(%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_0D000001 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : 1 1 1 1 array_tmp5 1 array_const_0D000001 + array_tmp6 , array_tmp8 : -----------, 1 1 1 array_tmp7 1 array_tmp9 : array_tmp8 + array_const_0D0 , 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_0D000001 + array_tmp3 , array_tmp5 : -----------, 1 1 1 1 array_tmp4 1 array_tmp6 : array_x array_x , array_tmp7 : 1 1 1 1 array_tmp5 1 array_const_0D000001 + array_tmp6 , array_tmp8 : -----------, 1 1 1 array_tmp7 1 array_tmp9 : array_tmp8 + array_const_0D0 , 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(------------) 1.0E-6 + x x 1.0 (%o56) exact_soln_y(x) := block(------------) 1.0E-6 + 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/sing1postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /\ ( x * x + 0.000001);"), 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:-1.5,"), 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:500,"), 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 + 0.000001)) "), 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_0D000001, 1 + 1 + max_terms), 1 term : 1, while term <= 1 + max_terms do (array_const_0D000001 : 0.0, term term : 1 + term), array_const_0D000001 : 1.0E-6, 1 array(array_m1, 1 + 1 + max_terms), term : 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 : - 1.5, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 500, 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 + 0.000001) /( x * x + 0.000001);"), 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, "2013-01-28T19:00:15-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing1"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.00\ 0001) /( x * x + 0.000001);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 1 logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_max_terms), 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, "sing1 diffeq.max"), logitem_str(html_log_file, "sing1 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/sing1postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /\ ( x * x + 0.000001);"), 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:-1.5,"), 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:500,"), 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 + 0.000001)) "), 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_0D000001, 1 + 1 + max_terms), 1 term : 1, while term <= 1 + max_terms do (array_const_0D000001 : 0.0, term term : 1 + term), array_const_0D000001 : 1.0E-6, 1 array(array_m1, 1 + 1 + max_terms), term : 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 : - 1.5, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 500, 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 + 0.000001) /( x * x + 0.000001);"), 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, "2013-01-28T19:00:15-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sing1"), logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.00\ 0001) /( x * x + 0.000001);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), 1 logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_max_terms), 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, "sing1 diffeq.max"), logitem_str(html_log_file, "sing1 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/sing1postode.ode#################" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-2.0," "x_end:-1.5," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:500," "/* 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 + 0.000001)) " "));" "" "" "/* 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 = 0.5 "" estimated_steps = 500. "" step_error = 2.0000000000000E-13 "" est_needed_step_err = 2.0000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.00605517883980280000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 "" max_value3 = 1.00605517883980280000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 "" value3 = 1.00605517883980280000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-85 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = -2. " " y[1] (analytic) = 0.24999993750001562 " " y[1] (numeric) = 0.24999993750001562 " " 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 = 2.000001576134246 " " Order of pole = 0.9999999990931698 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.999 " " y[1] (analytic) = 0.2502501249999374 " " y[1] (numeric) = 0.25025012499993743 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.21822671342408800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9989989853931587 " " Order of pole = 1.0000000008854517 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9980000000000002 " " y[1] (analytic) = 0.2505006882506409 " " y[1] (numeric) = 0.250500688250641 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.216007932709374600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.997998906363145 " " Order of pole = 1.0000000009149161 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9970000000000003 " " y[1] (analytic) = 0.2507516280049447 " " y[1] (numeric) = 0.2507516280049448 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.42758052443537200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9970014896427475 " " Order of pole = 0.9999999991732391 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9960000000000004 " " y[1] (analytic) = 0.25100294501755377 " " y[1] (numeric) = 0.2510029450175539 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.42314740389804450000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9959992589600057 " " Order of pole = 1.0000000006649206 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9950000000000006 " " y[1] (analytic) = 0.25125464004506487 " " y[1] (numeric) = 0.25125464004506504 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.62807475571014900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9950006949204941 " " Order of pole = 0.9999999996331681 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9940000000000007 " " y[1] (analytic) = 0.25150671384597256 " " y[1] (numeric) = 0.2515067138459728 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.82857564832307400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9939992228601064 " " Order of pole = 1.0000000006604957 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9930000000000008 " " y[1] (analytic) = 0.25175916718067476 " " y[1] (numeric) = 0.251759167180675 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.81972272992471400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9930021641328561 " " Order of pole = 0.9999999986540473 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9920000000000009 " " y[1] (analytic) = 0.2520120008114784 " " y[1] (numeric) = 0.2520120008114787 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.10135928155230640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9919997970340153 " " Order of pole = 1.0000000003235385 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.991000000000001 " " y[1] (analytic) = 0.2522652155026054 " " y[1] (numeric) = 0.25226521550260567 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.1002537769755360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9910015767486058 " " Order of pole = 0.9999999990676809 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.990000000000001 " " y[1] (analytic) = 0.2525188120201982 " " y[1] (numeric) = 0.2525188120201985 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.09914882751027790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.990002067384955 " " Order of pole = 0.9999999987001456 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9890000000000012 " " y[1] (analytic) = 0.2527727911323257 " " y[1] (numeric) = 0.2527727911323261 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.53726220641914550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9890002225862293 " " Order of pole = 1.0000000000316405 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9880000000000013 " " y[1] (analytic) = 0.2530271536089892 " " y[1] (numeric) = 0.2530271536089896 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.53571683148001850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.98799705009833 " " Order of pole = 1.0000000022518147 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9870000000000014 " " y[1] (analytic) = 0.2532819002221278 " " y[1] (numeric) = 0.25328190022212826 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.75333969565372450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9869973824431026 " " Order of pole = 1.0000000020041515 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9860000000000015 " " y[1] (analytic) = 0.25353703174562486 " " y[1] (numeric) = 0.2535370317456253 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.75157532922299050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9860006916733235 " " Order of pole = 0.999999999683121 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9850000000000017 " " y[1] (analytic) = 0.2537925489553133 " " y[1] (numeric) = 0.2537925489553138 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.96853833234201030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9850024505253696 " " Order of pole = 0.9999999984529566 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9840000000000018 " " y[1] (analytic) = 0.25404845262898185 " " y[1] (numeric) = 0.25404845262898235 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.96655541850887880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9839998979183657 " " Order of pole = 1.000000000249397 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9830000000000019 " " y[1] (analytic) = 0.2543047435463809 " " y[1] (numeric) = 0.2543047435463814 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.96457350387646950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9830004460645798 " " Order of pole = 0.9999999998762608 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.982000000000002 " " y[1] (analytic) = 0.25456142248922836 " " y[1] (numeric) = 0.25456142248922886 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.9625925884447820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9820019306098844 " " Order of pole = 0.9999999987743333 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.981000000000002 " " y[1] (analytic) = 0.2548184902412157 " " y[1] (numeric) = 0.2548184902412163 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.17845852468201900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9810018215694547 " " Order of pole = 0.9999999989329691 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9800000000000022 " " y[1] (analytic) = 0.255075947588014 " " y[1] (numeric) = 0.2550759475880146 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.3938857007799240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9799999144948075 " " Order of pole = 1.000000000207189 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9790000000000023 " " y[1] (analytic) = 0.25533379531727973 " " y[1] (numeric) = 0.25533379531728034 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.3914682456549538000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9790007401107417 " " Order of pole = 0.9999999996408739 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9780000000000024 " " y[1] (analytic) = 0.2555920342186609 " " y[1] (numeric) = 0.25559203421866156 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.606238558300340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.977996874611829 " " Order of pole = 1.0000000023944153 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9770000000000025 " " y[1] (analytic) = 0.2558506650838032 " " y[1] (numeric) = 0.2558506650838039 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.6036039990629050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9769962512216943 " " Order of pole = 1.0000000028321114 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9760000000000026 " " y[1] (analytic) = 0.256109688706356 " " y[1] (numeric) = 0.25610968870635664 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.6009707720930990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9759996754653373 " " Order of pole = 1.0000000003935288 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9750000000000028 " " y[1] (analytic) = 0.2563691058819782 " " y[1] (numeric) = 0.2563691058819789 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.81486711717349960000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9750007951641324 " " Order of pole = 0.9999999996198827 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9740000000000029 " " y[1] (analytic) = 0.25662891740834487 " " y[1] (numeric) = 0.2566289174083456 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.8120173412027410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9739997536632978 " " Order of pole = 1.000000000332573 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.973000000000003 " " y[1] (analytic) = 0.25688912408515285 " " y[1] (numeric) = 0.2568891240851536 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.80916900852191400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9729987579353852 " " Order of pole = 1.0000000010624888 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.972000000000003 " " y[1] (analytic) = 0.2571497267141271 " " y[1] (numeric) = 0.2571497267141279 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 3.0221930513718670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9720009487635985 " " Order of pole = 0.9999999994710649 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9710000000000032 " " y[1] (analytic) = 0.2574107260990271 " " y[1] (numeric) = 0.25741072609902793 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 3.2347807765731430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9709989394653953 " " Order of pole = 1.0000000008928929 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9700000000000033 " " y[1] (analytic) = 0.25767212304565273 " " y[1] (numeric) = 0.2576721230456535 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 3.0160659525435660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9700001624190986 " " Order of pole = 1.0000000000800249 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9690000000000034 " " y[1] (analytic) = 0.2579339183618505 " " y[1] (numeric) = 0.2579339183618513 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 3.22821935849760800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9689994607372263 " " Order of pole = 1.0000000005517773 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9680000000000035 " " y[1] (analytic) = 0.25819611285752 " " y[1] (numeric) = 0.25819611285752087 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.439937223959090300000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9680011603907228 " " Order of pole = 0.9999999993183053 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9670000000000036 " " y[1] (analytic) = 0.2584587073446201 " " y[1] (numeric) = 0.258458707344621 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.43644224187757100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9669987129589264 " " Order of pole = 1.000000001061652 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9660000000000037 " " y[1] (analytic) = 0.2587217026371752 " " y[1] (numeric) = 0.2587217026371761 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.432949036152889700000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9659976531835666 " " Order of pole = 1.0000000018708466 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9650000000000039 " " y[1] (analytic) = 0.2589850995512814 " " y[1] (numeric) = 0.2589850995512823 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.4294576067850490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9649975629331982 " " Order of pole = 1.0000000019519995 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.964000000000004 " " y[1] (analytic) = 0.2592488989051131 " " y[1] (numeric) = 0.259248898905114 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.42596795377404730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9639976463680417 " " Order of pole = 1.0000000018967317 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.963000000000004 " " y[1] (analytic) = 0.2595131015189291 " " y[1] (numeric) = 0.25951310151893003 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 3.6363850819398790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.963001481274079 " " Order of pole = 0.9999999990913686 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9620000000000042 " " y[1] (analytic) = 0.25977770821507923 " " y[1] (numeric) = 0.2597777082150802 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 3.8463682239253840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9619995566649042 " " Order of pole = 1.0000000004691874 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9610000000000043 " " y[1] (analytic) = 0.2600427198180105 " " y[1] (numeric) = 0.2600427198180116 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 4.05591771279747050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9610022251384558 " " Order of pole = 0.999999998545178 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9600000000000044 " " y[1] (analytic) = 0.2603081371542738 " " y[1] (numeric) = 0.26030813715427487 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 4.05178218754189360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9599996121600274 " " Order of pole = 1.0000000004178187 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9590000000000045 " " y[1] (analytic) = 0.26057396105253 " " y[1] (numeric) = 0.26057396105253106 " " absolute error = 1.0547118733938987000000000000000E-15 " " relative error = 4.04764877171006300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9589972126295785 " " Order of pole = 1.0000000021847129 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9580000000000046 " " y[1] (analytic) = 0.2608401923435566 " " y[1] (numeric) = 0.2608401923435577 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 4.25633417400208300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9579987257044242 " " Order of pole = 1.000000001140446 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9570000000000047 " " y[1] (analytic) = 0.26110683186025435 " " y[1] (numeric) = 0.2611068318602555 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 4.46458703340371100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9569996016079347 " " Order of pole = 1.000000000456735 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9560000000000048 " " y[1] (analytic) = 0.2613738804376536 " " y[1] (numeric) = 0.26137388043765475 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 4.46002551557358460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9560022152065681 " " Order of pole = 0.9999999985581951 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.955000000000005 " " y[1] (analytic) = 0.26164133891292074 " " y[1] (numeric) = 0.26164133891292196 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 4.6676313925076120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9550022269783682 " " Order of pole = 0.9999999985528838 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.954000000000005 " " y[1] (analytic) = 0.26190920812536517 " " y[1] (numeric) = 0.2619092081253664 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 4.6628575445240256000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9540005112820702 " " Order of pole = 0.999999999786521 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9530000000000052 " " y[1] (analytic) = 0.26217748891644527 " " y[1] (numeric) = 0.26217748891644654 " " absolute error = 1.27675647831893000000000000000E-15 " " relative error = 4.8698173271688716000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.953001583139706 " " Order of pole = 0.9999999989679296 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9520000000000053 " " y[1] (analytic) = 0.26244618212977555 " " y[1] (numeric) = 0.2624461821297769 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.0763460102132560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9520022823236398 " " Order of pole = 0.9999999984954329 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9510000000000054 " " y[1] (analytic) = 0.26271528861113314 " " y[1] (numeric) = 0.26271528861113447 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.0711461696551230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9509993838793593 " " Order of pole = 1.0000000006313616 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9500000000000055 " " y[1] (analytic) = 0.2629848092084642 " " y[1] (numeric) = 0.26298480920846556 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 5.2770302017002590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9500004626333363 " " Order of pole = 0.9999999998363318 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9490000000000056 " " y[1] (analytic) = 0.26325474477189087 " " y[1] (numeric) = 0.26325474477189226 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 5.2716192522339920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9489995036488037 " " Order of pole = 1.0000000005144205 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9480000000000057 " " y[1] (analytic) = 0.2635250961537179 " " y[1] (numeric) = 0.26352509615371933 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 5.4768595214582980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9480004544695007 " " Order of pole = 0.9999999998378257 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9470000000000058 " " y[1] (analytic) = 0.26379586420843937 " " y[1] (numeric) = 0.2637958642084408 " " absolute error = 1.4432899320127035000000000000000E-15 " " relative error = 5.4712379071731090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9470021403165567 " " Order of pole = 0.9999999986043981 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.946000000000006 " " y[1] (analytic) = 0.26406704979274537 " " y[1] (numeric) = 0.26406704979274687 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 5.6758353017550070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9459958761132474 " " Order of pole = 1.0000000032688803 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.945000000000006 " " y[1] (analytic) = 0.2643386537655289 " " y[1] (numeric) = 0.26433865376553045 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 5.8800035951378870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.945002291039981 " " Order of pole = 0.9999999984571115 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9440000000000062 " " y[1] (analytic) = 0.26461067698789265 " " y[1] (numeric) = 0.2646106769878942 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 5.8739588748580140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.944001566492704 " " Order of pole = 0.9999999990069899 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9430000000000063 " " y[1] (analytic) = 0.2648831203231557 " " y[1] (numeric) = 0.26488312032315725 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 5.8679172632026090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9430004543913988 " " Order of pole = 0.9999999998283773 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9420000000000064 " " y[1] (analytic) = 0.26515598463686046 " " y[1] (numeric) = 0.2651559846368621 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 6.0712315730349490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.941999051191873 " " Order of pole = 1.0000000009059686 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9410000000000065 " " y[1] (analytic) = 0.2654292707967797 " " y[1] (numeric) = 0.26542927079678136 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 6.2741178918912940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9409981213721759 " " Order of pole = 1.0000000016133157 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9400000000000066 " " y[1] (analytic) = 0.2657029796729231 " " y[1] (numeric) = 0.2657029796729248 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 6.2676547285534390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9399996805172532 " " Order of pole = 1.000000000411024 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9390000000000067 " " y[1] (analytic) = 0.2659771121375445 " " y[1] (numeric) = 0.26597711213754616 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 6.2611948958846590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9390003230099793 " " Order of pole = 0.9999999999441371 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9380000000000068 " " y[1] (analytic) = 0.2662516690651486 " " y[1] (numeric) = 0.26625166906515024 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 6.2547383938849510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9380007942521824 " " Order of pole = 0.9999999995770175 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.937000000000007 " " y[1] (analytic) = 0.2665266513324981 " " y[1] (numeric) = 0.26652665133249975 " " absolute error = 1.6653345369377348000000000000000E-15 " " relative error = 6.2482852225543170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9370015132771694 " " Order of pole = 0.9999999990408632 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.936000000000007 " " y[1] (analytic) = 0.26680205981862065 " " y[1] (numeric) = 0.2668020598186224 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 6.4498965612891850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9359984742803935 " " Order of pole = 1.000000001364203 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9350000000000072 " " y[1] (analytic) = 0.26707789540481597 " " y[1] (numeric) = 0.26707789540481774 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.6510814633602920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9349995009795258 " " Order of pole = 1.0000000005504095 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9340000000000073 " " y[1] (analytic) = 0.2673541589746627 " " y[1] (numeric) = 0.26735415897466447 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 6.6442087387486540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.933999617324797 " " Order of pole = 1.0000000004634497 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9330000000000074 " " y[1] (analytic) = 0.26763085141402554 " " y[1] (numeric) = 0.26763085141402737 " " absolute error = 1.8318679906315083000000000000000E-15 " " relative error = 6.8447564283147780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9330001286671217 " " Order of pole = 1.0000000001076668 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9320000000000075 " " y[1] (analytic) = 0.2679079736110625 " " y[1] (numeric) = 0.2679079736110644 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 7.0448785693955630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.932000761409201 " " Order of pole = 0.9999999996034639 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9310000000000076 " " y[1] (analytic) = 0.2681855264562319 " " y[1] (numeric) = 0.2681855264562338 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 7.0375876237705460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9310010213024524 " " Order of pole = 0.9999999993836894 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9300000000000077 " " y[1] (analytic) = 0.2684635108422994 " " y[1] (numeric) = 0.26846351084230136 " " absolute error = 1.942890293094024000000000000000E-15 " " relative error = 7.2370739956362820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9300001998338514 " " Order of pole = 1.000000000050731 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9290000000000078 " " y[1] (analytic) = 0.26874192766434557 " " y[1] (numeric) = 0.26874192766434757 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 7.4361357071950960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9290008245784047 " " Order of pole = 0.9999999996205737 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.928000000000008 " " y[1] (analytic) = 0.2690207778197727 " " y[1] (numeric) = 0.2690207778197747 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 7.4284278728243340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9280002990297345 " " Order of pole = 0.9999999999359304 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.927000000000008 " " y[1] (analytic) = 0.2693000622083121 " " y[1] (numeric) = 0.26930006220831415 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 7.626855258458030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.927000948992503 " " Order of pole = 0.9999999994291358 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9260000000000081 " " y[1] (analytic) = 0.2695797817320316 " " y[1] (numeric) = 0.2695797817320337 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 7.6189415332273510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9260024880242275 " " Order of pole = 0.9999999982999253 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9250000000000083 " " y[1] (analytic) = 0.26985993729534263 " " y[1] (numeric) = 0.26985993729534474 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 7.8167354811143460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9249967107783694 " " Order of pole = 1.0000000027215954 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9240000000000084 " " y[1] (analytic) = 0.2701405298050075 " " y[1] (numeric) = 0.27014052980500963 " " absolute error = 2.1094237467877974000000000000000E-15 " " relative error = 7.808616309112960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.924000109473631 " " Order of pole = 1.0000000001107363 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9230000000000085 " " y[1] (analytic) = 0.27042156017014685 " " y[1] (numeric) = 0.270421560170149 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 8.0057777074316760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.92299904745261 " " Order of pole = 1.000000000943361 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9220000000000086 " " y[1] (analytic) = 0.270703029302247 " " y[1] (numeric) = 0.27070302930224915 " " absolute error = 2.1649348980190553000000000000000E-15 " " relative error = 7.9974535327487930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.922000833022112 " " Order of pole = 0.9999999995496491 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9210000000000087 " " y[1] (analytic) = 0.2709849381151672 " " y[1] (numeric) = 0.27098493811516944 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 8.1939832696776480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9210009730926179 " " Order of pole = 0.9999999994585913 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9200000000000088 " " y[1] (analytic) = 0.2712672875251474 " " y[1] (numeric) = 0.2712672875251496 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 8.1854545364024780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9199986097642552 " " Order of pole = 1.0000000012609789 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.919000000000009 " " y[1] (analytic) = 0.27155007845081514 " " y[1] (numeric) = 0.2715500784508174 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 8.3813535001198940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9189992822481512 " " Order of pole = 1.0000000007618315 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.918000000000009 " " y[1] (analytic) = 0.2718333118131936 " " y[1] (numeric) = 0.27183331181319587 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 8.3726206523416460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9179993713329087 " " Order of pole = 1.0000000006513048 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9170000000000091 " " y[1] (analytic) = 0.27211698853570865 " " y[1] (numeric) = 0.272116988535711 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 8.567889731026040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9170023472377151 " " Order of pole = 0.9999999983974384 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9160000000000093 " " y[1] (analytic) = 0.2724011095441967 " " y[1] (numeric) = 0.2724011095441991 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 8.7627378131394960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9160024281494596 " " Order of pole = 0.9999999983021173 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9150000000000094 " " y[1] (analytic) = 0.27268567576691216 " " y[1] (numeric) = 0.27268567576691455 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 8.7535932946637160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9150037611879864 " " Order of pole = 0.9999999972861708 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9140000000000095 " " y[1] (analytic) = 0.27297068813453473 " " y[1] (numeric) = 0.2729706881345371 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 8.7444535501469440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9140001776724613 " " Order of pole = 1.0000000000604388 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9130000000000096 " " y[1] (analytic) = 0.2732561475801774 " " y[1] (numeric) = 0.27325614758017985 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 8.9384655233005560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9130027423239726 " " Order of pole = 0.9999999980868992 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9120000000000097 " " y[1] (analytic) = 0.2735420550393941 " " y[1] (numeric) = 0.27354205503939655 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 8.9291229965483350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9120008217156679 " " Order of pole = 0.9999999995219451 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9110000000000098 " " y[1] (analytic) = 0.273828411450187 " " y[1] (numeric) = 0.27382841145018944 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 8.9197853547774230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.911001076589265 " " Order of pole = 0.999999999379062 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.91000000000001 " " y[1] (analytic) = 0.2741152177530144 " " y[1] (numeric) = 0.2741152177530169 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 9.1129628843057250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9099984021489957 " " Order of pole = 1.000000001432431 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.90900000000001 " " y[1] (analytic) = 0.27440247489079866 " " y[1] (numeric) = 0.27440247489080116 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 9.1034230154108790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9089991178559518 " " Order of pole = 1.0000000008918946 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9080000000000101 " " y[1] (analytic) = 0.27469018380893356 " " y[1] (numeric) = 0.2746901838089361 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 9.2959745456867460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9080013200056578 " " Order of pole = 0.9999999991793036 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9070000000000102 " " y[1] (analytic) = 0.27497834545529243 " " y[1] (numeric) = 0.27497834545529504 " " absolute error = 2.609024107869118000000000000000E-15 " " relative error = 9.488107521882329000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9069997553270939 " " Order of pole = 1.0000000003549356 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9060000000000104 " " y[1] (analytic) = 0.2752669607802357 " " y[1] (numeric) = 0.2752669607802383 " " absolute error = 2.609024107869118000000000000000E-15 " " relative error = 9.4781593129590250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9059988295048538 " " Order of pole = 1.0000000011158843 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9050000000000105 " " y[1] (analytic) = 0.27555603073661883 " " y[1] (numeric) = 0.2755560307366215 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 9.6696677331921080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9049989300179178 " " Order of pole = 1.0000000010176677 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9040000000000106 " " y[1] (analytic) = 0.2758455562798003 " " y[1] (numeric) = 0.275845556279803 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 9.8607584875233230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.904001620272942 " " Order of pole = 0.9999999989104289 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9030000000000107 " " y[1] (analytic) = 0.27613553836764926 " " y[1] (numeric) = 0.276135538367652 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 9.8504032708391920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9030008367434175 " " Order of pole = 0.9999999995357545 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.9020000000000108 " " y[1] (analytic) = 0.2764259779605536 " " y[1] (numeric) = 0.27642597796055635 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 9.840053494247881000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.902002255314211 " " Order of pole = 0.9999999984334593 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.901000000000011 " " y[1] (analytic) = 0.27671687602142797 " " y[1] (numeric) = 0.27671687602143075 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 1.0030315467091216000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.9009997232836824 " " Order of pole = 1.0000000004205845 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.900000000000011 " " y[1] (analytic) = 0.27700823351572157 " " y[1] (numeric) = 0.27700823351572434 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 1.0019765572799715000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.900002116052538 " " Order of pole = 0.9999999985194794 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8990000000000111 " " y[1] (analytic) = 0.2773000514114263 " " y[1] (numeric) = 0.2773000514114291 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.0209405654215807000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8990015068795907 " " Order of pole = 0.9999999989688835 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8980000000000112 " " y[1] (analytic) = 0.27759233067908473 " " y[1] (numeric) = 0.27759233067908756 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.0198656086313326000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8979996085037463 " " Order of pole = 1.000000000580103 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8970000000000113 " " y[1] (analytic) = 0.2778850722917982 " " y[1] (numeric) = 0.2778850722918011 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.0387675164480596000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8969996527488457 " " Order of pole = 1.0000000004606022 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8960000000000115 " " y[1] (analytic) = 0.2781782772252351 " " y[1] (numeric) = 0.27817827722523797 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.0376726367056346000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8959999233854283 " " Order of pole = 1.0000000002638405 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8950000000000116 " " y[1] (analytic) = 0.2784719464576385 " " y[1] (numeric) = 0.27847194645764145 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.056512533015320900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8950005641608867 " " Order of pole = 0.9999999997883915 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8940000000000117 " " y[1] (analytic) = 0.2787660809698349 " " y[1] (numeric) = 0.2787660809698379 " " absolute error = 2.9976021664879227000000000000000E-15 " " relative error = 1.075310940290577000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.893998146003217 " " Order of pole = 1.0000000017204975 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8930000000000118 " " y[1] (analytic) = 0.279060681745242 " " y[1] (numeric) = 0.27906068174524506 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.0940678918380933000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8930006012772354 " " Order of pole = 0.9999999996951008 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.892000000000012 " " y[1] (analytic) = 0.27935574976987715 " " y[1] (numeric) = 0.27935574976988026 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.1127834209645612000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8920001840583152 " " Order of pole = 1.0000000001027072 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.891000000000012 " " y[1] (analytic) = 0.2796512860323655 " " y[1] (numeric) = 0.2796512860323686 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.1116074283279573000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8909990035181983 " " Order of pole = 1.0000000010158843 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8900000000000121 " " y[1] (analytic) = 0.27994729152394826 " " y[1] (numeric) = 0.27994729152395137 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.1104320574162473000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8900016597070062 " " Order of pole = 0.9999999988671018 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8890000000000122 " " y[1] (analytic) = 0.2802437672384911 " " y[1] (numeric) = 0.2802437672384942 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.109257308229431000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8890018292223083 " " Order of pole = 0.9999999987422044 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8880000000000123 " " y[1] (analytic) = 0.2805407141724924 " " y[1] (numeric) = 0.28054071417249554 " " absolute error = 3.164135620181696000000000000000E-15 " " relative error = 1.1278703804240713000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8880019068635183 " " Order of pole = 0.9999999986469277 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8870000000000124 " " y[1] (analytic) = 0.28083813332509167 " " y[1] (numeric) = 0.2808381333250949 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 1.1464421634244258000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8870013156047973 " " Order of pole = 0.9999999991046344 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8860000000000126 " " y[1] (analytic) = 0.2811360256980781 " " y[1] (numeric) = 0.2811360256980813 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 1.1452273906975716000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.886000504386525 " " Order of pole = 0.9999999998224602 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8850000000000127 " " y[1] (analytic) = 0.28143439229589856 " " y[1] (numeric) = 0.28143439229590184 " " absolute error = 3.2751579226442120000000000000000E-15 " " relative error = 1.163737628484556000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8850013636387335 " " Order of pole = 0.9999999990839612 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8840000000000128 " " y[1] (analytic) = 0.28173323412566664 " " y[1] (numeric) = 0.28173323412567 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.1822066658950964000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.883999306082709 " " Order of pole = 1.0000000007661392 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8830000000000129 " " y[1] (analytic) = 0.2820325521971707 " " y[1] (numeric) = 0.2820325521971741 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 1.2006345362358838000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8830005193069543 " " Order of pole = 0.9999999997797779 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.882000000000013 " " y[1] (analytic) = 0.28233234752288267 " " y[1] (numeric) = 0.28233234752288605 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 1.1993596393811311000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8820026932351606 " " Order of pole = 0.9999999979871834 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.881000000000013 " " y[1] (analytic) = 0.28263262111796633 " " y[1] (numeric) = 0.2826326211179698 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 1.2177261643486928000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8809980856571402 " " Order of pole = 1.0000000017732393 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8800000000000132 " " y[1] (analytic) = 0.28293337400028634 " " y[1] (numeric) = 0.2829333740002898 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 1.216431744222052100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.880000050104495 " " Order of pole = 1.0000000002011689 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8790000000000133 " " y[1] (analytic) = 0.2832346071904163 " " y[1] (numeric) = 0.2832346071904198 " " absolute error = 3.497202527569243000000000000000E-15 " " relative error = 1.2347370126342302000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.878999475572574 " " Order of pole = 1.000000000664805 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8780000000000134 " " y[1] (analytic) = 0.283536321711648 " " y[1] (numeric) = 0.28353632171165155 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.2530012583056482000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8780043507845527 " " Order of pole = 0.9999999966376087 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8770000000000135 " " y[1] (analytic) = 0.28383851858999964 " " y[1] (numeric) = 0.28383851859000325 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 1.2712245145429973000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8770010152746655 " " Order of pole = 0.9999999993631885 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8760000000000137 " " y[1] (analytic) = 0.2841411988542249 " " y[1] (numeric) = 0.2841411988542285 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 1.2698703477642867000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8760004211557386 " " Order of pole = 0.9999999998808544 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8750000000000138 " " y[1] (analytic) = 0.2844443635358213 " " y[1] (numeric) = 0.284444363535825 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 1.2880325472863963000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8749997266942018 " " Order of pole = 1.000000000439826 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8740000000000139 " " y[1] (analytic) = 0.2847480136690394 " " y[1] (numeric) = 0.2847480136690431 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.306153846192279200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8740015688897502 " " Order of pole = 0.9999999988996713 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.873000000000014 " " y[1] (analytic) = 0.2850521502908915 " " y[1] (numeric) = 0.2850521502908952 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.3047602442917333000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8729996363001815 " " Order of pole = 1.0000000005203749 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.872000000000014 " " y[1] (analytic) = 0.28535677444116014 " " y[1] (numeric) = 0.2853567744411639 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.3228206308113700000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8720015506828223 " " Order of pole = 0.999999998894241 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8710000000000142 " " y[1] (analytic) = 0.2856618871624076 " " y[1] (numeric) = 0.2856618871624114 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.340840205532621000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.870999369996761 " " Order of pole = 1.0000000007349588 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8700000000000143 " " y[1] (analytic) = 0.28596748949998435 " " y[1] (numeric) = 0.2859674894999882 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.3394073017370040000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8699993123175025 " " Order of pole = 1.000000000782567 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8690000000000144 " " y[1] (analytic) = 0.2862735825020381 " " y[1] (numeric) = 0.28627358250204205 " " absolute error = 3.941291737419305700000000000000E-15 " " relative error = 1.376757052806731000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.869000695484268 " " Order of pole = 0.99999999959498 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8680000000000145 " " y[1] (analytic) = 0.2865801672195231 " " y[1] (numeric) = 0.28658016721952706 " " absolute error = 3.941291737419305700000000000000E-15 " " relative error = 1.3752841920844575000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8679992835669212 " " Order of pole = 1.0000000008470913 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8670000000000146 " " y[1] (analytic) = 0.2868872447062086 " " y[1] (numeric) = 0.2868872447062126 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.3931615860940602000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8669987111925936 " " Order of pole = 1.0000000013267467 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8660000000000148 " " y[1] (analytic) = 0.2871948160186884 " " y[1] (numeric) = 0.2871948160186924 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.3916695795757270000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8659997576622611 " " Order of pole = 1.0000000004245102 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8650000000000149 " " y[1] (analytic) = 0.2875028822163896 " " y[1] (numeric) = 0.2875028822163937 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.4287944383184710000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.865001538861347 " " Order of pole = 0.9999999989178594 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.864000000000015 " " y[1] (analytic) = 0.28781144436158207 " " y[1] (numeric) = 0.2878114443615862 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.427262630304705000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8640014217132412 " " Order of pole = 0.9999999990168522 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.863000000000015 " " y[1] (analytic) = 0.2881205035193873 " " y[1] (numeric) = 0.2881205035193914 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.4257316438559772000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8630021001204637 " " Order of pole = 0.999999998434733 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8620000000000152 " " y[1] (analytic) = 0.2884300607577876 " " y[1] (numeric) = 0.2884300607577917 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.4242014789722876000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8620015710198514 " " Order of pole = 0.9999999988955146 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8610000000000153 " " y[1] (analytic) = 0.2887401171476356 " " y[1] (numeric) = 0.28874011714763975 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 1.441897434784091000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8610021686329572 " " Order of pole = 0.9999999983531076 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8600000000000154 " " y[1] (analytic) = 0.2890506737626632 " " y[1] (numeric) = 0.2890506737626674 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 1.4595529007621863000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8599999334285722 " " Order of pole = 1.0000000002707523 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8590000000000155 " " y[1] (analytic) = 0.28936173167949114 " " y[1] (numeric) = 0.2893617316794954 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.4771679102132643000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8590009617680199 " " Order of pole = 0.9999999994342055 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8580000000000156 " " y[1] (analytic) = 0.28967329197763814 " " y[1] (numeric) = 