 absolute error = 0.0005424 relative error = 0.0189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.525 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=11371.3MB, alloc=52.3MB, time=142.39 x[1] = 2.7483 2.827 h = 0.001 0.001 y[1] (numeric) = 1.93097114577 2.12508726427 y[1] (closed_form) = 1.93051822797 2.1253862983 absolute error = 0.0005427 relative error = 0.0189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.526 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 x[1] = 2.7493 2.828 h = 0.001 0.003 y[1] (numeric) = 1.93148728506 2.12610031423 y[1] (closed_form) = 1.93103437952 2.12639943163 absolute error = 0.0005428 relative error = 0.0189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.528 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7503 2.831 h = 0.0001 0.004 y[1] (numeric) = 1.93150639604 2.12864291144 y[1] (closed_form) = 1.93105319391 2.12894232802 absolute error = 0.0005432 relative error = 0.0189 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.53 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11417.0MB, alloc=52.3MB, time=142.95 x[1] = 2.7504 2.835 h = 0.003 0.006 y[1] (numeric) = 1.93058782032 2.13172702969 y[1] (closed_form) = 1.93013395676 2.13202657781 absolute error = 0.0005438 relative error = 0.01891 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.532 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7534 2.841 h = 0.0001 0.005 y[1] (numeric) = 1.93138784632 2.1370635263 y[1] (closed_form) = 1.93093307909 2.13736474003 absolute error = 0.0005455 relative error = 0.01894 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.538 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 x[1] = 2.7535 2.846 h = 0.0001 0.003 y[1] (numeric) = 1.93021656916 2.14091444033 y[1] (closed_form) = 1.92976076708 2.14121584937 absolute error = 0.0005464 relative error = 0.01896 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.54 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11462.7MB, alloc=52.3MB, time=143.51 x[1] = 2.7536 2.849 h = 0.001 0.001 y[1] (numeric) = 1.92954317179 2.14323522218 y[1] (closed_form) = 1.92908699903 2.14353671146 absolute error = 0.0005468 relative error = 0.01896 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.542 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 x[1] = 2.7546 2.85 h = 0.001 0.003 y[1] (numeric) = 1.93005825539 2.14425075198 y[1] (closed_form) = 1.92960209493 2.14455232452 absolute error = 0.0005468 relative error = 0.01896 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.543 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] = 2.7556 2.853 h = 0.0001 0.004 y[1] (numeric) = 1.93007277549 2.14679725284 y[1] (closed_form) = 1.92961631893 2.14709912438 absolute error = 0.0005472 relative error = 0.01896 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.546 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11508.5MB, alloc=52.3MB, time=144.08 x[1] = 2.7557 2.857 h = 0.003 0.006 y[1] (numeric) = 1.92914720177 2.14988439579 y[1] (closed_form) = 1.9286900846 2.15018639909 absolute error = 0.0005479 relative error = 0.01897 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.548 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] = 2.7587 2.863 h = 0.0001 0.005 y[1] (numeric) = 1.92993876273 2.15523046572 y[1] (closed_form) = 1.92948074379 2.15553413322 absolute error = 0.0005495 relative error = 0.019 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.554 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 x[1] = 2.7588 2.868 h = 0.0001 0.003 y[1] (numeric) = 1.92875872577 2.15908511629 y[1] (closed_form) = 1.92829967325 2.15938897943 absolute error = 0.0005505 relative error = 0.01902 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.556 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 memory used=11554.4MB, alloc=52.3MB, time=144.64 x[1] = 2.7589 2.871 h = 0.001 0.001 y[1] (numeric) = 1.92808010253 2.16140821109 y[1] (closed_form) = 1.92762067978 2.16171215456 absolute error = 0.0005509 relative error = 0.01902 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.558 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] = 2.7599 2.872 h = 0.001 0.003 y[1] (numeric) = 1.92859413294 2.16242621849 y[1] (closed_form) = 1.92813472252 2.16273024512 absolute error = 0.0005509 relative error = 0.01901 % Correct digits = 4 Radius of convergence (given) for eq 1 = 5.559 Order of pole (given) = 0.5 0 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 Finished! diff ( y , x , 1 ) = sinh ( sqrt ( 0.1 * x + 0.2 ) ) ; Iterations = 754 Total Elapsed Time = 2 Minutes 25 Seconds Expected Time Remaining = 0 Seconds Optimized Time Remaining = 0 Seconds Expected Total Time = 2 Minutes 25 Seconds > quit memory used=11596.5MB, alloc=52.3MB, time=145.13