(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 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, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 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, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_m1 array_const_2D0 , 1 1 1 array_tmp2 : array_x array_tmp1 , array_tmp3 : array_x array_x , 1 1 1 1 1 1 array_tmp2 1 array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 , 1 1 1 1 1 1 array_tmp5 1 array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 , 1 array_tmp7 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp9 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_m1 array_const_2D0 , 1 1 1 array_tmp2 : array_x array_tmp1 , array_tmp3 : array_x array_x , 1 1 1 1 1 1 array_tmp2 1 array_tmp4 : array_const_1D0 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_const_1D0 + array_tmp6 , 1 1 1 1 1 1 array_tmp5 1 array_tmp8 : -----------, array_tmp9 : array_tmp8 + array_const_0D0 , 1 array_tmp7 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_m1 array_const_2D0 , 2 2 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 2 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp4 : array_tmp3 , array_tmp5 : 2 2 2 array_tmp2 - ats(2, array_tmp4, array_tmp5, 2) 2 -----------------------------------------------, array_tmp4 1 array_tmp6 : array_x array_x + array_x array_x , 2 2 1 1 2 array_tmp7 : array_tmp6 , array_tmp8 : 2 2 2 array_tmp5 - ats(2, array_tmp7, array_tmp8, 2) 2 -----------------------------------------------, array_tmp9 : array_tmp8 , array_tmp7 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 array_tmp1 : array_m1 array_const_2D0 , 3 3 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 3 1 kkk 2 kkk - 1 array_tmp3 : array_x array_x , array_tmp4 : array_tmp3 , 3 2 2 3 3 array_tmp2 - ats(3, array_tmp4, array_tmp5, 2) 3 array_tmp5 : -----------------------------------------------, 3 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : array_tmp6 , 3 2 2 3 3 array_tmp5 - ats(3, array_tmp7, array_tmp8, 2) 3 array_tmp8 : -----------------------------------------------, 3 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp1 : array_m1 array_const_2D0 , 4 4 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 4 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 4 4 4 array_tmp2 - ats(4, array_tmp4, array_tmp5, 2) 4 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 4 4 1 array_tmp5 - ats(4, array_tmp7, array_tmp8, 2) 4 array_tmp8 : -----------------------------------------------, 4 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp1 : array_m1 array_const_2D0 , 5 5 1 array_tmp2 : array_x array_tmp1 + array_x array_tmp1 , 5 1 kkk 2 kkk - 1 array_tmp4 : array_tmp3 , array_tmp5 : 5 5 5 array_tmp2 - ats(5, array_tmp4, array_tmp5, 2) 5 -----------------------------------------------, array_tmp7 : array_tmp6 , array_tmp4 5 5 1 array_tmp5 - ats(5, array_tmp7, array_tmp8, 2) 5 array_tmp8 : -----------------------------------------------, 5 array_tmp7 1 array_tmp9 : array_tmp8 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp9 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_m1 array_const_2D0 , kkk kkk 1 array_tmp2 : array_tmp1 array_x + array_tmp1 array_x , kkk kkk 1 kkk - 1 2 array_tmp4 : array_tmp3 , array_tmp5 : kkk kkk kkk array_tmp2 - ats(kkk, array_tmp4, array_tmp5, 2) kkk ---------------------------------------------------, array_tmp4 1 array_tmp7 : array_tmp6 , array_tmp8 : kkk kkk kkk array_tmp5 - ats(kkk, array_tmp7, array_tmp8, 2) kkk ---------------------------------------------------, array_tmp7 1 array_tmp9 : array_tmp8 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp9 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole_debug(typ, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%o27) display_pole_debug(typ, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%i28) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o28) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i33) log_revs(file, revs) := printf(file, revs) (%o33) log_revs(file, revs) := printf(file, revs) (%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i36) logstart(file) := printf(file, "") (%o36) logstart(file) := printf(file, "") (%i37) logend(file) := printf(file, "~%") (%o37) logend(file) := printf(file, "~%") (%i38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i41) factorial_2(nnn) := nnn! (%o41) factorial_2(nnn) := nnn! (%i42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i44) convfp(mmm) := mmm (%o44) convfp(mmm) := mmm (%i45) convfloat(mmm) := mmm (%o45) convfloat(mmm) := mmm (%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i47) Si(x) := 0.0 (%o47) Si(x) := 0.0 (%i48) Ci(x) := 0.0 (%o48) Ci(x) := 0.0 (%i49) ln(x) := log(x) (%o49) ln(x) := log(x) (%i50) arcsin(x) := asin(x) (%o50) arcsin(x) := asin(x) (%i51) arccos(x) := acos(x) (%o51) arccos(x) := acos(x) (%i52) arctan(x) := atan(x) (%o52) arctan(x) := atan(x) (%i53) omniabs(x) := abs(x) (%o53) omniabs(x) := abs(x) (%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), 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, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) 1.0 (%i56) exact_soln_y(x) := block(---------) 1.0 + x x 1.0 (%o56) exact_soln_y(x) := block(---------) 1.0 + x x (%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, 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, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:50,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), 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 : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 50, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\ = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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, "2013-01-28T19:11:14-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 maxima results" ), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, 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, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sing4postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-2.0,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:50,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (1.0 / (x * x + 1.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), 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 : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 2.0, x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 50, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\ = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), 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, "2013-01-28T19:11:14-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing4"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "sing4 diffeq.max"), logitem_str(html_log_file, "sing4 maxima results" ), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) main() "##############ECHO OF PROBLEM#################" "##############temp/sing4postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:1.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:50," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (1.0 / (x * x + 1.0)) " "));" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 3. "" estimated_steps = 3000. "" step_error = 3.333333333333333700000000000000E-14 "" est_needed_step_err = 3.333333333333333700000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.75032816273783700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" max_value3 = 1.75032816273783700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" value3 = 1.75032816273783700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-89 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -2. " " y[1] (analytic) = 0.2 " " y[1] (numeric) = 0.2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.236067977499734 " " Order of pole = 0.999999999999325 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.999 " " y[1] (analytic) = 0.2001600880384131 " " y[1] (numeric) = 0.20016008803841315 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.773337670625154000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2351735950479843 " " Order of pole = 0.999999999999261 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9980000000000002 " " y[1] (analytic) = 0.20032035230740997 " " y[1] (numeric) = 0.20032035230741002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.771118889910440500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2342793021463225 " " Order of pole = 0.9999999999985238 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9970000000000003 " " y[1] (analytic) = 0.20048079303786334 " " y[1] (numeric) = 0.20048079303786343 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.153351829128128500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.233385098902368 " " Order of pole = 0.9999999999976481 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9960000000000004 " " y[1] (analytic) = 0.2006414104609615 " " y[1] (numeric) = 0.20064141046096162 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.533369318300176000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2324909854241373 " " Order of pole = 1.0000000000000924 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9950000000000006 " " y[1] (analytic) = 0.2008022048082087 " " y[1] (numeric) = 0.20080220480820882 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.52893841820889700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.231596961819242 " " Order of pole = 1.0000000000023572 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9940000000000007 " " y[1] (analytic) = 0.2009631763114253 " " y[1] (numeric) = 0.20096317631142543 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.90563717320458500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.230703028195323 " " Order of pole = 0.9999999999994067 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9930000000000008 " " y[1] (analytic) = 0.20112432520274826 " " y[1] (numeric) = 0.20112432520274845 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.66014573888785600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.229809184661336 " " Order of pole = 1.0000000000001243 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9920000000000009 " " y[1] (analytic) = 0.20128565171463156 " " y[1] (numeric) = 0.20128565171463175 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.65240332106987600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.22891543132533 " " Order of pole = 1.0000000000004796 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.991000000000001 " " y[1] (analytic) = 0.20144715607984626 " " y[1] (numeric) = 0.20144715607984645 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 9.64466478903248200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2280217682958945 " " Order of pole = 1.0000000000009859 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.990000000000001 " " y[1] (analytic) = 0.20160883853148104 " " y[1] (numeric) = 0.20160883853148126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.10136344488864880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2271281956815128 " " Order of pole = 0.9999999999988756 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9890000000000012 " " y[1] (analytic) = 0.20177069930294256 " " y[1] (numeric) = 0.2017706993029428 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.23803992058135870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2262347135915888 " " Order of pole = 1.0000000000005986 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9880000000000013 " " y[1] (analytic) = 0.20193273862795566 " " y[1] (numeric) = 0.20193273862795594 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.3744960725148320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2253413221343967 " " Order of pole = 0.9999999999968914 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9870000000000014 " " y[1] (analytic) = 0.20209495674056382 " " y[1] (numeric) = 0.20209495674056407 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.23605350954569940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.224448021420276 " " Order of pole = 1.0000000000015632 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9860000000000015 " " y[1] (analytic) = 0.2022573538751293 " " y[1] (numeric) = 0.20225735387512958 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.37229005936490180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2235548115572787 " " Order of pole = 0.9999999999986926 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9850000000000017 " " y[1] (analytic) = 0.20241993026633373 " " y[1] (numeric) = 0.20241993026633406 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.64542546254864670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2226616926558314 " " Order of pole = 0.9999999999991189 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9840000000000018 " " y[1] (analytic) = 0.20258268614917835 " " y[1] (numeric) = 0.20258268614917868 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.64410351999322550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.221768664825431 " " Order of pole = 1.000000000000469 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9830000000000019 " " y[1] (analytic) = 0.2027456217589842 " " y[1] (numeric) = 0.20274562175898456 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.7796807638692540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2208757281755975 " " Order of pole = 0.9999999999985896 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.982000000000002 " " y[1] (analytic) = 0.20290873733139267 " " y[1] (numeric) = 0.20290873733139303 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.77825010272414650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.219982882816849 " " Order of pole = 0.9999999999994476 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.981000000000002 " " y[1] (analytic) = 0.20307203310236563 " " y[1] (numeric) = 0.20307203310236602 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.91349863731815920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2190901288589755 " " Order of pole = 0.9999999999981881 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9800000000000022 " " y[1] (analytic) = 0.20323550930818596 " " y[1] (numeric) = 0.20323550930818637 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.04852801388711120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.21819746641266 " " Order of pole = 0.9999999999987317 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9790000000000023 " " y[1] (analytic) = 0.20339916618545775 " " y[1] (numeric) = 0.2033991661854582 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.1833383989644560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2173048955884176 " " Order of pole = 1.0000000000009628 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9780000000000024 " " y[1] (analytic) = 0.2035630039711067 " " y[1] (numeric) = 0.20356300397110713 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.18158113796107940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.216412416496557 " " Order of pole = 1.000000000000263 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9770000000000025 " " y[1] (analytic) = 0.20372702290238032 " " y[1] (numeric) = 0.2037270229023808 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.31606381295713040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2155200292481805 " " Order of pole = 0.9999999999995843 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9760000000000026 " " y[1] (analytic) = 0.2038912232168485 " " y[1] (numeric) = 0.20389122321684897 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.31419861052018420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2146277339544853 " " Order of pole = 1.0000000000010036 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9750000000000028 " " y[1] (analytic) = 0.2040556051524036 " " y[1] (numeric) = 0.2040556051524041 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.4483540195241510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2137355307262157 " " Order of pole = 0.9999999999990958 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9740000000000029 " " y[1] (analytic) = 0.2042201689472609 " " y[1] (numeric) = 0.20422016894726142 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.58229115868147730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2128434196750826 " " Order of pole = 0.9999999999980975 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.973000000000003 " " y[1] (analytic) = 0.20438491483995896 " " y[1] (numeric) = 0.20438491483995952 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.71601019452561540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2119514009128576 " " Order of pole = 1.0000000000009273 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.972000000000003 " " y[1] (analytic) = 0.20454984306935992 " " y[1] (numeric) = 0.20454984306936047 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.7138202796095420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2110594745505936 " " Order of pole = 