0.2896732919776424 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.4755791311049898000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8580017548102996 " " Order of pole = 0.9999999987068691 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8570000000000157 " " y[1] (analytic) = 0.2899853557395302 " " y[1] (numeric) = 0.28998535573953454 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 1.4931339498147878000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8570018078322732 " " Order of pole = 0.9999999986865085 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8560000000000159 " " y[1] (analytic) = 0.29029792405051036 " " y[1] (numeric) = 0.2902979240505147 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 1.4915262691595188000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8559987242465645 " " Order of pole = 1.0000000013419452 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.855000000000016 " " y[1] (analytic) = 0.29061099799884765 " " y[1] (numeric) = 0.29061099799885204 " " absolute error = 4.385380947269368300000000000000E-15 " " relative error = 1.5090209859458786000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.855000195866965 " " Order of pole = 1.0000000000873435 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.854000000000016 " " y[1] (analytic) = 0.290924578675747 " " y[1] (numeric) = 0.2909245786757514 " " absolute error = 4.385380947269368300000000000000E-15 " " relative error = 1.5073944481525364000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8539981066448084 " " Order of pole = 1.0000000017864004 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8530000000000162 " " y[1] (analytic) = 0.29123866717535846 " " y[1] (numeric) = 0.2912386671753629 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 1.5248291518333001000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8529997337911972 " " Order of pole = 1.000000000424114 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8520000000000163 " " y[1] (analytic) = 0.2915532645947868 " " y[1] (numeric) = 0.29155326459479136 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 1.5612633963435762000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8520001882383126 " " Order of pole = 1.0000000001163833 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8510000000000164 " " y[1] (analytic) = 0.2918683720341014 " " y[1] (numeric) = 0.2918683720341059 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 1.5595778224408996000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8510007557946055 " " Order of pole = 0.9999999995493969 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8500000000000165 " " y[1] (analytic) = 0.2921839905963452 " " y[1] (numeric) = 0.2921839905963498 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 1.5768918559811168000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8499998588739142 " " Order of pole = 1.000000000339634 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8490000000000166 " " y[1] (analytic) = 0.2925001213875451 " " y[1] (numeric) = 0.2925001213875497 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 1.57518756926936000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8490020041185378 " " Order of pole = 0.9999999984585202 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8480000000000167 " " y[1] (analytic) = 0.2928167655167211 " " y[1] (numeric) = 0.29281676551672575 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 1.592441845055276900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8480017094183305 " " Order of pole = 0.9999999987425348 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8470000000000169 " " y[1] (analytic) = 0.29313392409589634 " " y[1] (numeric) = 0.293133924095901 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 1.5907188899433614000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8469970858268303 " " Order of pole = 1.0000000027576164 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.846000000000017 " " y[1] (analytic) = 0.29345159824010664 " " y[1] (numeric) = 0.29345159824011136 " " absolute error = 4.718447854656915300000000000000E-15 " " relative error = 1.6079134967928200000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8460001928598906 " " Order of pole = 1.0000000000370175 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.845000000000017 " " y[1] (analytic) = 0.29376978906741064 " " y[1] (numeric) = 0.2937697890674153 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 1.587275777481552000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8449986190577783 " " Order of pole = 1.0000000014100703 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8440000000000172 " " y[1] (analytic) = 0.29408849769889905 " " y[1] (numeric) = 0.2940884976989038 " " absolute error = 4.718447854656915300000000000000E-15 " " relative error = 1.6044312822760830000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8439997118889517 " " Order of pole = 1.0000000004746372 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8430000000000173 " " y[1] (analytic) = 0.2944077252587053 " " y[1] (numeric) = 0.29440772525871 " " absolute error = 4.718447854656915300000000000000E-15 " " relative error = 1.6026915905520710000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8429996483581452 " " Order of pole = 1.0000000005675176 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8420000000000174 " " y[1] (analytic) = 0.29472747287401463 " " y[1] (numeric) = 0.2947274728740194 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 1.6197875818413673000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.842001364141917 " " Order of pole = 0.9999999990128412 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8410000000000175 " " y[1] (analytic) = 0.2950477416750748 " " y[1] (numeric) = 0.29504774167507963 " " absolute error = 4.829470157119431000000000000000E-15 " " relative error = 1.6368436273062373000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8410005552334165 " " Order of pole = 0.9999999997502496 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8400000000000176 " " y[1] (analytic) = 0.2953685327952056 " " y[1] (numeric) = 0.2953685327952104 " " absolute error = 4.829470157119431000000000000000E-15 " " relative error = 1.6350658993414016000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8400010614814455 " " Order of pole = 0.9999999992986837 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8390000000000177 " " y[1] (analytic) = 0.2956898473708089 " " y[1] (numeric) = 0.2956898473708137 " " absolute error = 4.829470157119431000000000000000E-15 " " relative error = 1.6332891372705974000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8389985858166062 " " Order of pole = 1.0000000015091484 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8380000000000178 " " y[1] (analytic) = 0.2960116865413789 " " y[1] (numeric) = 0.29601168654138377 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.6502663680029495000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.837999667960831 " " Order of pole = 1.000000000543766 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.837000000000018 " " y[1] (analytic) = 0.2963340514495122 " " y[1] (numeric) = 0.29633405144951713 " " absolute error = 4.9404924595819466000000000000000E-15 " " relative error = 1.6672037639331777000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8370001272107994 " " Order of pole = 1.0000000000954081 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.836000000000018 " " y[1] (analytic) = 0.29665694324091785 " " y[1] (numeric) = 0.29665694324092284 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 1.6841013583679731000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8360007881953648 " " Order of pole = 0.9999999995723954 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8350000000000182 " " y[1] (analytic) = 0.2969803630644276 " " y[1] (numeric) = 0.2969803630644326 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 1.6822673254424433000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.834999221057017 " " Order of pole = 1.0000000009343744 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8340000000000183 " " y[1] (analytic) = 0.2973043120720059 " " y[1] (numeric) = 0.29730431207201097 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 1.6991057838478324000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8339996035395802 " " Order of pole = 1.0000000006172982 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8330000000000184 " " y[1] (analytic) = 0.2976287914187607 " " y[1] (numeric) = 0.2976287914187658 " " absolute error = 5.10702591327572000000000000000E-15 " " relative error = 1.7159045295756306000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8330010223692847 " " Order of pole = 0.999999999306123 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8320000000000185 " " y[1] (analytic) = 0.2979538022629531 " " y[1] (numeric) = 0.29795380226295826 " " absolute error = 5.162537064506978000000000000000E-15 " " relative error = 1.7326635959325282000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8320018500480157 " " Order of pole = 0.9999999985487253 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8310000000000186 " " y[1] (analytic) = 0.2982793457660081 " " y[1] (numeric) = 0.2982793457660133 " " absolute error = 5.162537064506978000000000000000E-15 " " relative error = 1.7307725586057995000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.831000381050756 " " Order of pole = 0.9999999998920135 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8300000000000187 " " y[1] (analytic) = 0.29860542309252486 " " y[1] (numeric) = 0.2986054230925301 " " absolute error = 5.218048215738236000000000000000E-15 " " relative error = 1.747472688773435100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.829998704507515 " " Order of pole = 1.0000000013657644 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8290000000000188 " " y[1] (analytic) = 0.298932035410287 " " y[1] (numeric) = 0.2989320354102923 " " absolute error = 5.2735593669694940000000000000000E-15 " " relative error = 1.7641332283880130000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8289996527103434 " " Order of pole = 1.0000000005630092 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.828000000000019 " " y[1] (analytic) = 0.2992591838902734 " " y[1] (numeric) = 0.2992591838902787 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.7807542107562227000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8279996227341313 " " Order of pole = 1.0000000005840182 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.827000000000019 " " y[1] (analytic) = 0.29958686970666826 " " y[1] (numeric) = 0.2995868697066736 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 1.7788064354818203000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8270016216494138 " " Order of pole = 0.9999999987913348 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8260000000000192 " " y[1] (analytic) = 0.29991509403687183 " " y[1] (numeric) = 0.2999150940368772 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 1.795368681500913200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8260016652362157 " " Order of pole = 0.9999999986594474 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8250000000000193 " " y[1] (analytic) = 0.3002438580615112 " " y[1] (numeric) = 0.3002438580615166 " " absolute error = 5.384581669432009000000000000000E-15 " " relative error = 1.7934027707334035000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8250012146141168 " " Order of pole = 0.9999999991006767 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8240000000000194 " " y[1] (analytic) = 0.3005731629644505 " " y[1] (numeric) = 0.30057316296445596 " " absolute error = 5.440092820663267000000000000000E-15 " " relative error = 1.80990636922122000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8239995799128896 " " Order of pole = 1.0000000006488552 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8230000000000195 " " y[1] (analytic) = 0.3009030099328019 " " y[1] (numeric) = 0.3009030099328074 " " absolute error = 5.495603971894525000000000000000E-15 " " relative error = 1.8263705547916625000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8230031299721048 " " Order of pole = 0.9999999973889278 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8220000000000196 " " y[1] (analytic) = 0.3012334001569361 " " y[1] (numeric) = 0.3012334001569416 " " absolute error = 5.495603971894525000000000000000E-15 " " relative error = 1.824367407143907000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8220024523232203 " " Order of pole = 0.9999999980216625 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8210000000000197 " " y[1] (analytic) = 0.3015643348304932 " " y[1] (numeric) = 0.3015643348304987 " " absolute error = 5.495603971894525000000000000000E-15 " " relative