0.9999999999998241 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9710000000000032 " " y[1] (analytic) = 0.20471495387464966 " " y[1] (numeric) = 0.20471495387465025 " " absolute error = 5.8286708792820720000000000000000E-16 " " relative error = 2.84721304866231900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.21016764070056 " " Order of pole = 0.9999999999996323 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9700000000000033 " " y[1] (analytic) = 0.20488024749533842 " " y[1] (numeric) = 0.20488024749533906 " " absolute error = 6.383782391594650000000000000000E-16 " " relative error = 3.11586034751344100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2092758994748523 " " Order of pole = 1.0000000000011084 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9690000000000034 " " y[1] (analytic) = 0.205045724171261 " " y[1] (numeric) = 0.20504572417126166 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.2487086354393660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.208384250985285 " " Order of pole = 0.9999999999995239 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9680000000000035 " " y[1] (analytic) = 0.20521138414257703 " " y[1] (numeric) = 0.20521138414257767 " " absolute error = 6.383782391594650000000000000000E-16 " " relative error = 3.11083248050182170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2074926953447407 " " Order of pole = 1.0000000000010196 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9670000000000036 " " y[1] (analytic) = 0.20537722764977123 " " y[1] (numeric) = 0.20537722764977193 " " absolute error = 6.9388939039072280000000000000000E-16 " " relative error = 3.37860919796818400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.206601232665433 " " Order of pole = 1.000000000001629 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9660000000000037 " " y[1] (analytic) = 0.2055432549336541 " " y[1] (numeric) = 0.20554325493365483 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 3.51091533623560940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2057098630599987 " " Order of pole = 1.0000000000003872 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9650000000000039 " " y[1] (analytic) = 0.20570946623536185 " " y[1] (numeric) = 0.20570946623536257 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 3.50807854987423840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.204818586641501 " " Order of pole = 0.9999999999994831 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.964000000000004 " " y[1] (analytic) = 0.2058758617963568 " " y[1] (numeric) = 0.20587586179635756 " " absolute error = 7.4940054162198070000000000000000E-16 " " relative error = 3.6400602532182920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.203927403523092 " " Order of pole = 1.0000000000000586 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.963000000000004 " " y[1] (analytic) = 0.206042441858428 " " y[1] (numeric) = 0.20604244185842874 " " absolute error = 7.4940054162198070000000000000000E-16 " " relative error = 3.63711735729134230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2030363138178304 " " Order of pole = 1.000000000000103 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9620000000000042 " " y[1] (analytic) = 0.20620920666369108 " " y[1] (numeric) = 0.20620920666369183 " " absolute error = 7.4940054162198070000000000000000E-16 " " relative error = 3.63417596016547660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2021453176390047 " " Order of pole = 0.9999999999982858 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9610000000000043 " " y[1] (analytic) = 0.20637615645458895 " " y[1] (numeric) = 0.2063761564545898 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 4.03470673537854930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.201254415100731 " " Order of pole = 1.0000000000012186 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9600000000000044 " " y[1] (analytic) = 0.2065432914738922 " " y[1] (numeric) = 0.206543291473893 " " absolute error = 8.0491169285323850000000000000000E-16 " " relative error = 3.89706045211825340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2003636063160315 " " Order of pole = 1.0000000000002007 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9590000000000045 " " y[1] (analytic) = 0.20671061196469886 " " y[1] (numeric) = 0.2067106119646997 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 4.02817862399375340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.199472891399089 " " Order of pole = 0.9999999999984954 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9580000000000046 " " y[1] (analytic) = 0.20687811817043536 " " y[1] (numeric) = 0.2068781181704362 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 4.02491706630316140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.198582270464333 " " Order of pole = 1.0000000000002345 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9570000000000047 " " y[1] (analytic) = 0.20704581033485644 " " y[1] (numeric) = 0.20704581033485733 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.2897676522102474000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1976917436255814 " " Order of pole = 1.0000000000000764 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9560000000000048 " " y[1] (analytic) = 0.2072136887020458 " " y[1] (numeric) = 0.20721368870204668 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.28629221005396100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1968013109972704 " " Order of pole = 0.9999999999980922 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.955000000000005 " " y[1] (analytic) = 0.20738175351641602 " " y[1] (numeric) = 0.20738175351641694 " " absolute error = 9.1593399531575410000000000000000E-16 " " relative error = 4.41665662376246700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1959109726944366 " " Order of pole = 0.9999999999994689 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.954000000000005 " " y[1] (analytic) = 0.2075500050227093 " " y[1] (numeric) = 0.2075500050227102 " " absolute error = 9.1593399531575410000000000000000E-16 " " relative error = 4.4130762377747780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.195020728831477 " " Order of pole = 0.9999999999995808 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9530000000000052 " " y[1] (analytic) = 0.20771844346599738 " " y[1] (numeric) = 0.20771844346599833 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 4.54311882558402160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.194130579523395 " " Order of pole = 0.9999999999990354 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9520000000000053 " " y[1] (analytic) = 0.20788706909168228 " " y[1] (numeric) = 0.20788706909168325 " " absolute error = 9.714451465470120000000000000000E-16 " " relative error = 4.6729464742156984000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.193240524885416 " " Order of pole = 0.9999999999989928 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9510000000000054 " " y[1] (analytic) = 0.20805588214549633 " " y[1] (numeric) = 0.20805588214549728 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 4.53575049741418930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1923505650328723 " " Order of pole = 0.9999999999998135 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9500000000000055 " " y[1] (analytic) = 0.20822488287350244 " " y[1] (numeric) = 0.20822488287350344 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 4.7986614681861050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.191460700081159 " " Order of pole = 1.0000000000004992 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9490000000000056 " " y[1] (analytic) = 0.20839407152209477 " " y[1] (numeric) = 0.20839407152209577 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 4.7947655845703930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1905709301458933 " " Order of pole = 1.000000000000611 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9480000000000057 " " y[1] (analytic) = 0.2085634483379986 " " y[1] (numeric) = 0.20856344833799964 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.9239514687826846000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1896812553428893 " " Order of pole = 0.9999999999999627 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9470000000000058 " " y[1] (analytic) = 0.2087330135682711 " " y[1] (numeric) = 0.20873301356827212 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.9199514740028390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1887916757882633 " " Order of pole = 0.9999999999999165 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.946000000000006 " " y[1] (analytic) = 0.2089027674603012 " " y[1] (numeric) = 0.20890276746030226 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 5.0488171421392520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1879021915982557 " " Order of pole = 1.0000000000011795 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.945000000000006 " " y[1] (analytic) = 0.2090727102618103 " " y[1] (numeric) = 0.20907271026181135 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 5.0447132582398770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1870128028889098 " " Order of pole = 0.9999999999999485 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9440000000000062 " " y[1] (analytic) = 0.20924284222085224 " " y[1] (numeric) = 0.20924284222085335 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.3059068250149990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.186123509776985 " " Order of pole = 0.9999999999989502 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9430000000000063 " " y[1] (analytic) = 0.20941316358581402 " " y[1] (numeric) = 0.20941316358581513 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.3015913881182810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1852343123792597 " " Order of pole = 0.9999999999989804 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9420000000000064 " " y[1] (analytic) = 0.20958367460541572 " " y[1] (numeric) = 0.20958367460541685 " " absolute error = 1.1379786002407855000000000000000E-15 " " relative error = 5.4297101259593040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1843452108125323 " " Order of pole = 0.999999999998952 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9410000000000065 " " y[1] (analytic) = 0.209754375528711 " " y[1] (numeric) = 0.20975437552871215 " " absolute error = 1.1379786002407855000000000000000E-15 " " relative error = 5.4252913550545690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1834562051941417 " " Order of pole = 1.0000000000021476 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9400000000000066 " " y[1] (analytic) = 0.20992526660508748 " " y[1] (numeric) = 0.20992526660508862 " " absolute error = 1.1379786002407855000000000000000E-15 " " relative error = 5.4208748601070340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1825672956405198 " " Order of pole = 0.9999999999987494 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9390000000000067 " " y[1] (analytic) = 0.21009634808426683 " " y[1] (numeric) = 0.210096348084268 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 5.5485694372414980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1816784822700215 " " Order of pole = 0.9999999999999982 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9380000000000068 " " y[1] (analytic) = 0.21026762021630535 " " y[1] (numeric) = 0.21026762021630654 " " absolute error = 1.1934897514720433000000000000000E-15 " " relative error = 5.6760510735998390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1807897651997195 " " Order of pole = 0.999999999999508 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.937000000000007 " " y[1] (analytic) = 0.21043908325159408 " " y[1] (numeric) = 0.21043908325159533 " " absolute error = 1.2490009027033011000000000000000E-15 " " relative error = 5.9352135706181370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.179901144547592 " " Order of pole = 0.9999999999996589 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.936000000000007 " " y[1] (analytic) = 0.2106107374408593 " " y[1] (numeric) = 0.21061073744086053 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 5.79859005256370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.179012620431611 " " Order of pole = 1.0000000000005826 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9350000000000072 " " y[1] (analytic) = 0.21078258303516256 " " y[1] (numeric) = 0.21078258303516384 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 6.0572200033526610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1781241929696016 " " Order of pole = 0.9999999999984741 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9340000000000073 " " y[1] (analytic) = 0.2109546202859013 " " y[1] (numeric) = 0.21095462028590262 " " absolute error = 1.304512053934559000000000000000E-15 " " relative error = 6.1838515419410470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1772358622804875 " " Order of pole = 1.0000000000006288 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9330000000000074 " " y[1] (analytic) = 0.21112684944480897 " " y[1] (numeric) = 0.2111268494448103 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.3102709724205790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1763476284821017 " " Order of pole = 0.9999999999990017 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9320000000000075 " " y[1] (analytic) = 0.21129927076395547 " " y[1] (numeric) = 0.21129927076395677 " " absolute error = 1.304512053934559000000000000000E-15 " " relative error = 6.1737650547400260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1754594916935903 " " Order of pole = 0.9999999999991811 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9310000000000076 " " y[1] (analytic) = 0.21147188449574716 " " y[1] (numeric) = 0.2114718844957485 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.2999752081794150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1745714520337995 " " Order of pole = 1.0000000000009965 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9300000000000077 " " y[1] (analytic) = 0.21164469089292762 " " y[1] (numeric) = 0.21164469089292898 " " absolute error = 1.3600232051658168000000000000000E-15 " " relative error = 6.4259736420880090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.173683509621239 " " Order of pole = 0.9999999999979945 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9290000000000078 " " y[1] (analytic) = 0.21181769020857766 " " y[1] (numeric) = 0.21181769020857902 " " absolute error = 1.3600232051658168000000000000000E-15 " " relative error = 6.4207253125392740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.172795664575907 " " Order of pole = 0.9999999999995239 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.928000000000008 " " y[1] (analytic) = 0.21199088269611563 " " y[1] (numeric) = 0.21199088269611702 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 6.5464078602417860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1719079170164504 " " Order of pole = 0.9999999999964011 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.927000000000008 " " y[1] (analytic) = 0.2121642686092979 " " y[1] (numeric) = 0.2121642686092993 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 6.5410579730418730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1710202670633048 " " Order of pole = 0.9999999999988631 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9260000000000081 " " y[1] (analytic) = 0.21233784820221896 " " y[1] (numeric) = 0.21233784820222038 " " absolute error = 1.4155343563970746000000000000000E-15 " " relative error = 6.6664250786275140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1701327148355407 " " Order of pole = 0.9999999999984563 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9250000000000083 " " y[1] (analytic) = 0.2125116217293119 " " y[1] (numeric) = 0.21251162172931332 " " absolute error = 1.4155343563970746000000000000000E-15 " " relative error = 6.6609738558210290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.169245260453471 " " Order of pole = 0.9999999999994849 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9240000000000084 " " y[1] (analytic) = 0.21268558944534854 " " y[1] (numeric) = 0.21268558944535002 " " absolute error = 1.4710455076283324000000000000000E-15 " " relative error = 6.9165264626747580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1683579040371264 " " Order of pole = 1.000000000000691 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9230000000000085 " " y[1] (analytic) = 0.21285975160544 " " y[1] (numeric) = 0.21285975160544146 " " absolute error = 1.4710455076283324000000000000000E-15 " " relative error = 6.9108673506069120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1674706457066355 " " Order of pole = 0.9999999999997318 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9220000000000086 " " y[1] (analytic) = 0.21303410846503662 " " y[1] (numeric) = 0.21303410846503812 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 7.0354981840381960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.166583485582865 " " Order of pole = 1.0000000000010179 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9210000000000087 " " y[1] (analytic) = 0.21320866027992863 " " y[1] (numeric) = 0.21320866027993018 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.2900989689373400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1656964237861334 " " Order of pole = 1.0000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9200000000000088 " " y[1] (analytic) = 0.21338340730624633 " " y[1] (numeric) = 0.21338340730624786 " " absolute error = 1.5265566588595902000000000000000E-15 " " relative error = 7.1540551260796360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1648094604376187 " " Order of pole = 1.0000000000004992 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.919000000000009 " " y[1] (analytic) = 0.21355834980046018 " " y[1] (numeric) = 0.21355834980046173 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.278161850976570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.163922595658038 " " Order of pole = 0.9999999999982894 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.918000000000009 " " y[1] (analytic) = 0.2137334880193815 " " y[1] (numeric) = 0.21373348801938305 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.2721979549328890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1630358295691208 " " Order of pole = 0.9999999999992681 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9170000000000091 " " y[1] (analytic) = 0.21390882222016236 " " y[1] (numeric) = 0.21390882222016394 " " absolute error = 1.582067810090848000000000000000E-15 " " relative error = 7.395991402647850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1621491622919704 " " Order of pole = 0.9999999999995364 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9160000000000093 " " y[1] (analytic) = 0.21408435266029616 " " y[1] (numeric) = 0.2140843526602978 " " absolute error = 1.6375789613221060000000000000000E-15 " " relative error = 7.6492230327574500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1612625939483068 " " Order of pole = 1.0000000000003588 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9150000000000094 " " y[1] (analytic) = 0.21426007959761792 " " y[1] (numeric) = 0.21426007959761956 " " absolute error = 1.6375789613221060000000000000000E-15 " " relative error = 7.6429494677566250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.160376124659621 " " Order of pole = 0.9999999999980034 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9140000000000095 " " y[1] (analytic) = 0.21443600329030438 " " y[1] (numeric) = 0.21443600329030602 " " absolute error = 1.6375789613221060000000000000000E-15 " " relative error = 7.6366791779137220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.159489754548717 " " Order of pole = 1.0000000000023608 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9130000000000096 " " y[1] (analytic) = 0.2146121239968744 " " y[1] (numeric) = 0.2146121239968761 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.8890702026602270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.158603483736961 " " Order of pole = 1.0000000000036682 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9120000000000097 " " y[1] (analytic) = 0.2147884419761894 " " y[1] (numeric) = 0.21478844197619112 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 8.0118169876187230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.157717312346691 " " Order of pole = 1.0000000000016502 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9110000000000098 " " y[1] (analytic) = 0.21496495748745348 " " y[1] (numeric) = 0.21496495748745517 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.8761214494794190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1568312405014614 " " Order of pole = 1.0000000000085016 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.91000000000001 " " y[1] (analytic) = 0.21514167079021362 " " y[1] (numeric) = 0.21514167079021534 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 7.9986628431783590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.155945268322488 " " Order of pole = 1.0000000000058495 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.90900000000001 " " y[1] (analytic) = 0.21531858214436028 " " y[1] (numeric) = 0.21531858214436206 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 8.2499003184467020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1550593959333426 " " Order of pole = 1.0000000000015365 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9080000000000101 " " y[1] (analytic) = 0.21549569181012754 " " y[1] (numeric) = 0.21549569181012931 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 8.2431199643907130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1541736234570754 " " Order of pole = 0.9999999999948006 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9070000000000102 " " y[1] (analytic) = 0.21567300004809326 " " y[1] (numeric) = 0.21567300004809506 " " absolute error = 1.8041124150158794000000000000000E-15 " " relative error = 8.3650360249710320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1532879510181147 " " Order of pole = 0.9999999999993072 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9060000000000104 " " y[1] (analytic) = 0.2158505071191796 " " y[1] (numeric) = 0.2158505071191814 " " absolute error = 1.8041124150158794000000000000000E-15 " " relative error = 8.3581569443325760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1524023787380635 " " Order of pole = 0.9999999999922391 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9050000000000105 " " y[1] (analytic) = 0.21602821328465313 " " y[1] (numeric) = 0.21602821328465496 " " absolute error = 1.8318679906315083000000000000000E-15 " " relative error = 8.479762725333090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1515169067406177 " " Order of pole = 0.9999999999738236 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9040000000000106 " " y[1] (analytic) = 0.2162061188061252 " " y[1] (numeric) = 0.21620611880612708 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 8.7295362050100130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1506315351548113 " " Order of pole = 1.0000000000064642 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9030000000000107 " " y[1] (analytic) = 0.21638422394555237 " " y[1] (numeric) = 0.21638422394555423 " " absolute error = 1.8596235662471372000000000000000E-15 " " relative error = 8.5940810856666920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.149746264095613 " " Order of pole = 0.9999999999803428 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9020000000000108 " " y[1] (analytic) = 0.21656252896523634 " " y[1] (numeric) = 0.2165625289652382 " " absolute error = 1.8596235662471372000000000000000E-15 " " relative error = 8.5870052179971220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.148861093695738 " " Order of pole = 0.9999999999977565 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.901000000000011 " " y[1] (analytic) = 0.21674103412782456 " " y[1] (numeric) = 0.21674103412782644 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 8.707991772105650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1479760240746613 " " Order of pole = 0.9999999999987317 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.900000000000011 " " y[1] (analytic) = 0.2169197396963104 " " y[1] (numeric) = 0.2169197396963123 " " absolute error = 1.915134717478395000000000000000E-15 " " relative error = 8.8287710475754810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.147091055358519 " " Order of pole = 1.0000000000014566 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8990000000000111 " " y[1] (analytic) = 0.21709864593403347 " " y[1] (numeric) = 0.21709864593403538 " " absolute error = 1.915134717478395000000000000000E-15 " " relative error = 8.8214954507837820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1462061876718552 " " Order of pole = 1.000000000002581 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8980000000000112 " " y[1] (analytic) = 0.2172777531046798 " " y[1] (numeric) = 0.21727775310468175 " " absolute error = 1.942890293094024000000000000000E-15 " " relative error = 8.941966056497190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1453214211395326 " " Order of pole = 1.0000000000002878 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8970000000000113 " " y[1] (analytic) = 0.2174570614722823 " " y[1] (numeric) = 0.21745706147228427 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 9.0622298276611120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1444367558871 " " Order of pole = 0.9999999999987281 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8960000000000115 " " y[1] (analytic) = 0.21763657130122088 " " y[1] (numeric) = 0.21763657130122288 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 9.1822869308090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1435521920401026 " " Order of pole = 0.9999999999996803 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8950000000000116 " " y[1] (analytic) = 0.21781628285622284 " " y[1] (numeric) = 0.21781628285622484 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 9.1747109909335640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1426677297239336 " " Order of pole = 1.0000000000007656 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8940000000000117 " " y[1] (analytic) = 0.21799619640236306 " " y[1] (numeric) = 0.2179961964023651 " " absolute error = 2.0261570199409107000000000000000E-15 " " relative error = 9.2944604235257520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1417833690639836 " " Order of pole = 0.9999999999972484 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8930000000000118 " " y[1] (analytic) = 0.21817631220506442 " " y[1] (numeric) = 0.21817631220506645 " " absolute error = 2.0261570199409107000000000000000E-15 " " relative error = 9.2867873668912380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1408991101871173 " " Order of pole = 0.9999999999998543 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.892000000000012 " " y[1] (analytic) = 0.21835663053009785 " " y[1] (numeric) = 0.21835663053009993 " " absolute error = 2.0816681711721685000000000000000E-15 " " relative error = 9.5333407834631130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1400149532187682 " " Order of pole = 0.9999999999996696 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.891000000000012 " " y[1] (analytic) = 0.21853715164358298 " " y[1] (numeric) = 0.21853715164358503 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 9.3984596216679460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.139130898285685 " " Order of pole = 1.000000000001343 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8900000000000121 " " y[1] (analytic) = 0.21871787581198796 " " y[1] (numeric) = 0.21871787581199 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 9.3906937781441480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1382469455139153 " " Order of pole = 0.9999999999987139 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8890000000000122 " " y[1] (analytic) = 0.21889880330213002 " " y[1] (numeric) = 0.21889880330213213 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 9.6365248003494750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1373630950307745 " " Order of pole = 0.9999999999985505 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8880000000000123 " " y[1] (analytic) = 0.21907993438117582 " " y[1] (numeric) = 0.21907993438117795 " " absolute error = 2.1371793224034263000000000000000E-15 " " relative error = 9.7552490530007240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1364793469627865 " " Order of pole = 0.9999999999957314 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8870000000000124 " " y[1] (analytic) = 0.2192612693166415 " " y[1] (numeric) = 0.21926126931664364 " " absolute error = 2.1371793224034263000000000000000E-15 " " relative error = 9.7471812010586520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1355957014376816 " " Order of pole = 0.9999999999973355 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8860000000000126 " " y[1] (analytic) = 0.21944280837639302 " " y[1] (numeric) = 0.2194428083763952 " " absolute error = 2.192690473634684200000000000000E-15 " " relative error = 9.9920817175914670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.134712158582454 " " Order of pole = 0.9999999999991864 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8850000000000127 " " y[1] (analytic) = 0.21962455182864665 " " y[1] (numeric) = 0.21962455182864882 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 9.8574357010329150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1338287185245792 " " Order of pole = 1.0000000000005649 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8840000000000128 " " y[1] (analytic) = 0.21980649994196877 " " y[1] (numeric) = 0.21980649994197096 " " absolute error = 2.192690473634684200000000000000E-15 " " relative error = 9.9755488314202610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.132945381391658 " " Order of pole = 0.9999999999998774 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8830000000000129 " " y[1] (analytic) = 0.21998865298527664 " " y[1] (numeric) = 0.2199886529852789 " " absolute error = 2.248201624865942000000000000000E-15 " " relative error = 1.021962539593535000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.132062147311937 " " Order of pole = 1.000000000000961 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.882000000000013 " " y[1] (analytic) = 0.22017101122783853 " " y[1] (numeric) = 0.22017101122784075 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.0085097201795289000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1311790164132107 " " Order of pole = 0.9999999999998117 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.881000000000013 " " y[1] (analytic) = 0.22035357493927366 " " y[1] (numeric) = 0.22035357493927593 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 1.032866020489476000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1302959888238364 " " Order of pole = 0.9999999999968221 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8800000000000132 " " y[1] (analytic) = 0.220536344389553 " " y[1] (numeric) = 0.22053634438955527 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 1.0320100329863746000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.129413064673158 " " Order of pole = 1.0000000000019273 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8790000000000133 " " y[1] (analytic) = 0.22071931984899906 " " y[1] (numeric) = 0.22071931984900137 " " absolute error = 2.3037127760971998000000000000E-15 " " relative error = 1.0437295555609909000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.128530244088785 " " Order of pole = 1.0000000000017373 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8780000000000134 " " y[1] (analytic) = 0.22090250158828653 " " y[1] (numeric) = 0.22090250158828886 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 1.0554286777875295000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.127647527199821 " " Order of pole = 0.9999999999984759 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8770000000000135 " " y[1] (analytic) = 0.2210858898784423 " " y[1] (numeric) = 0.22108588987844463 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 1.0545532114214613000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1267649141361264 " " Order of pole = 1.000000000001119 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8760000000000137 " " y[1] (analytic) = 0.2212694849908458 " " y[1] (numeric) = 0.22126948499084814 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 1.0536782113490636000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1258824050263163 " " Order of pole = 1.000000000001199 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8750000000000138 " " y[1] (analytic) = 0.22145328719722931 " " y[1] (numeric) = 0.22145328719723167 " " absolute error = 2.3592239273284576000000000000000E-15 " " relative error = 1.0653370546842687000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.124999999999995 " " Order of pole = 0.9999999999997957 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8740000000000139 " " y[1] (analytic) = 0.22163729676967817 " " y[1] (numeric) = 0.22163729676968055 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 1.0769755531825477000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.124117699187375 " " Order of pole = 1.0000000000028795 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.873000000000014 " " y[1] (analytic) = 0.2218215139806311 " " y[1] (numeric) = 0.22182151398063346 " " absolute error = 2.3592239273284576000000000000000E-15 " " relative error = 1.0635685804283436000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.12323550271761 " " Order of pole = 1.000000000001279 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.872000000000014 " " y[1] (analytic) = 0.22200593910288025 " " y[1] (numeric) = 0.2220059391028827 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.1001915822817086000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1223534107210638 " " Order of pole = 0.9999999999979483 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8710000000000142 " " y[1] (analytic) = 0.22219057240957193 " " y[1] (numeric) = 0.22219057240957435 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.0867855698704205000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1214714233286314 " " Order of pole = 0.9999999999998757 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8700000000000143 " " y[1] (analytic) = 0.22237541417420625 " " y[1] (numeric) = 0.2223754141742087 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.0983636222761238000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1205895406702275 " " Order of pole = 0.9999999999997495 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8690000000000144 " " y[1] (analytic) = 0.2225604646706379 " " y[1] (numeric) = 0.22256046467064036 " " absolute error = 2.4702462297909733000000000000000E-15 " " relative error = 1.1099214020093971000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.119707762876787 " " Order of pole = 1.0000000000001705 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8680000000000145 " " y[1] (analytic) = 0.22274572417307606 " " y[1] (numeric) = 0.22274572417307859 " " absolute error = 2.525757381022231000000000000000E-15 " " relative error = 1.1339195804538488000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1188260900792755 " " Order of pole = 1.0000000000016342 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8670000000000146 " " y[1] (analytic) = 0.22293119295608496 " " y[1] (numeric) = 0.2229311929560875 " " absolute error = 2.525757381022231000000000000000E-15 " " relative error = 1.132976210072037000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1179445224084423 " " Order of pole = 0.9999999999996305 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8660000000000148 " " y[1] (analytic) = 0.2231168712945838 " " y[1] (numeric) = 0.22311687129458635 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 1.144473271708094000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1170630599959703 " " Order of pole = 0.9999999999984226 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8650000000000149 " " y[1] (analytic) = 0.2233027594638473 " " y[1] (numeric) = 0.22330275946384986 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 1.1435205560239722000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.116181702973431 " " Order of pole = 0.9999999999985114 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.864000000000015 " " y[1] (analytic) = 0.22348885773950578 " " y[1] (numeric) = 0.22348885773950833 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 1.142568351042442000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1153004514724776 " " Order of pole = 0.9999999999988969 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.863000000000015 " " y[1] (analytic) = 0.22367516639754537 " " y[1] (numeric) = 0.22367516639754795 " " absolute error = 2.581268532253489000000000000000E-15 " " relative error = 1.1540255334674543000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1144193056250127 " " Order of pole = 0.9999999999991598 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8620000000000152 " " y[1] (analytic) = 0.22386168571430848 " " y[1] (numeric) = 0.2238616857143111 " " absolute error = 2.609024107869118000000000000000E-15 " " relative error = 1.1654625486912241000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.113538265563158 " " Order of pole = 0.9999999999990496 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8610000000000153 " " y[1] (analytic) = 0.2240484159664938 " " y[1] (numeric) = 0.2240484159664965 " " absolute error = 2.6922908347160046000000000000000E-15 " " relative error = 1.2016558220695628000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.112657331419518 " " Order of pole = 1.0000000000016662 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8600000000000154 " " y[1] (analytic) = 0.22423535743115688 " " y[1] (numeric) = 0.22423535743115955 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 1.1882761441484188000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1117765033260936 " " Order of pole = 1.0000000000003624 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8590000000000155 " " y[1] (analytic) = 0.2244225103857098 " " y[1] (numeric) = 0.22442251038571254 " " absolute error = 2.7478019859472624000000000000000E-15 " " relative error = 1.2243878660944835000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.11089578141601 " " Order of pole = 0.9999999999995719 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8580000000000156 " " y[1] (analytic) = 0.2246098751079221 " " y[1] (numeric) = 0.22460987510792485 " " absolute error = 2.7478019859472624000000000000000E-15 " " relative error = 1.2233665080963067000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1100151658224107 " " Order of pole = 1.0000000000014797 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8570000000000157 " " y[1] (analytic) = 0.22479745187592054 " " y[1] (numeric) = 0.2247974518759233 " " absolute error = 2.7478019859472624000000000000000E-15 " " relative error = 1.2223456996585273000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.109134656678008 " " Order of pole = 1.0000000000005667 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8560000000000159 " " y[1] (analytic) = 0.22498524096818948 " " y[1] (numeric) = 0.22498524096819228 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.2459986820090474000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1082542541164377 " " Order of pole = 0.9999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.855000000000016 " " y[1] (analytic) = 0.22517324266357128 " " y[1] (numeric) = 0.22517324266357408 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.2449583725038404000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1073739582712743 " " Order of pole = 0.9999999999996536 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.854000000000016 " " y[1] (analytic) = 0.22536145724126624 " " y[1] (numeric) = 0.22536145724126905 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.243918623661261000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1064937692763714 " " Order of pole = 1.0000000000003375 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8530000000000162 " " y[1] (analytic) = 0.2255498849808331 " " y[1] (numeric) = 0.22554988498083592 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.2551851724662724000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1056136872654436 " " Order of pole = 0.9999999999986251 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8520000000000163 " " y[1] (analytic) = 0.22573852616218912 " " y[1] (numeric) = 0.22573852616219198 " " absolute error = 2.858824288409778000000000000000E-15 " " relative error = 1.2664317150523804000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1047337123731418 " " Order of pole = 0.9999999999999005 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8510000000000164 " " y[1] (analytic) = 0.22592738106561047 " " y[1] (numeric) = 0.22592738106561336 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.2776582680729298000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.103853844733344 " " Order of pole = 0.9999999999977405 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8500000000000165 " " y[1] (analytic) = 0.2261164499717323 " " y[1] (numeric) = 0.2261164499717352 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.276589944865254000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.102974084481285 " " Order of pole = 0.9999999999995293 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8490000000000166 " " y[1] (analytic) = 0.22630573316154903 " " y[1] (numeric) = 0.22630573316155195 " " absolute error = 2.914335439641036000000000000000E-15 " " relative error = 1.2877868355021430000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.1020944317512993 " " Order of pole = 0.9999999999993037 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8480000000000167 " " y[1] (analytic) = 0.22649523091641466 " " y[1] (numeric) = 0.22649523091641757 " " absolute error = 2.914335439641036000000000000000E-15 " " relative error = 1.2867094056901074000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.101214886678633 " " Order of pole = 0.9999999999995399 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8470000000000169 " " y[1] (analytic) = 0.22668494351804286 " " y[1] (numeric) = 0.2266849435180458 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.297876678352257200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.100335449398481 " " Order of pole = 0.9999999999995879 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.846000000000017 " " y[1] (analytic) = 0.22687487124850733 " " y[1] (numeric) = 0.2268748712485103 " " absolute error = 2.9698465908722940000000000000000E-15 " " relative error = 1.309024033613345000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.099456120046431 " " Order of pole = 1.0000000000010107 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.845000000000017 " " y[1] (analytic) = 0.22706501439024204 " " y[1] (numeric) = 0.227065014390245 " " absolute error = 2.9698465908722940000000000000000E-15 " " relative error = 1.307927863236654000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.098576898757868 " " Order of pole = 1.0000000000003695 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8440000000000172 " " y[1] (analytic) = 0.22725537322604128 " " y[1] (numeric) = 0.22725537322604428 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 1.319045672687498800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.097697785668746 " " Order of pole = 0.9999999999985612 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8430000000000173 " " y[1] (analytic) = 0.22744594803906007 " " y[1] (numeric) = 0.2274459480390631 " " absolute error = 3.0253577421035516000000000000000E-15 " " relative error = 1.3301436091462032000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.09681878091551 " " Order of pole = 0.9999999999998277 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8420000000000174 " " y[1] (analytic) = 0.22763673911281437 " " y[1] (numeric) = 0.22763673911281737 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 1.3168358403703642000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.095939884634202 " " Order of pole = 1.0000000000010534 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8410000000000175 " " y[1] (analytic) = 0.2278277467311811 " " y[1] (numeric) = 0.22782774673118414 " " absolute error = 3.0253577421035516000000000000000E-15 " " relative error = 1.3279145255618213000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.095061096961143 " " Order of pole = 0.999999999999897 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8400000000000176 " " y[1] (analytic) = 0.22801897117839867 " " y[1] (numeric) = 0.22801897117840172 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.3389733766189435000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.094182418033432 " " Order of pole = 1.0000000000008278 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8390000000000177 " " y[1] (analytic) = 0.228210412739067 " " y[1] (numeric) = 0.22821041273907006 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.3378501362293546000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0933038479876824 " " Order of pole = 0.9999999999999218 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8380000000000178 " " y[1] (analytic) = 0.2284020716981477 " " y[1] (numeric) = 0.2284020716981508 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.3610316429435648000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0924253869613496 " " Order of pole = 1.0000000000008242 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.837000000000018 " " y[1] (analytic) = 0.22859394834096455 " " y[1] (numeric) = 0.22859394834096766 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.3598892234512255000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0915470350915384 " " Order of pole = 1.000000000000405 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.836000000000018 " " y[1] (analytic) = 0.2287860429532034 " " y[1] (numeric) = 0.2287860429532065 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.35874742568378000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.090668792515827 " " Order of pole = 0.9999999999986233 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8350000000000182 " " y[1] (analytic) = 0.22897835582091253 " " y[1] (numeric) = 0.2289783558209157 " " absolute error = 3.164135620181696000000000000000E-15 " " relative error = 1.381849218384822000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.089790659372293 " " Order of pole = 0.9999999999988862 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8340000000000183 " " y[1] (analytic) = 0.229170887230503 " " y[1] (numeric) = 0.22917088723050616 " " absolute error = 3.164135620181696000000000000000E-15 " " relative error = 1.3806882970257772000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0889126357986187 " " Order of pole = 0.9999999999973088 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8330000000000184 " " y[1] (analytic) = 0.22936363746874852 " " y[1] (numeric) = 0.22936363746875174 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 1.403730254256907000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.088034721933606 " " Order of pole = 1.000000000000826 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8320000000000185 " " y[1] (analytic) = 0.22955660682278609 " " y[1] (numeric) = 0.2295566068227893 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 1.4025502537151843000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.087156917914867 " " Order of pole = 0.9999999999994724 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8310000000000186 " " y[1] (analytic) = 0.2297497955801158 " " y[1] (numeric) = 0.22974979558011904 " " absolute error = 3.247402347028583000000000000000E-15 " " relative error = 1.4134516806985295000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.086279223881478 " " Order of pole = 0.9999999999983658 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8300000000000187 " " y[1] (analytic) = 0.22994320402860136 " " y[1] (numeric) = 0.2299432040286046 " " absolute error = 3.247402347028583000000000000000E-15 " " relative error = 1.4122628066992823000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0854016399723125 " " Order of pole = 0.9999999999975167 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8290000000000188 " " y[1] (analytic) = 0.23013683245647 " " y[1] (numeric) = 0.23013683245647332 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.447255981723595000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.084524166326614 " " Order of pole = 0.9999999999988347 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.828000000000019 " " y[1] (analytic) = 0.2303306811523131 " " y[1] (numeric) = 0.23033068115231642 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.4460379560432787000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0836468030834925 " " Order of pole = 0.999999999999968 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.827000000000019 " " y[1] (analytic) = 0.23052475040508588 " " y[1] (numeric) = 0.23052475040508927 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 1.468900939771724000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0827695503823245 " " Order of pole = 0.9999999999991847 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8260000000000192 " " y[1] (analytic) = 0.23071904050410813 " " y[1] (numeric) = 0.23071904050411152 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 1.4676639681354922000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.081892408363424 " " Order of pole = 1.0000000000034373 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8250000000000193 " " y[1] (analytic) = 0.23091355173906392 " " y[1] (numeric) = 0.23091355173906733 " " absolute error = 3.4139358007223564000000000000000E-15 " " relative error = 1.4784475727003496000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0810153771654947 " " Order of pole = 0.9999999999976126 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8240000000000194 " " y[1] (analytic) = 0.2311082844000021 " " y[1] (numeric) = 0.23110828440000555 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 1.4892115984821677000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0801384569303627 " " Order of pole = 1.0000000000016218 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8230000000000195 " " y[1] (analytic) = 0.23130323877733652 " " y[1] (numeric) = 0.23130323877733996 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 