error = 1.822365358616945800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.820999055881762 " " Order of pole = 1.000000001081391 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8200000000000198 " " y[1] (analytic) = 0.3018958151503934 " " y[1] (numeric) = 0.3018958151503989 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 1.8387519284957365000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8200008745022616 " " Order of pole = 0.9999999994296527 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.81900000000002 " " y[1] (analytic) = 0.30222784231684785 " " y[1] (numeric) = 0.3022278423168534 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 1.8367318777024313000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8190003587410941 " " Order of pole = 0.9999999999466365 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.81800000000002 " " y[1] (analytic) = 0.3025604175333695 " " y[1] (numeric) = 0.30256041753337515 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 1.871407195874794000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8179999944685057 " " Order of pole = 1.0000000002258087 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8170000000000202 " " y[1] (analytic) = 0.30289354200678414 " " y[1] (numeric) = 0.3028935420067898 " " absolute error = 5.662137425588298000000000000000E-15 " " relative error = 1.8693490089205925000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8169998821974918 " " Order of pole = 1.0000000003512284 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8160000000000203 " " y[1] (analytic) = 0.3032272169472411 " " y[1] (numeric) = 0.3032272169472468 " " absolute error = 5.717648576819556000000000000000E-15 " " relative error = 1.885598738260483000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8160032791520664 " " Order of pole = 0.9999999972359159 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8150000000000204 " " y[1] (analytic) = 0.30356144356822434 " " y[1] (numeric) = 0.3035614435682301 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.901809287829835000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.815001101630851 " " Order of pole = 0.9999999991987867 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8140000000000205 " " y[1] (analytic) = 0.3038962230865637 " " y[1] (numeric) = 0.3038962230865695 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.8997142081645257000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8139982893616156 " " Order of pole = 1.0000000018206237 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8130000000000206 " " y[1] (analytic) = 0.3042315567224457 " " y[1] (numeric) = 0.30423155672245145 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.8976202831311614000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8130014120237965 " " Order of pole = 0.9999999989945234 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8120000000000207 " " y[1] (analytic) = 0.30456744569942457 " " y[1] (numeric) = 0.30456744569943034 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.8955275127297433000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8120011374880363 " " Order of pole = 0.9999999991547082 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8110000000000208 " " y[1] (analytic) = 0.30490389124443384 " " y[1] (numeric) = 0.3049038912444396 " " absolute error = 5.773159728050814000000000000000E-15 " " relative error = 1.8934358969602705000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.811001363003819 " " Order of pole = 0.9999999989376427 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.810000000000021 " " y[1] (analytic) = 0.30524089458779713 " " y[1] (numeric) = 0.305240894587803 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 1.9277174634347197000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8099981457111098 " " Order of pole = 1.0000000019611193 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.809000000000021 " " y[1] (analytic) = 0.30557845696323976 " " y[1] (numeric) = 0.30557845696324565 " " absolute error = 5.88418203051333000000000000000E-15 " " relative error = 1.925587977957877000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8090010880687812 " " Order of pole = 0.9999999991957509 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8080000000000211 " " y[1] (analytic) = 0.30591657960789953 " " y[1] (numeric) = 0.3059165796079055 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 1.9597513611913547000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8079999539134308 " " Order of pole = 1.0000000002838156 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8070000000000213 " " y[1] (analytic) = 0.3062552637623387 " " y[1] (numeric) = 0.3062552637623447 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 1.957584094824984200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8069990842190529 " " Order of pole = 1.0000000011613306 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8060000000000214 " " y[1] (analytic) = 0.3065945106705548 " " y[1] (numeric) = 0.3065945106705608 " " absolute error = 5.995204332975845000000000000000E-15 " " relative error = 1.95541802749948000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.806001075059092 " " Order of pole = 0.999999999213598 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8050000000000215 " " y[1] (analytic) = 0.30693432157999234 " " y[1] (numeric) = 0.3069343215799984 " " absolute error = 6.050715484207103000000000000000E-15 " " relative error = 1.9713388366149803000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.804999675976698 " " Order of pole = 1.0000000005424958 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8040000000000216 " " y[1] (analytic) = 0.30727469774155436 " " y[1] (numeric) = 0.3072746977415604 " " absolute error = 6.050715484207103000000000000000E-15 " " relative error = 1.96915513339673000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8039993406911885 " " Order of pole = 1.0000000008764633 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8030000000000217 " " y[1] (analytic) = 0.30761564040961353 " " y[1] (numeric) = 0.3076156404096197 " " absolute error = 6.161737786669619000000000000000E-15 " " relative error = 2.003063881428395000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8029996755559106 " " Order of pole = 1.0000000005422738 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.8020000000000218 " " y[1] (analytic) = 0.30795715084202435 " " y[1] (numeric) = 0.3079571508420305 " " absolute error = 6.161737786669619000000000000000E-15 " " relative error = 2.0008425749563005000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8020001560669094 " " Order of pole = 1.0000000000943103 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.801000000000022 " " y[1] (analytic) = 0.3082992303001341 " " y[1] (numeric) = 0.3082992303001403 " " absolute error = 6.161737786669619000000000000000E-15 " " relative error = 1.9986225008317637000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.8009991898034046 " " Order of pole = 1.0000000010019345 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.800000000000022 " " y[1] (analytic) = 0.3086418800487949 " " y[1] (numeric) = 0.3086418800488011 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 2.014389277604827200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.799999882464877 " " Order of pole = 1.0000000003841425 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7990000000000221 " " y[1] (analytic) = 0.3089851013563752 " " y[1] (numeric) = 0.30898510135638146 " " absolute error = 6.2727600891321340000000000000000E-15 " " relative error = 2.0301173297987918000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7990000511915085 " " Order of pole = 1.0000000001826148 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7980000000000222 " " y[1] (analytic) = 0.3093288954947716 " " y[1] (numeric) = 0.30932889549477793 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 2.0458066907203484000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.798001153501406 " " Order of pole = 0.9999999991761044 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7970000000000224 " " y[1] (analytic) = 0.30967326373942083 " " y[1] (numeric) = 0.30967326373942716 " " absolute error = 6.328271240363392000000000000000E-15 " " relative error = 2.043531677209437800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7970018261415177 " " Order of pole = 0.9999999985153156 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7960000000000225 " " y[1] (analytic) = 0.310018207369311 " " y[1] (numeric) = 0.3100182073693174 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 2.059163700662888000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7959997666154726 " " Order of pole = 1.0000000004764011 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7950000000000226 " " y[1] (analytic) = 0.3103637276669942 " " y[1] (numeric) = 0.31036372766700066 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.074757121661771000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7950003290198642 " " Order of pole = 0.9999999999273168 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7940000000000227 " " y[1] (analytic) = 0.31070982591859797 " " y[1] (numeric) = 0.3107098259186044 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.0724460592092510000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7940005720258787 " " Order of pole = 0.9999999997547828 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7930000000000228 " " y[1] (analytic) = 0.3110565034138372 " " y[1] (numeric) = 0.31105650341384367 " " absolute error = 6.439293542825908000000000000000E-15 " " relative error = 2.0701362846154397000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7930009018340702 " " Order of pole = 0.9999999993994582 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.792000000000023 " " y[1] (analytic) = 0.31140376144602655 " " y[1] (numeric) = 0.31140376144603304 " " absolute error = 6.494804694057166000000000000000E-15 " " relative error = 2.0856538995862017000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7920011191818093 " " Order of pole = 0.999999999167235 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.791000000000023 " " y[1] (analytic) = 0.3117516013120921 " " y[1] (numeric) = 0.31175160131209867 " " absolute error = 6.5503158452884240000000000000000E-15 " " relative error = 2.1011330231247000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.790999537950244 " " Order of pole = 1.000000000750184 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7900000000000231 " " y[1] (analytic) = 0.3121000243125838 " " y[1] (numeric) = 0.31210002431259043 " " absolute error = 6.6058269965196810000000000000000E-15 " " relative error = 2.1165736885376257000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7900028141708053 " " Order of pole = 0.9999999975421936 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7890000000000232 " " y[1] (analytic) = 0.31244903175168737 " " y[1] (numeric) = 0.31244903175169403 " " absolute error = 6.661338147750939000000000000000E-15 " " relative error = 2.1319759291316687000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.789000502126849 " " Order of pole = 0.9999999998111679 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7880000000000233 " " y[1] (analytic) = 0.3127986249372366 " " y[1] (numeric) = 0.3127986249372433 " " absolute error = 6.716849298982197000000000000000E-15 " " relative error = 2.1473397782135203000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7879991547934506 " " Order of pole = 1.0000000010800179 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7870000000000235 " " y[1] (analytic) = 0.3131488051807256 " " y[1] (numeric) = 0.31314880518073235 " " absolute error = 6.772360450213455000000000000000E-15 " " relative error = 2.162665269089871000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7870018141097923 " " Order of pole = 0.9999999984813304 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7860000000000236 " " y[1] (analytic) = 0.31349957379732113 " " y[1] (numeric) = 0.3134995737973279 " " absolute error = 6.772360450213455000000000000000E-15 " " relative error = 2.16024550470101000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7859996620123555 " " Order of pole = 1.000000000583487 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7850000000000237 " " y[1] (analytic) = 0.3138509321058749 " " y[1] (numeric) = 0.3138509321058817 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 2.1755142021185360000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7850027481691615 " " Order of pole = 0.999999997590244 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7840000000000238 " " y[1] (analytic) = 0.31420288142893604 " " y[1] (numeric) = 0.31420288142894287 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 