1.487956413637217000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0792616477975066 " " Order of pole = 1.0000000000044391 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8220000000000196 " " y[1] (analytic) = 0.23149841516184597 " " y[1] (numeric) = 0.23149841516184944 " " absolute error = 3.469446951953614000000000000000E-15 " " relative error = 1.4986914487203046000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0783849499070093 " " Order of pole = 0.9999999999996838 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8210000000000197 " " y[1] (analytic) = 0.23169381384467466 " " y[1] (numeric) = 0.23169381384467813 " " absolute error = 3.469446951953614000000000000000E-15 " " relative error = 1.4974275291957076000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0775083634004674 " " Order of pole = 0.9999999999965716 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8200000000000198 " " y[1] (analytic) = 0.23188943511733218 " " y[1] (numeric) = 0.2318894351173357 " " absolute error = 3.524958103184872000000000000000E-15 " " relative error = 1.5201029324174695000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.076631888419878 " " Order of pole = 1.0000000000064837 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.81900000000002 " " y[1] (analytic) = 0.23208527927169392 " " y[1] (numeric) = 0.23208527927169748 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.5307794143382383000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.075755525166981 " " Order of pole = 1.0000000007576944 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.81800000000002 " " y[1] (analytic) = 0.23228134660000108 " " y[1] (numeric) = 0.23228134660000466 " " absolute error = 3.58046925441613000000000000000E-15 " " relative error = 1.5414364118449247000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.074879273595895 " " Order of pole = 0.9999999999934879 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8170000000000202 " " y[1] (analytic) = 0.23247763739486096 " " y[1] (numeric) = 0.23247763739486452 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.5281958809510146000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0740031340383522 " " Order of pole = 1.000000000002423 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8160000000000203 " " y[1] (analytic) = 0.23267415194924695 " " y[1] (numeric) = 0.2326741519492506 " " absolute error = 3.635980405647387700000000000000E-15 " " relative error = 1.562692020229432800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0731271065716 " " Order of pole = 1.000000000005402 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8150000000000204 " " y[1] (analytic) = 0.2328708905564992 " " y[1] (numeric) = 0.2328708905565028 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 1.5494529270743396000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0722511913372252 " " Order of pole = 0.999999999995568 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8140000000000205 " " y[1] (analytic) = 0.23306785351032414 " " y[1] (numeric) = 0.23306785351032777 " " absolute error = 3.635980405647387700000000000000E-15 " " relative error = 1.560052298454933000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.071375388479572 " " Order of pole = 0.9999999999965805 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8130000000000206 " " y[1] (analytic) = 0.23326504110479515 " " y[1] (numeric) = 0.23326504110479881 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 1.5706322575859408000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0704996981405595 " " Order of pole = 1.0000000000002096 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8120000000000207 " " y[1] (analytic) = 0.2334624536343526 " " y[1] (numeric) = 0.2334624536343563 " " absolute error = 3.6914915568786455000000000000000E-15 " " relative error = 1.5811928211207082000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.069624120462555 " " Order of pole = 1.000000000000954 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8110000000000208 " " y[1] (analytic) = 0.23366009139380406 " " y[1] (numeric) = 0.23366009139380775 " " absolute error = 3.6914915568786455000000000000000E-15 " " relative error = 1.579855393729650800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0687486555885743 " " Order of pole = 0.9999999999984279 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.810000000000021 " " y[1] (analytic) = 0.23385795467832424 " " y[1] (numeric) = 0.23385795467832798 " " absolute error = 3.747002708109903300000000000000E-15 " " relative error = 1.6022558280149040000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.067873303662415 " " Order of pole = 0.9999999999989342 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.809000000000021 " " y[1] (analytic) = 0.23405604378345565 " " y[1] (numeric) = 0.23405604378345937 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.589041270788655000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0669980648273634 " " Order of pole = 0.999999999999968 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8080000000000211 " " y[1] (analytic) = 0.23425435900510813 " " y[1] (numeric) = 0.23425435900511196 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.635089930118768000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0661229392271467 " " Order of pole = 1.0000000000015934 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8070000000000213 " " y[1] (analytic) = 0.23445290063955984 " " y[1] (numeric) = 0.23445290063956364 " " absolute error = 3.802513859341161000000000000000E-15 " " relative error = 1.6218668436041320000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.065247927005482 " " Order of pole = 1.0000000000010587 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8060000000000214 " " y[1] (analytic) = 0.23465166898345655 " " y[1] (numeric) = 0.23465166898346038 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.6323214113711812000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0643730283068673 " " Order of pole = 1.0000000000022968 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8050000000000215 " " y[1] (analytic) = 0.23485066433381244 " " y[1] (numeric) = 0.2348506643338163 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.6427566945642924000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.06349824327529 " " Order of pole = 1.0000000000003801 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8040000000000216 " " y[1] (analytic) = 0.23504988698801008 " " y[1] (numeric) = 0.23504988698801388 " " absolute error = 3.802513859341161000000000000000E-15 " " relative error = 1.6177475803403077000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0626235720557267 " " Order of pole = 0.9999999999995595 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8030000000000217 " " y[1] (analytic) = 0.23524933724380032 " " y[1] (numeric) = 0.23524933724380417 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.6399727437166636000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.061749014792785 " " Order of pole = 0.9999999999969127 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8020000000000218 " " y[1] (analytic) = 0.23544901539930307 " " y[1] (numeric) = 0.23544901539930693 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.6385819257003523000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0608745716322434 " " Order of pole = 1.0000000000008864 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.801000000000022 " " y[1] (analytic) = 0.2356489217530068 " " y[1] (numeric) = 0.2356489217530107 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 1.6489702381328492000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0600002427184543 " " Order of pole = 1.0000000000000284 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.800000000000022 " " y[1] (analytic) = 0.23584905660376917 " " y[1] (numeric) = 0.2358490566037731 " " absolute error = 3.913536161803677000000000000000E-15 " " relative error = 1.65933933260479000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.059126028197257 " " Order of pole = 0.9999999999980425 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7990000000000221 " " y[1] (analytic) = 0.23604942025081696 " " y[1] (numeric) = 0.2360494202508209 " " absolute error = 3.941291737419305700000000000000E-15 " " relative error = 1.6696892257695198000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.05825192821483 " " Order of pole = 0.9999999999999556 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7980000000000222 " " y[1] (analytic) = 0.23625001299374626 " " y[1] (numeric) = 0.23625001299375023 " " absolute error = 3.969047313034934600000000000000E-15 " " relative error = 1.680019934280384000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0573779429166077 " " Order of pole = 0.9999999999991012 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7970000000000224 " " y[1] (analytic) = 0.23645083513252263 " " y[1] (numeric) = 0.23645083513252665 " " absolute error = 4.0245584642661925000000000000000E-15 " " relative error = 1.7020698878101084000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0565040724492545 " " Order of pole = 1.0000000000008438 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7960000000000225 " " y[1] (analytic) = 0.2366518869674814 " " y[1] (numeric) = 0.23665188696748543 " " absolute error = 4.0245584642661925000000000000000E-15 " " relative error = 1.7006238639538976000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.05563031695866 " " Order of pole = 0.9999999999984777 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7950000000000226 " " y[1] (analytic) = 0.23685316879932752 " " y[1] (numeric) = 0.23685316879933158 " " absolute error = 4.052314039881821400000000000000E-15 " " relative error = 1.7108971184232374000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0547566765921013 " " Order of pole = 0.9999999999992273 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7940000000000227 " " y[1] (analytic) = 0.23705468092913598 " " y[1] (numeric) = 0.23705468092914006 " " absolute error = 4.08006961549745030000000000000E-15 " " relative error = 1.7211512548520935000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0538831514964193 " " Order of pole = 1.0000000000023004 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7930000000000228 " " y[1] (analytic) = 0.23725642365835184 " " y[1] (numeric) = 0.23725642365835595 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.7313862898938107000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0530097418182423 " " Order of pole = 1.0000000000015312 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.792000000000023 " " y[1] (analytic) = 0.2374583972887904 " " y[1] (numeric) = 0.2374583972887945 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.7299136345627966000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.052136447705145 " " Order of pole = 0.9999999999994422 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.791000000000023 " " y[1] (analytic) = 0.23766060212263723 " " y[1] (numeric) = 0.2376606021226414 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 1.7517991224292107000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0512632693051365 " " Order of pole = 1.0000000000009255 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7900000000000231 " " y[1] (analytic) = 0.23786303846244863 " " y[1] (numeric) = 0.2378630384624528 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 1.7503082316850171000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0503902067655915 " " Order of pole = 1.0000000000004778 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7890000000000232 " " y[1] (analytic) = 0.23806570661115134 " " y[1] (numeric) = 0.23806570661115556 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 1.7721357492562007000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.049517260234743 " " Order of pole = 1.0000000000001261 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7880000000000233 " " y[1] (analytic) = 0.2382686068720431 " " y[1] (numeric) = 0.23826860687204732 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 1.7706266675077484000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0486444298610262 " " Order of pole = 1.000000000001549 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7870000000000235 " " y[1] (analytic) = 0.2384717395487924 " " y[1] (numeric) = 0.2384717395487966 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 1.7691184295287950000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.047771715792633 " " Order of pole = 1.0000000000006537 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7860000000000236 " " y[1] (analytic) = 0.2386751049454388 " " y[1] (numeric) = 0.23867510494544308 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.7908690752577536000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0468991181785774 " " Order of pole = 1.0000000000004494 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7850000000000237 " " y[1] (analytic) = 0.2388787033663933 " " y[1] (numeric) = 0.23887870336639755 " " absolute error = 4.246603069191224000000000000000E-15 " " relative error = 1.777723593332539200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0460266371678015 " " Order of pole = 1.0000000000002878 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7840000000000238 " " y[1] (analytic) = 0.2390825351164379 " " y[1] (numeric) = 0.23908253511644217 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.7878171831853615000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0451542729094903 " " Order of pole = 0.9999999999995932 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.783000000000024 " " y[1] (analytic) = 0.23928660050072628 " " y[1] (numeric) = 0.23928660050073056 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.7862925194567590000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0442820255531973 " " Order of pole = 0.9999999999994049 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.782000000000024 " " y[1] (analytic) = 0.23949089982478355 " " y[1] (numeric) = 0.23949089982478786 " " absolute error = 4.3021142204224816000000000000000E-15 " " relative error = 1.796358117811573000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.043409895248693 " " Order of pole = 1.0000000000005596 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7810000000000241 " " y[1] (analytic) = 0.23969543339450666 " " y[1] (numeric) = 0.239695433394511 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 1.8064047924149323000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0425378821457527 " " Order of pole = 1.0000000000010907 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7800000000000242 " " y[1] (analytic) = 0.2399002015161643 " " y[1] (numeric) = 0.23990020151616867 " " absolute error = 4.3576253716537394000000000000000E-15 " " relative error = 1.8164325599201822000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.041665986394463 " " Order of pole = 0.9999999999999662 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7790000000000243 " " y[1] (analytic) = 0.24010520449639716 " " y[1] (numeric) = 0.24010520449640155 " " absolute error = 4.385380947269368300000000000000E-15 " " relative error = 1.8264414369806684000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.040794208145527 " " Order of pole = 1.0000000000007159 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7780000000000244 " " y[1] (analytic) = 0.2403104426422179 " " y[1] (numeric) = 0.24031044264222232 " " absolute error = 4.413136522884997000000000000000E-15 " " relative error = 1.836431440249736000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.039922547549294 " " Order of pole = 0.9999999999997513 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7770000000000246 " " y[1] (analytic) = 0.24051591626101151 " " y[1] (numeric) = 0.2405159162610159 " " absolute error = 4.385380947269368300000000000000E-15 " " relative error = 1.8233225540509704000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0390510047568364 " " Order of pole = 0.9999999999993374 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7760000000000247 " " y[1] (analytic) = 0.24072162566053507 " " y[1] (numeric) = 0.2407216256605395 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.8448247374181326000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0381795799193863 " " Order of pole = 1.000000000000819 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7750000000000248 " " y[1] (analytic) = 0.24092757114891822 " " y[1] (numeric) = 0.24092757114892271 " " absolute error = 4.496403249731884000000000000000E-15 " " relative error = 1.86628837384188000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0373082731880485 " " Order of pole = 1.0000000000011209 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.774000000000025 " " y[1] (analytic) = 0.24113375303466317 " " y[1] (numeric) = 0.24113375303466764 " " absolute error = 4.468647674116255000000000000000E-15 " " relative error = 1.8531821521783737000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.036437084714391 " " Order of pole = 0.9999999999998792 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.773000000000025 " " y[1] (analytic) = 0.24134017162664448 " " y[1] (numeric) = 0.241340171626649 " " absolute error = 4.524158825347513000000000000000E-15 " " relative error = 1.8745983293433754000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.03556601465042 " " Order of pole = 0.9999999999991296 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.772000000000025 " " y[1] (analytic) = 0.24154682723410972 " " y[1] (numeric) = 0.24154682723411425 " " absolute error = 4.524158825347513000000000000000E-15 " " relative error = 1.87299451503979000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0346950631482525 " " Order of pole = 0.9999999999993552 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7710000000000252 " " y[1] (analytic) = 0.24175372016667915 " " y[1] (numeric) = 0.24175372016668367 " " absolute error = 4.524158825347513000000000000000E-15 " " relative error = 1.8713916055679694000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0338242303600698 " " Order of pole = 0.9999999999989342 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7700000000000253 " " y[1] (analytic) = 0.24196085073434592 " " y[1] (numeric) = 0.2419608507343505 " " absolute error = 4.579669976578771000000000000000E-15 " " relative error = 1.892731804620281200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0329535164385764 " " Order of pole = 0.9999999999996501 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7690000000000254 " " y[1] (analytic) = 0.24216821924747636 " " y[1] (numeric) = 0.24216821924748094 " " absolute error = 4.579669976578771000000000000000E-15 " " relative error = 1.89111105941557000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0320829215363507 " " Order of pole = 0.9999999999988773 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7680000000000256 " " y[1] (analytic) = 0.24237582601680976 " " y[1] (numeric) = 0.24237582601681437 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 1.9009426921457323000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.031212445806647 " " Order of pole = 0.9999999999992042 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7670000000000257 " " y[1] (analytic) = 0.2425836713534587 " " y[1] (numeric) = 0.24258367135346337 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 1.9221972680228272000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0303420894026556 " " Order of pole = 0.9999999999995577 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7660000000000258 " " y[1] (analytic) = 0.24279175556890914 " " y[1] (numeric) = 0.2427917555689138 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 1.920549852485507200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0294718524778528 " " Order of pole = 0.9999999999993907 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7650000000000259 " " y[1] (analytic) = 0.2430000789750203 " " y[1] (numeric) = 0.24300007897502496 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 1.9189033695355276000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.028601735186169 " " Order of pole = 1.0000000000007265 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.764000000000026 " " y[1] (analytic) = 0.2432086418840249 " " y[1] (numeric) = 0.24320864188402963 " " absolute error = 4.718447854656915300000000000000E-15 " " relative error = 1.940082317020185000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0277317376813566 " " Order of pole = 1.0000000000004832 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.763000000000026 " " y[1] (analytic) = 0.24341744460852938 " " y[1] (numeric) = 0.24341744460853412 " " absolute error = 4.746203430272544000000000000000E-15 " " relative error = 1.9498205799939766000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.026861860117789 " " Order of pole = 1.0000000000001474 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7620000000000262 " " y[1] (analytic) = 0.2436264874615137 " " y[1] (numeric) = 0.24362648746151847 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 1.95954021897652990000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0259921026499113 " " Order of pole = 0.9999999999991527 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7610000000000263 " " y[1] (analytic) = 0.24383577075633156 " " y[1] (numeric) = 0.24383577075633636 " " absolute error = 4.801714581503802000000000000000E-15 " " relative error = 1.96924125062119000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0251224654326405 " " Order of pole = 0.9999999999996536 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7600000000000264 " " y[1] (analytic) = 0.24404529480671058 " " y[1] (numeric) = 0.24404529480671538 " " absolute error = 4.801714581503802000000000000000E-15 " " relative error = 1.9675505669170426000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.024252948620683 " " Order of pole = 0.9999999999983267 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7590000000000265 " " y[1] (analytic) = 0.24425505992675212 " " y[1] (numeric) = 0.24425505992675692 " " absolute error = 4.801714581503802000000000000000E-15 " " relative error = 1.9658608435558114000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0233835523697192 " " Order of pole = 1.0000000000006217 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7580000000000267 " " y[1] (analytic) = 0.24446506643093155 " " y[1] (numeric) = 0.24446506643093638 " " absolute error = 4.829470157119431000000000000000E-15 " " relative error = 1.9755256763787543000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0225142768347393 " " Order of pole = 1.000000000000755 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7570000000000268 " " y[1] (analytic) = 0.2446753146340983 " " y[1] (numeric) = 0.2446753146341032 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.9965157971313838000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0216451221715075 " " Order of pole = 0.9999999999992717 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7560000000000269 " " y[1] (analytic) = 0.24488580485147599 " " y[1] (numeric) = 0.24488580485148087 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.99479970319776020000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0207760885362918 " " Order of pole = 0.9999999999998206 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.755000000000027 " " y[1] (analytic) = 0.2450965373986622 " " y[1] (numeric) = 0.2450965373986671 " " absolute error = 4.912736883966317700000000000000E-15 " " relative error = 2.004408930500514200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.019907176085238 " " Order of pole = 1.000000000001629 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.754000000000027 " " y[1] (analytic) = 0.24530751259162892 " " y[1] (numeric) = 0.24530751259163383 " " absolute error = 4.912736883966317700000000000000E-15 " " relative error = 2.0026850511279304000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0190383849744094 " " Order of pole = 0.9999999999999254 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7530000000000272 " " y[1] (analytic) = 0.2455187307467223 " " y[1] (numeric) = 0.24551873074672723 " " absolute error = 4.912736883966317700000000000000E-15 " " relative error = 2.0009621543027234000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.018169715360976 " " Order of pole = 1.0000000000003162 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7520000000000273 " " y[1] (analytic) = 0.2457301921806629 " " y[1] (numeric) = 0.24573019218066788 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 2.033125667821926000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.017301167401672 " " Order of pole = 1.0000000000001528 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7510000000000274 " " y[1] (analytic) = 0.2459418972105458 " " y[1] (numeric) = 0.24594189721055076 " " absolute error = 4.9682480351975755000000000000000E-15 " " relative error = 2.0200901479361855000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0164327412537477 " " Order of pole = 1.0000000000000195 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7500000000000275 " " y[1] (analytic) = 0.24615384615384034 " " y[1] (numeric) = 0.2461538461538453 " " absolute error = 4.9682480351975755000000000000000E-15 " " relative error = 2.0183507642990628000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0155644370747625 " " Order of pole = 1.0000000000012204 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7490000000000276 " " y[1] (analytic) = 0.2463660393283905 " " y[1] (numeric) = 0.24636603932839546 " " absolute error = 4.9682480351975755000000000000000E-15 " " relative error = 2.016612374311547000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.014696255022077 " " Order of pole = 0.9999999999996572 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7480000000000278 " " y[1] (analytic) = 0.24657847705241473 " " y[1] (numeric) = 0.24657847705241975 " " absolute error = 5.023759186428833000000000000000E-15 " " relative error = 2.0373875475599365000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0138281952540082 " " Order of pole = 0.9999999999997566 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7470000000000279 " " y[1] (analytic) = 0.24679115964450618 " " y[1] (numeric) = 0.2467911596445113 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 2.0693714963826937000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0129602579285697 " " Order of pole = 0.9999999999992717 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.746000000000028 " " y[1] (analytic) = 0.24700408742363278 " " y[1] (numeric) = 0.24700408742363783 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 2.045113833837368700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.012092443204368 " " Order of pole = 1.000000000000071 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.745000000000028 " " y[1] (analytic) = 0.2472172607091367 " " y[1] (numeric) = 0.24721726070914185 " " absolute error = 5.162537064506978000000000000000E-15 " " relative error = 2.0882591489357846000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.011224751239733 " " Order of pole = 0.9999999999976872 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7440000000000282 " " y[1] (analytic) = 0.2474306798207354 " " y[1] (numeric) = 0.24743067982074055 " " absolute error = 5.134781488891349000000000000000E-15 " " relative error = 2.075240423948849200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.010357182194395 " " Order of pole = 1.000000000001462 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7430000000000283 " " y[1] (analytic) = 0.24764434507852073 " " y[1] (numeric) = 0.2476443450785259 " " absolute error = 5.162537064506978000000000000000E-15 " " relative error = 2.0846577630795846000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0094897362266715 " " Order of pole = 1.0000000000007105 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7420000000000284 " " y[1] (analytic) = 0.24785825680295948 " " y[1] (numeric) = 0.24785825680296467 " " absolute error = 5.190292640122607000000000000000E-15 " " relative error = 2.094056783530414000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.008622413496433 " " Order of pole = 1.0000000000004068 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7410000000000285 " " y[1] (analytic) = 0.24807241531489327 " " y[1] (numeric) = 0.2480724153148985 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 2.1034375019546822000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.007755214163305 " " Order of pole = 0.9999999999995097 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7400000000000286 " " y[1] (analytic) = 0.24828682093553864 " " y[1] (numeric) = 0.24828682093554383 " " absolute error = 5.190292640122607000000000000000E-15 " " relative error = 2.0904422637358328000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0068881383874992 " " Order of pole = 1.000000000001025 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7390000000000287 " " y[1] (analytic) = 0.24850147398648675 " " y[1] (numeric) = 0.24850147398649203 " " absolute error = 5.2735593669694940000000000000000E-15 " " relative error = 2.1221440993369176000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.006021186328795 " " Order of pole = 0.9999999999996589 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7380000000000289 " " y[1] (analytic) = 0.2487163747897041 " " y[1] (numeric) = 0.24871637478970937 " " absolute error = 5.2735593669694940000000000000000E-15 " " relative error = 2.1203104827450223000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.005154358148058 " " Order of pole = 1.0000000000001474 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.737000000000029 " " y[1] (analytic) = 0.2489315236675318 " " y[1] (numeric) = 0.24893152366753707 " " absolute error = 5.2735593669694940000000000000000E-15 " " relative error = 2.118477920865000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.004287654005815 " " Order of pole = 1.0000000000000941 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.736000000000029 " " y[1] (analytic) = 0.24914692094268598 " " y[1] (numeric) = 0.24914692094269128 " " absolute error = 5.3013149425851220000000000000000E-15 " " relative error = 2.1277866579794666000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0034210740629232 " " Order of pole = 0.9999999999980052 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7350000000000292 " " y[1] (analytic) = 0.24936256693825776 " " y[1] (numeric) = 0.2493625669382631 " " absolute error = 5.35682609381638000000000000000E-15 " " relative error = 2.148207792207533800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0025546184811507 " " Order of pole = 1.0000000000002558 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7340000000000293 " " y[1] (analytic) = 0.2495784619777133 " " y[1] (numeric) = 0.24957846197771869 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 2.1574704911487270000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.0016882874214765 " " Order of pole = 1.0000000000006644 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7330000000000294 " " y[1] (analytic) = 0.24979460638489367 " " y[1] (numeric) = 0.24979460638489906 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 2.1556036566839348000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.000822081045627 " " Order of pole = 0.999999999998952 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7320000000000295 " " y[1] (analytic) = 0.2500110004840149 " " y[1] (numeric) = 0.2500110004840203 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 2.1537378991354766000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9999559995160299 " " Order of pole = 1.0000000000001776 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7310000000000296 " " y[1] (analytic) = 0.2502276445996681 " " y[1] (numeric) = 0.25022764459967356 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 2.1740574784879232000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9990900429945206 " " Order of pole = 0.9999999999991989 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7300000000000297 " " y[1] (analytic) = 0.2504445390568194 " " y[1] (numeric) = 0.25044453905682484 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 2.172174662362692000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.998224211643916 " " Order of pole = 0.9999999999995417 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7290000000000298 " " y[1] (analytic) = 0.2506616841808098 " " y[1] (numeric) = 0.2506616841808153 " " absolute error = 5.495603971894525000000000000000E-15 " " relative error = 2.1924387805239431000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.997358505626847 " " Order of pole = 0.9999999999994227 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.72800000000003 " " y[1] (analytic) = 0.25087908029735545 " " y[1] (numeric) = 0.25087908029736095 " " absolute error = 5.495603971894525000000000000000E-15 " " relative error = 2.190538950230859200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9964929251064882 " " Order of pole = 1.0000000000004725 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.72700000000003 " " y[1] (analytic) = 0.2510967277325473 " " y[1] (numeric) = 0.25109672773255287 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 2.2107476960187575000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9956274702458803 " " Order of pole = 0.9999999999996056 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7260000000000302 " " y[1] (analytic) = 0.2513146268128515 " " y[1] (numeric) = 0.25131462681285704 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 2.2088308959667424000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9947621412087677 " " Order of pole = 0.9999999999990443 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7250000000000303 " " y[1] (analytic) = 0.25153277786510897 " " y[1] (numeric) = 0.2515327778651145 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 2.2069152061377517000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.99389693815903 " " Order of pole = 0.9999999999995417 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7240000000000304 " " y[1] (analytic) = 0.2517511812165356 " " y[1] (numeric) = 0.2517511812165412 " " absolute error = 5.6066262743570400000000000000000E-15 " " relative error = 2.227050632797104000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9930318612605362 " " Order of pole = 0.9999999999985985 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7230000000000305 " " y[1] (analytic) = 0.25196983719472243 " " y[1] (numeric) = 0.25196983719472804 " " absolute error = 5.6066262743570400000000000000000E-15 " " relative error = 2.225118028720333200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9921669106779563 " " Order of pole = 1.0000000000001332 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7220000000000306 " " y[1] (analytic) = 0.2521887461276351 " " y[1] (numeric) = 0.25218874612764075 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 2.245198293948707000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9913020865755302 " " Order of pole = 0.999999999999865 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7210000000000307 " " y[1] (analytic) = 0.2524079083436143 " " y[1] (numeric) = 0.25240790834362 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 2.2432488200330766000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9904373891183806 " " Order of pole = 1.0000000000008704 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7200000000000308 " " y[1] (analytic) = 0.25262732417137557 " " y[1] (numeric) = 0.2526273241713813 " " absolute error = 5.717648576819556000000000000000E-15 " " relative error = 2.263274012648314000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.989572818471404 " " Order of pole = 1.000000000000428 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.719000000000031 " " y[1] (analytic) = 0.2528469939400093 " " y[1] (numeric) = 0.252846993940015 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 2.2393532694842724000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9887083748000962 " " Order of pole = 0.9999999999997957 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.718000000000031 " " y[1] (analytic) = 0.2530669179789805 " " y[1] (numeric) = 0.2530669179789862 " " absolute error = 5.717648576819556000000000000000E-15 " " relative error = 2.259342557486893000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.98784405827025 " " Order of pole = 1.000000000000691 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7170000000000312 " " y[1] (analytic) = 0.25328709661812915 " " y[1] (numeric) = 0.25328709661813487 " " absolute error = 5.717648576819556000000000000000E-15 " " relative error = 2.2573785452007555000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9869798690474707 " " Order of pole = 0.9999999999993872 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7160000000000313 " " y[1] (analytic) = 0.2535075301876698 " " y[1] (numeric) = 0.2535075301876755 " " absolute error = 5.717648576819556000000000000000E-15 " " relative error = 2.2554156764443337000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9861158072982332 " " Order of pole = 0.9999999999994102 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7150000000000314 " " y[1] (analytic) = 0.2537282190181917 " " y[1] (numeric) = 0.2537282190181975 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.2753321449187694000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9852518731889126 " " Order of pole = 0.9999999999999325 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7140000000000315 " " y[1] (analytic) = 0.2539491634406588 " " y[1] (numeric) = 0.2539491634406646 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.273352528448020800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9843880668861307 " " Order of pole = 0.9999999999999005 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7130000000000316 " " y[1] (analytic) = 0.2541703637864096 " " y[1] (numeric) = 0.2541703637864154 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 2.2713740666092175000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9835243885569263 " " Order of pole = 1.0000000000000604 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7120000000000317 " " y[1] (analytic) = 0.25439182038715696 " " y[1] (numeric) = 0.2543918203871628 " " absolute error = 5.828670879282072000000000000000E-15 " " relative error = 2.2912178820889217000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9826608383685034 " " Order of pole = 0.9999999999999591 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7110000000000318 " " y[1] (analytic) = 0.25461353357498845 " " y[1] (numeric) = 0.25461353357499433 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 2.3110248492664387000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9817974164883734 " " Order of pole = 0.999999999999643 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.710000000000032 " " y[1] (analytic) = 0.2548355036823659 " " y[1] (numeric) = 0.25483550368237184 " " absolute error = 5.9396931817445870000000000000000E-15 " " relative error = 2.3307950014484588000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9809341230844006 " " Order of pole = 1.000000000000158 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.709000000000032 " " y[1] (analytic) = 0.25505773104212565 " " y[1] (numeric) = 0.25505773104213153 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 2.3070000687575673000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9800709583245972 " " Order of pole = 1.0000000000011333 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7080000000000322 " " y[1] (analytic) = 0.25528021598747797 " " y[1] (numeric) = 0.25528021598748396 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 2.348479810621095200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9792079223771064 " " Order of pole = 1.0000000000005684 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7070000000000323 " " y[1] (analytic) = 0.2555029588520078 " " y[1] (numeric) = 0.2555029588520138 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 2.346432448341384000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9783450154106281 " " Order of pole = 0.9999999999998987 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7060000000000324 " " y[1] (analytic) = 0.2557259599696739 " " y[1] (numeric) = 0.25572595996967995 " " absolute error = 6.050715484207103000000000000000E-15 " " relative error = 2.3660935655201557000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9774822375940662 " " Order of pole = 0.9999999999997726 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7050000000000325 " " y[1] (analytic) = 0.25594921967480927 " " y[1] (numeric) = 0.2559492196748153 " " absolute error = 6.050715484207103000000000000000E-15 " " relative error = 2.3640296664684926000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9766195890965825 " " Order of pole = 1.000000000000691 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7040000000000326 " " y[1] (analytic) = 0.2561727383021208 " " y[1] (numeric) = 0.2561727383021269 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 2.383636399372403000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9757570700873492 " " Order of pole = 1.0000000000001013 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7030000000000327 " " y[1] (analytic) = 0.25639651618668935 " " y[1] (numeric) = 0.25639651618669546 " " absolute error = 6.106226635438361000000000000000E-15 " " relative error = 2.3815560079577092000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9748946807361882 " " Order of pole = 0.9999999999999325 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7020000000000328 " " y[1] (analytic) = 0.2566205536639696 " " y[1] (numeric) = 0.25662055366397574 " " absolute error = 6.161737786669619000000000000000E-15 " " relative error = 2.4011084454046006000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9740324212130267 " " Order of pole = 1.0000000000001563 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.701000000000033 " " y[1] (analytic) = 0.25684485106978994 " " y[1] (numeric) = 0.2568448510697961 " " absolute error = 6.161737786669619000000000000000E-15 " " relative error = 2.399011606035797200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.973170291688059 " " Order of pole = 1.0000000000006732 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.700000000000033 " " y[1] (analytic) = 0.25706940874035245 " " y[1] (numeric) = 0.25706940874035866 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.4185098368435112000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9723082923316446 " " Order of pole = 1.0000000000001563 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6990000000000332 " " y[1] (analytic) = 0.2572942270122328 " " y[1] (numeric) = 0.25729422701223903 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.4163965939295184000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9714464233146818 " " Order of pole = 1.0000000000004157 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6980000000000333 " " y[1] (analytic) = 0.25751930622238 " " y[1] (numeric) = 0.2575193062223863 " " absolute error = 6.2727600891321340000000000000000E-15 " " relative error = 2.435840706915897000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9705846848079753 " " Order of pole = 0.9999999999989058 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6970000000000334 " " y[1] (analytic) = 0.25774464670811653 " " y[1] (numeric) = 0.2577446467081228 " " absolute error = 6.2727600891321340000000000000000E-15 " " relative error = 2.4337111048656368000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9697230769831555 " " Order of pole = 0.9999999999996305 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6960000000000335 " " y[1] (analytic) = 0.25797024880713804 " " y[1] (numeric) = 0.2579702488071443 " " absolute error = 6.2727600891321340000000000000000E-15 " " relative error = 2.4315827573673943000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9688616000115693 " " Order of pole = 1.0000000000000142 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6950000000000336 " " y[1] (analytic) = 0.2581961128575133 " " y[1] (numeric) = 0.25819611285751964 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 2.450955272070915200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9680002540650494 " " Order of pole = 0.9999999999999556 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6940000000000337 " " y[1] (analytic) = 0.25842223919768437 " " y[1] (numeric) = 0.2584222391976907 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 2.4488106209475557000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9671390393158052 " " Order of pole = 1.000000000000579 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6930000000000338 " " y[1] (analytic) = 0.25864862816646583 " " y[1] (numeric) = 0.2586486281664722 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 2.4681292287721154000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9662779559360455 " " Order of pole = 0.9999999999997566 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.692000000000034 " " y[1] (analytic) = 0.2588752801030454 " " y[1] (numeric) = 0.2588752801030518 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 2.465968318432561000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9654170040986674 " " Order of pole = 1.000000000000199 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.691000000000034 " " y[1] (analytic) = 0.2591021953469832 " " y[1] (numeric) = 0.25910219534698964 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.485233108196002200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9645561839764074 " " Order of pole = 0.9999999999994884 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6900000000000341 " " y[1] (analytic) = 0.2593293742382122 " " y[1] (numeric) = 0.2593293742382186 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.4830559830491727000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.96369549574267 " " Order of pole = 0.9999999999998082 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6890000000000343 " " y[1] (analytic) = 0.25955681711703754 " " y[1] (numeric) = 0.259556817117044 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.480880145761052000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9628349395708615 " " Order of pole = 1.000000000000087 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6880000000000344 " " y[1] (analytic) = 0.2597845243241368 " " y[1] (numeric) = 0.25978452432414323 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.4787055963316398000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9619745156347577 " " Order of pole = 1.0000000000003677 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6870000000000345 " " y[1] (analytic) = 0.26001249620055955 " " y[1] (numeric) = 0.26001249620056605 " " absolute error = 6.494804694057166000000000000000E-15 " " relative error = 2.49788175143991000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9611142241084294 " " Order of pole = 1.0000000000008473 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6860000000000346 " " y[1] (analytic) = 0.26024073308772755 " " y[1] (numeric) = 0.2602407330877341 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 2.5170217465842680000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9602540651660696 " " Order of pole = 0.9999999999999485 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6850000000000347 " " y[1] (analytic) = 0.26046923532743443 " " y[1] (numeric) = 0.260469235327441 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 2.5148136351128220000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9593940389825444 " " Order of pole = 1.0000000000006253 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6840000000000348 " " y[1] (analytic) = 0.26069800326184545 " " y[1] (numeric) = 0.260698003261852 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 2.512606833704544000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9585341457326109 " " Order of pole = 1.000000000001327 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.683000000000035 " " y[1] (analytic) = 0.2609270372334974 " " y[1] (numeric) = 0.260927037233504 " " absolute error = 6.6058269965196810000000000000000E-15 " " relative error = 2.5316759300065494000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.957674385591308 " " Order of pole = 1.0000000000005524 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.682000000000035 " " y[1] (analytic) = 0.26115633758529866 " " y[1] (numeric) = 0.2611563375853053 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.5507089773669456000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9568147587342588 " " Order of pole = 1.0000000000002913 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6810000000000351 " " y[1] (analytic) = 0.26138590466052875 " " y[1] (numeric) = 0.2613859046605354 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.5484687693478570000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9559552653371262 " " Order of pole = 0.9999999999997176 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6800000000000352 " " y[1] (analytic) = 0.2616157388028383 " " y[1] (numeric) = 0.26161573880284494 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.546229893596398000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9550959055760184 " " Order of pole = 0.9999999999999805 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6790000000000354 " " y[1] (analytic) = 0.2618458403562488 " " y[1] (numeric) = 0.2618458403562555 " " absolute error = 6.716849298982197000000000000000E-15 " " relative error = 2.5651922863635070000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9542366796270885 " " Order of pole = 0.9999999999993552 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6780000000000355 " " y[1] (analytic) = 0.26207620966515277 " " y[1] (numeric) = 0.2620762096651595 " " absolute error = 6.716849298982197000000000000000E-15 " " relative error = 2.5629374400538385000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9533775876670998 " " Order of pole = 1.000000000000064 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6770000000000356 " " y[1] (analytic) = 0.26230684707431307 " " y[1] (numeric) = 0.2623068470743198 " " absolute error = 6.716849298982197000000000000000E-15 " " relative error = 2.56068393711403000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9525186298727386 " " Order of pole = 0.9999999999999964 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6760000000000357 " " y[1] (analytic) = 0.2625377529288629 " " y[1] (numeric) = 0.2625377529288697 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 2.60071990609853000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.951659806421254 " " Order of pole = 1.000000000000373 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6750000000000358 " " y[1] (analytic) = 0.26276892757430603 " " y[1] (numeric) = 0.26276892757431286 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 2.5984318863248856000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9508011174900073 " " Order of pole = 1.0000000000004228 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.674000000000036 " " y[1] (analytic) = 0.26300037135651605 " " y[1] (numeric) = 0.2630003713565229 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 2.5961452321255620000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.949942563256691 " " Order of pole = 0.999999999999849 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.673000000000036 " " y[1] (analytic) = 0.26323208462173636 " " y[1] (numeric) = 0.26323208462174325 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 2.6149482357241405000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9490841438994542 " " Order of pole = 1.0000000000004174 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6720000000000361 " " y[1] (analytic) = 0.26346406771658015 " " y[1] (numeric) = 0.2634640677165871 " " absolute error = 6.938893903907228000000000000000E-15 " " relative error = 2.633715467936865000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.948225859596406 " " Order of pole = 1.000000000000096 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6710000000000362 " " y[1] (analytic) = 0.26369632098803003 " " y[1] (numeric) = 0.263696320988037 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 2.652446962070428000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.94736771052622 " " Order of pole = 1.0000000000000249 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6700000000000363 " " y[1] (analytic) = 0.2639288447834379 " " y[1] (numeric) = 0.2639288447834449 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 2.650110131341506000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9465096968677755 " " Order of pole = 1.0000000000004512 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6690000000000365 " " y[1] (analytic) = 0.26416163945052473 " " y[1] (numeric) = 0.2641616394505317 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 2.6477746994935950000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9456518188000986 " " Order of pole = 1.0000000000000266 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6680000000000366 " " y[1] (analytic) = 0.2643947053373803 " " y[1] (numeric) = 0.2643947053373873 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 2.6454406665266955000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.944794076502702 " " Order of pole = 0.9999999999996341 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6670000000000367 " " y[1] (analytic) = 0.264628042792463 " " y[1] (numeric) = 0.26462804279247004 " " absolute error = 7.049916206369744000000000000000E-15 " " relative error = 2.6640850803173216000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9439364701553516 " " Order of pole = 0.9999999999997851 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6660000000000368 " " y[1] (analytic) = 0.2648616521645997 " " y[1] (numeric) = 0.26486165216460683 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.6826938892555485000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9430789999380382 " " Order of pole = 1.0000000000002522 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.665000000000037 " " y[1] (analytic) = 0.2650955338029856 " " y[1] (numeric) = 0.2650955338029927 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.6803270714027310000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9422216660310156 " " Order of pole = 1.0000000000005027 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.664000000000037 " " y[1] (analytic) = 0.26532968805718365 " " y[1] (numeric) = 0.2653296880571908 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 2.6988832502184750000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9413644686148053 " " Order of pole = 0.9999999999997691 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6630000000000371 " " y[1] (analytic) = 0.2655641152771247 " " y[1] (numeric) = 0.26556411527713186 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 2.696500805976586600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.940507407870425 " " Order of pole = 0.9999999999996305 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6620000000000372 " " y[1] (analytic) = 0.26579881581310705 " " y[1] (numeric) = 0.2657988158131142 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 2.6941197939224000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.939650483979027 " " Order of pole = 0.9999999999998561 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6610000000000373 " " y[1] (analytic) = 0.2660337900157963 " " y[1] (numeric) = 0.26603379001580346 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 2.691740214055915000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9387936971220379 " " Order of pole = 1.0000000000000568 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6600000000000374 " " y[1] (analytic) = 0.2662690382362251 " " y[1] (numeric) = 0.26626903823623227 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 2.689362066377132000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9379370474811775 " " Order of pole = 0.9999999999998099 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6590000000000376 " " y[1] (analytic) = 0.2665045608257928 " " y[1] (numeric) = 0.26650456082580004 " " absolute error = 7.216449660063518000000000000000E-15 " " relative error = 2.7078146946913695000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9370805352386073 " " Order of pole = 1.0000000000004796 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6580000000000377 " " y[1] (analytic) = 0.26674035813626557 " " y[1] (numeric) = 0.2667403581362728 " " absolute error = 7.216449660063518000000000000000E-15 " " relative error = 2.7054209983391264000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9362241605765103 " " Order of pole = 1.0000000000002256 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6570000000000378 " " y[1] (analytic) = 0.2669764305197755 " " y[1] (numeric) = 0.26697643051978276 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.7238212740866374000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.935367923677648 " " Order of pole = 1.0000000000005773 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6560000000000379 " " y[1] (analytic) = 0.26721277832882095 " " y[1] (numeric) = 0.2672127783288282 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.721412073469856000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9345118247248325 " " Order of pole = 1.0000000000002185 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.655000000000038 " " y[1] (analytic) = 0.267449401916266 " " y[1] (numeric) = 0.26744940191627325 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.719004327245236300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9336558639013603 " " Order of pole = 0.9999999999999716 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.654000000000038 " " y[1] (analytic) = 0.26768630163534013 " " y[1] (numeric) = 0.26768630163534746 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 2.7373354249960824000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9328000413907511 " " Order of pole = 0.999999999999778 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6530000000000382 " " y[1] (analytic) = 0.2679234778396382 " " y[1] (numeric) = 0.26792347783964554 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 2.7349122300180750000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9319443573768094 " " Order of pole = 0.9999999999998881 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6520000000000383 " " y[1] (analytic) = 0.26816093088311993 " " y[1] (numeric) = 0.2681609308831273 " " absolute error = 7.382983113757291000000000000000E-15 " " relative error = 2.7531911861445700000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9310888120436733 " " Order of pole = 1.0000000000003126 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6510000000000384 " " y[1] (analytic) = 0.26839866112010974 " " y[1] (numeric) = 0.2683986611201171 " " absolute error = 7.382983113757291000000000000000E-15 " " relative error = 2.7507525868220967000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9302334055756218 " " Order of pole = 0.9999999999998064 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6500000000000385 " " y[1] (analytic) = 0.2686366689052964 " " y[1] (numeric) = 0.2686366689053038 " " absolute error = 7.382983113757291000000000000000E-15 " " relative error = 2.7483154640962454000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9293781381575568 " " Order of pole = 1.000000000000501 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6490000000000387 " " y[1] (analytic) = 0.26887495459373284 " " y[1] (numeric) = 0.2688749545937403 " " absolute error = 7.438494264988549000000000000000E-15 " " relative error = 2.7665255308840620000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9285230099742936 " " Order of pole = 1.000000000000476 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6480000000000388 " " y[1] (analytic) = 0.2691135185408357 " " y[1] (numeric) = 0.2691135185408432 " " absolute error = 7.494005416219807000000000000000E-15 " " relative error = 2.7847004702153805000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.927668021211174 " " Order of pole = 1.0000000000001634 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6470000000000389 " " y[1] (analytic) = 0.2693523611023853 " " y[1] (numeric) = 0.2693523611023928 " " absolute error = 7.494005416219807000000000000000E-15 " " relative error = 2.7822311954307355000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.926813172053857 " " Order of pole = 1.0000000000003428 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.646000000000039 " " y[1] (analytic) = 0.2695914826345249 " " y[1] (numeric) = 0.2695914826345325 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 2.800354259591228400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9259584626881134 " " Order of pole = 0.9999999999995559 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.645000000000039 " " y[1] (analytic) = 0.2698308834937609 " " y[1] (numeric) = 0.2698308834937685 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.8184422851130630000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9251038933003437 " " Order of pole = 0.9999999999999858 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6440000000000392 " " y[1] (analytic) = 0.27007056403696217 " " y[1] (numeric) = 0.2700705640369698 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.815940991496389000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9242494640768955 " " Order of pole = 1.0000000000002434 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6430000000000393 " " y[1] (analytic) = 0.27031052462135985 " " y[1] (numeric) = 0.27031052462136745 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.813441218885258000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9233951752045162 " " Order of pole = 0.9999999999996589 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6420000000000394 " " y[1] (analytic) = 0.270550765604547 " " y[1] (numeric) = 0.27055076560455465 " " absolute error = 7.66053886991358000000000000000E-15 " " relative error = 2.8314607991576250000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9225410268704528 " " Order of pole = 0.9999999999999218 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6410000000000395 " " y[1] (analytic) = 0.27079128734447844 " " y[1] (numeric) = 0.2707912873444861 " " absolute error = 7.66053886991358000000000000000E-15 " " relative error = 2.8289458442466325000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.921687019261991 " " Order of pole = 0.9999999999997158 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6400000000000396 " " y[1] (analytic) = 0.27103209019947005 " " y[1] (numeric) = 0.27103209019947777 " " absolute error = 7.716050021144838000000000000000E-15 " " relative error = 2.8469138158017000000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9208331525668887 " " Order of pole = 0.9999999999998224 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6390000000000398 " " y[1] (analytic) = 0.2712731745281989 " " y[1] (numeric) = 0.2712731745282066 " " absolute error = 7.716050021144838000000000000000E-15 " " relative error = 2.8443837229997670000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9199794269731691 " " Order of pole = 1.000000000000247 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6380000000000399 " " y[1] (analytic) = 0.27151454068970243 " " y[1] (numeric) = 0.2715145406897102 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 2.8623001746553767000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9191258426690296 " " Order of pole = 0.999999999999984 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.63700000000004 " " y[1] (analytic) = 0.27175618904337867 " " y[1] (numeric) = 0.27175618904338644 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 2.859754988371423000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9182723998431914 " " Order of pole = 1.0000000000000764 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.63600000000004 " " y[1] (analytic) = 0.2719981199489852 " " y[1] (numeric) = 0.27199811994899303 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 2.8776200089454170000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9174190986845028 " " Order of pole = 0.9999999999999112 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6350000000000402 " " y[1] (analytic) = 0.2722403337666395 " " y[1] (numeric) = 0.2722403337666473 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 2.875059773588365000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9165659393822692 " " Order of pole = 1.0000000000003038 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6340000000000403 " " y[1] (analytic) = 0.2724828308568179 " " y[1] (numeric) = 0.2724828308568258 " " absolute error = 7.882583474838611000000000000000E-15 " " relative error = 2.892873451898585000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9157129221258868 " " Order of pole = 0.9999999999999201 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6330000000000404 " " y[1] (analytic) = 0.272725611580356 " " y[1] (numeric) = 0.2727256115803639 " " absolute error = 7.882583474838611000000000000000E-15 " " relative error = 2.8902982118773550000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9148600471052997 " " Order of pole = 0.999999999999929 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6320000000000405 " " y[1] (analytic) = 0.2729686762984475 " " y[1] (numeric) = 0.27296867629845545 " " absolute error = 7.93809462606986900000000000000E-15 " " relative error = 2.9080606367416440000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9140073145106178 " " Order of pole = 1.000000000000023 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6310000000000406 " " y[1] (analytic) = 0.27321202537264444 " " y[1] (numeric) = 0.27321202537265243 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.9257884115453336000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9131547245322678 " " Order of pole = 0.9999999999999947 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6300000000000407 " " y[1] (analytic) = 0.2734556591648565 " " y[1] (numeric) = 0.2734556591648645 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.9231816967013550000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.912302277361018 " " Order of pole = 0.9999999999999538 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6290000000000409 " " y[1] (analytic) = 0.27369957803735057 " " y[1] (numeric) = 0.27369957803735856 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.9205765805785333000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9114499731879122 " " Order of pole = 0.9999999999998082 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.628000000000041 " " y[1] (analytic) = 0.2739437823527507 " " y[1] (numeric) = 0.2739437823527587 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.9179730631768663000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9105978122043676 " " Order of pole = 0.9999999999999378 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.627000000000041 " " y[1] (analytic) = 0.2741882724740373 " " y[1] (numeric) = 0.27418827247404537 " " absolute error = 8.049116928532385000000000000000E-15 " " relative error = 2.9356167774442465000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.909745794602025 " " Order of pole = 0.9999999999998863 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 1.0) /( x * x + 1.0);" Iterations = 374 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 21 Minutes 3 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 20 Minutes 57 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 23 Minutes 58 Seconds "Time to Timeout " Unknown Percent Done = 12.499999999998623 "%" (%o58) true (%o58) diffeq.max