2.1730773347439802000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7840001598568356 " " Order of pole = 1.0000000000887503 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.783000000000024 " " y[1] (analytic) = 0.3145554230927634 " " y[1] (numeric) = 0.31455542309277024 " " absolute error = 6.827871601444713000000000000000E-15 " " relative error = 2.1706418329437455000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7829996608502021 " " Order of pole = 1.0000000005963 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.782000000000024 " " y[1] (analytic) = 0.31490855842733817 " " y[1] (numeric) = 0.31490855842734505 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 2.1858354015691953000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7819988807197202 " " Order of pole = 1.0000000013611352 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7810000000000241 " " y[1] (analytic) = 0.3152622887663764 " " y[1] (numeric) = 0.31526228876638335 " " absolute error = 6.938893903907228000000000000000E-15 " " relative error = 2.200990778522598000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.780998593313014 " " Order of pole = 1.000000001611598 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7800000000000242 " " y[1] (analytic) = 0.31561661544734165 " " y[1] (numeric) = 0.31561661544734865 " " absolute error = 6.994405055138486000000000000000E-15 " " relative error = 2.216107997110644000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7800013513657458 " " Order of pole = 0.9999999989512105 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7790000000000243 " " y[1] (analytic) = 0.3159715398114574 " " y[1] (numeric) = 0.3159715398114645 " " absolute error = 7.049916206369744000000000000000E-15 " " relative error = 2.2311870906400247000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7790002043154243 " " Order of pole = 1.0000000000673577 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7780000000000244 " " y[1] (analytic) = 0.31632706320372017 " " y[1] (numeric) = 0.3163270632037272 " " absolute error = 7.049916206369744000000000000000E-15 " " relative error = 2.228679435445419000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7779997529923781 " " Order of pole = 1.000000000536712 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7770000000000246 " " y[1] (analytic) = 0.31668318697291165 " " y[1] (numeric) = 0.31668318697291875 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.243702112991803000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7769986466396488 " " Order of pole = 1.0000000015996875 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7760000000000247 " " y[1] (analytic) = 0.3170399124716122 " " y[1] (numeric) = 0.3170399124716193 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 2.2411775546516474000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7760015572330277 " " Order of pole = 0.9999999987911465 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7750000000000248 " " y[1] (analytic) = 0.3173972410562129 " " y[1] (numeric) = 0.31739724105622014 " " absolute error = 7.216449660063518000000000000000E-15 " " relative error = 2.2736333926687918000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7750023221784594 " " Order of pole = 0.9999999980267358 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.774000000000025 " " y[1] (analytic) = 0.31775517408692955 " " y[1] (numeric) = 0.3177551740869367 " " absolute error = 7.16093850883226000000000000000E-15 " " relative error = 2.2536024879560934000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7739997931509197 " " Order of pole = 1.0000000004526814 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.773000000000025 " " y[1] (analytic) = 0.31811371292781415 " " y[1] (numeric) = 0.3181137129278214 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.2859626969130112000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.772997267417175 " " Order of pole = 1.0000000029718912 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.772000000000025 " " y[1] (analytic) = 0.31847285894676935 " " y[1] (numeric) = 0.3184728589467766 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.2833847868054072000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7720006470862526 " " Order of pole = 0.9999999996595932 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7710000000000252 " " y[1] (analytic) = 0.31883261351556047 " " y[1] (numeric) = 0.31883261351556774 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.280808331089966000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7710010453787726 " " Order of pole = 0.9999999992402735 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7700000000000253 " " y[1] (analytic) = 0.31919297800982904 " " y[1] (numeric) = 0.3191929780098363 " " absolute error = 7.271960811294775000000000000000E-15 " " relative error = 2.2782333297666865000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7700016106148297 " " Order of pole = 0.9999999986706598 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7690000000000254 " " y[1] (analytic) = 0.3195539538091059 " " y[1] (numeric) = 0.3195539538091132 " " absolute error = 7.327471962526033000000000000000E-15 " " relative error = 2.293031231559505000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.769000477982149 " " Order of pole = 0.9999999997854196 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7680000000000256 " " y[1] (analytic) = 0.3199155422968244 " " y[1] (numeric) = 0.3199155422968318 " " absolute error = 7.382983113757291000000000000000E-15 " " relative error = 2.3077913191561053000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.768000481343167 " " Order of pole = 0.9999999998120703 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7670000000000257 " " y[1] (analytic) = 0.32027774486033356 " " y[1] (numeric) = 0.320277744860341 " " absolute error = 7.438494264988549000000000000000E-15 " " relative error = 2.322513625863177000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.767002379216419 " " Order of pole = 0.9999999979313383 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7660000000000258 " " y[1] (analytic) = 0.3206405628909116 " " y[1] (numeric) = 0.3206405628909191 " " absolute error = 7.494005416219807000000000000000E-15 " " relative error = 2.3371981849874118000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.765999601627662 " " Order of pole = 1.0000000006938805 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7650000000000259 " " y[1] (analytic) = 0.32100399778377897 " " y[1] (numeric) = 0.3210039977837865 " " absolute error = 7.549516567451064000000000000000E-15 " " relative error = 2.3518450298355004000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.764999916500714 " " Order of pole = 1.0000000003367813 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.764000000000026 " " y[1] (analytic) = 0.32136805093811205 " " y[1] (numeric) = 0.32136805093811965 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.3664541937141323000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7639987148130247 " " Order of pole = 1.000000001577769 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.763000000000026 " " y[1] (analytic) = 0.3217327237570565 " " y[1] (numeric) = 0.32173272375706413 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.3637719004377533000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7629991360946482 " " Order of pole = 1.0000000011680612 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7620000000000262 " " y[1] (analytic) = 0.3220980176477408 " " y[1] (numeric) = 0.3220980176477484 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.361091128166918000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7619996469253185 " " Order of pole = 1.0000000006306937 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7610000000000263 " " y[1] (analytic) = 0.3224639340212897 " " y[1] (numeric) = 0.3224639340212974 " " absolute error = 7.716050021144838000000000000000E-15 " " relative error = 2.3928412473673444000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.761001830139695 " " Order of pole = 0.9999999983932852 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7600000000000264 " " y[1] (analytic) = 0.3228304742928382 " " y[1] (numeric) = 0.32283047429284595 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 2.4073195659114090000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.759999239609027 " " Order of pole = 1.0000000010753602 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7590000000000265 " " y[1] (analytic) = 0.32319763988154476 " " y[1] (numeric) = 0.32319763988155253 " " absolute error = 7.771561172376096000000000000000E-15 " " relative error = 2.4045847535348502000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.759000368157895 " " Order of pole = 0.9999999999481428 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7580000000000267 " " y[1] (analytic) = 0.32356543221060535 " " y[1] (numeric) = 0.3235654322106132 " " absolute error = 7.827072323607354000000000000000E-15 " " relative error = 2.4190075775810296000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7579994822593341 " " Order of pole = 1.000000000785013 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7570000000000268 " " y[1] (analytic) = 0.32393385270726727 " " y[1] (numeric) = 0.32393385270727515 " " absolute error = 7.882583474838611000000000000000E-15 " " relative error = 2.433392931600128000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7569987644437632 " " Order of pole = 1.0000000015104948 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7560000000000269 " " y[1] (analytic) = 0.3243029028028428 " " y[1] (numeric) = 0.3243029028028507 " " absolute error = 7.882583474838611000000000000000E-15 " " relative error = 2.430623780025416800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7559999912715396 " " Order of pole = 1.0000000003001528 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.755000000000027 " " y[1] (analytic) = 0.324672583932723 " " y[1] (numeric) = 0.324672583932731 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.462051362783844200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7550018147675996 " " Order of pole = 0.9999999984217034 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.754000000000027 " " y[1] (analytic) = 0.3250428975363923 " " y[1] (numeric) = 0.3250428975364003 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 2.459246406516589000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7540002857435304 " " Order of pole = 1.0000000000404068 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7530000000000272 " " y[1] (analytic) = 0.3254138450574417 " " y[1] (numeric) = 0.32541384505744975 " " absolute error = 8.049116928532385000000000000000E-15 " " relative error = 2.4735016812550073000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7530010246738834 " " Order of pole = 0.9999999991989004 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7520000000000273 " " y[1] (analytic) = 0.32578542794358334 " " y[1] (numeric) = 0.32578542794359144 " " absolute error = 8.104628079763643000000000000000E-15 " " relative error = 2.4877196413975677000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7519984703655382 " " Order of pole = 1.000000001870001 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7510000000000274 " " y[1] (analytic) = 0.3261576476466645 " " y[1] (numeric) = 0.32615764764667265 " " absolute error = 8.1601392309949010000000000000E-15 " " relative error = 2.5019003202509615000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7509978748139456 " " Order of pole = 1.0000000024846596 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7500000000000275 " " y[1] (analytic) = 0.32653050562268177 " " y[1] (numeric) = 0.32653050562269 " " absolute error = 8.215650382226158000000000000000E-15 " " relative error = 2.5160437511218780000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7499993210934346 " " Order of pole = 1.0000000009789556 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7490000000000276 " " y[1] (analytic) = 0.32690400333179526 " " y[1] (numeric) = 0.3269040033318035 " " absolute error = 8.271161533457416000000000000000E-15 " " relative error = 2.5301499673170100000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.749003211845657 " " Order of pole = 0.9999999969930524 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7480000000000278 " " y[1] (analytic) = 0.327278142238343 " " y[1] (numeric) = 0.32727814223835133 " " absolute error = 8.326672684688674000000000000000E-15 " " relative error = 2.5442190021430470000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7480003158135367 " " Order of pole = 0.9999999999185185 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7470000000000279 " " y[1] (analytic) = 0.32765292381085515 " " y[1] (numeric) = 0.32765292381086353 " " absolute error = 8.382183835919932000000000000000E-15 " " relative error = 2.558250888906681000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7470001793467818 " " Order of pole = 1.0000000001021512 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.746000000000028 " " y[1] (analytic) = 0.3280283495220686 " " y[1] (numeric) = 0.328028349522077 " " absolute error = 8.382183835919932000000000000000E-15 " " relative error = 2.555322992092794000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7460013240220735 " " Order of pole = 0.999999998964519 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.745000000000028 " " y[1] (analytic) = 0.3284044208489411 " " y[1] (numeric) = 0.32840442084894955 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 2.5693000615945866000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7450014698814644 " " Order of pole = 0.9999999987939923 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7440000000000282 " " y[1] (analytic) = 0.3287811392726663 " " y[1] (numeric) = 0.32878113927267477 " " absolute error = 8.493206138382448000000000000000E-15 " " relative error = 2.583240071851817000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.743998203004867 " " Order of pole = 1.000000002150335 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7430000000000283 " " y[1] (analytic) = 0.3291585062786878 " " y[1] (numeric) = 0.3291585062786963 " " absolute error = 8.493206138382448000000000000000E-15 " " relative error = 2.580278490871363300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7430001202525005 " " Order of pole = 1.0000000001798348 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7420000000000284 " " y[1] (analytic) = 0.3295365233567142 " " y[1] (numeric) = 0.32953652335672273 " " absolute error = 8.548717289613705000000000000000E-15 " " relative error = 2.594163828195746300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7419985217987275 " " Order of pole = 1.0000000018360886 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7410000000000285 " " y[1] (analytic) = 0.32991519200073344 " " y[1] (numeric) = 0.32991519200074204 " " absolute error = 8.604228440844963000000000000000E-15 " " relative error = 2.608012195093409000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.74100044070577 " " Order of pole = 0.9999999998013358 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7400000000000286 " " y[1] (analytic) = 0.33029451370902807 " " y[1] (numeric) = 0.3302945137090367 " " absolute error = 8.604228440844963000000000000000E-15 " " relative error = 2.605017063173151000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7399993126333348 " " Order of pole = 1.000000001036458 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7390000000000287 " " y[1] (analytic) = 0.3306744899841894 " " y[1] (numeric) = 0.3306744899841981 " " absolute error = 8.659739592076221000000000000000E-15 " " relative error = 2.6188109014669597000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7390013490257694 " " Order of pole = 0.9999999988771293 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7380000000000289 " " y[1] (analytic) = 0.33105512233313306 " " y[1] (numeric) = 0.33105512233314177 " " absolute error = 8.715250743307479000000000000000E-15 " " relative error = 2.6325678581518897000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7379990227838455 " " Order of pole = 1.0000000013083454 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.737000000000029 " " y[1] (analytic) = 0.3314364122671134 " " y[1] (numeric) = 0.33143641226712217 " " absolute error = 8.770761894538737000000000000000E-15 " " relative error = 2.6462879665346320000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.736999430426615 " " Order of pole = 1.000000000912305 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.736000000000029 " " y[1] (analytic) = 0.33181836130173886 " " y[1] (numeric) = 0.33181836130174763 " " absolute error = 8.770761894538737000000000000000E-15 " " relative error = 2.6432418809286595000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7360010169818512 " " Order of pole = 0.9999999992709583 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7350000000000292 " " y[1] (analytic) = 0.3322009709569867 " " y[1] (numeric) = 0.3322009709569955 " " absolute error = 8.826273045769994000000000000000E-15 " " relative error = 2.6569076605476920000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7349998534168918 " " Order of pole = 1.0000000004182716 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7340000000000293 " " y[1] (analytic) = 0.33258424275721854 " " y[1] (numeric) = 0.33258424275722737 " " absolute error = 8.826273045769994000000000000000E-15 " " relative error = 2.653845826428115000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7340023891960885 " " Order of pole = 0.9999999977887537 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7330000000000294 " " y[1] (analytic) = 0.3329681782311951 " " y[1] (numeric) = 0.332968178231204 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 2.66745736610128000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7330018884798217 " " Order of pole = 0.9999999983015275 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7320000000000295 " " y[1] (analytic) = 0.3333527789120918 " " y[1] (numeric) = 0.33335277891210074 " " absolute error = 8.93729534823251000000000000000E-15 " " relative error = 2.681032201801250600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7320024830338563 " " Order of pole = 0.9999999976592839 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7310000000000296 " " y[1] (analytic) = 0.33373804633751386 " " y[1] (numeric) = 0.3337380463375228 " " absolute error = 8.93729534823251000000000000000E-15 " " relative error = 2.677937216422157700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7310010243108784 " " Order of pole = 0.9999999992166124 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7300000000000297 " " y[1] (analytic) = 0.3341239820495117 " " y[1] (numeric) = 0.33412398204952065 " " absolute error = 8.93729534823251000000000000000E-15 " " relative error = 2.6748440185021344000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7299994039289852 " " Order of pole = 1.0000000008880665 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7290000000000298 " " y[1] (analytic) = 0.3345105875945964 " " y[1] (numeric) = 0.3345105875946054 " " absolute error = 8.992806499463768000000000000000E-15 " " relative error = 2.6883473447370900000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7290004290081347 " " Order of pole = 0.9999999998212683 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.72800000000003 " " y[1] (analytic) = 0.3348978645237552 " " y[1] (numeric) = 0.3348978645237643 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 2.71838962451208000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7279998702699093 " " Order of pole = 1.0000000003875318 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.72700000000003 " " y[1] (analytic) = 0.3352858143924672 " " y[1] (numeric) = 0.3352858143924763 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 2.7152442516610140000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7270007432257644 " " Order of pole = 0.9999999994963211 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7260000000000302 " " y[1] (analytic) = 0.3356744387607185 " " y[1] (numeric) = 0.33567443876072767 " " absolute error = 9.159339953157541000000000000000E-15 " " relative error = 2.7286378989633664000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7260009502128233 " " Order of pole = 0.9999999992779411 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7250000000000303 " " y[1] (analytic) = 0.3360637391930185 " " y[1] (numeric) = 0.3360637391930277 " " absolute error = 9.159339953157541000000000000000E-15 " " relative error = 2.725477010745532000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7249998413820227 " " Order of pole = 1.0000000004623573 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7240000000000304 " " y[1] (analytic) = 0.33645371725841516 " " y[1] (numeric) = 0.33645371725842443 " " absolute error = 9.270362255620057000000000000000E-15 " " relative error = 2.755315747782303000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.724001827462798 " " Order of pole = 0.9999999983305976 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7230000000000305 " " y[1] (analytic) = 0.33684437453051125 " " y[1] (numeric) = 0.3368443745305205 " " absolute error = 9.270362255620057000000000000000E-15 " " relative error = 2.7521202539127904000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7229999660961457 " " Order of pole = 1.0000000003466845 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7220000000000306 " " y[1] (analytic) = 0.3372357125874796 " " y[1] (numeric) = 0.3372357125874889 " " absolute error = 9.325873406851315000000000000000E-15 " " relative error = 2.7653872525236090000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7220004797960187 " " Order of pole = 0.9999999998396074 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7210000000000307 " " y[1] (analytic) = 0.3376277330120797 " " y[1] (numeric) = 0.3376277330120891 " " absolute error = 9.381384558082573000000000000000E-15 " " relative error = 2.77861788022813970000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7209990482587603 " " Order of pole = 1.0000000013858248 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7200000000000308 " " y[1] (analytic) = 0.3380204373916734 " " y[1] (numeric) = 0.33802043739168286 " " absolute error = 9.43689570931383100000000000000E-15 " " relative error = 2.791812170333075000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7199998408489021 " " Order of pole = 1.000000000496934 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.719000000000031 " " y[1] (analytic) = 0.33841382731824093 " " y[1] (numeric) = 0.3384138273182504 " " absolute error = 9.492406860545088000000000000000E-15 " " relative error = 2.804970156145105000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7190017649375255 " " Order of pole = 0.999999998340531 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.718000000000031 " " y[1] (analytic) = 0.33880790438839714 " " y[1] (numeric) = 0.33880790438840663 " " absolute error = 9.492406860545088000000000000000E-15 " " relative error = 2.8017076159071360000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.71799938105078 " " Order of pole = 1.000000000946498 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7170000000000312 " " y[1] (analytic) = 0.3392026702034075 " " y[1] (numeric) = 0.33920267020341704 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 2.814812161133875000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7170007099262923 " " Order of pole = 0.9999999995137028 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7160000000000313 " " y[1] (analytic) = 0.33959812636920483 " " y[1] (numeric) = 0.3395981263692144 " " absolute error = 9.547918011776346000000000000000E-15 " " relative error = 2.8115343608804320000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.71599901856852 " " Order of pole = 1.0000000013614496 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7150000000000314 " " y[1] (analytic) = 0.339994274496405 " " y[1] (numeric) = 0.3399942744964146 " " absolute error = 9.603429163007604000000000000000E-15 " " relative error = 2.824585554339724000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7150001885124688 " " Order of pole = 1.0000000001094307 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7140000000000315 " " y[1] (analytic) = 0.340391116200324 " " y[1] (numeric) = 0.34039111620033363 " " absolute error = 9.658940314238862000000000000000E-15 " " relative error = 2.837600587835103000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7140007591747564 " " Order of pole = 0.9999999995117967 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7130000000000316 " " y[1] (analytic) = 0.34078865310099377 " " y[1] (numeric) = 0.3407886531010034 " " absolute error = 9.658940314238862000000000000000E-15 " " relative error = 2.8342904689894133000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7130005661442358 " " Order of pole = 0.9999999997081748 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7120000000000317 " " y[1] (analytic) = 0.34118688682317916 " " y[1] (numeric) = 0.3411868868231889 " " absolute error = 9.71445146547012000000000000000E-15 " " relative error = 2.8472522950463375000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7120003736894907 " " Order of pole = 0.9999999998802735 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7110000000000318 " " y[1] (analytic) = 0.3415858189963945 " " y[1] (numeric) = 0.3415858189964042 " " absolute error = 9.71445146547012000000000000000E-15 " " relative error = 2.843927038309707000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7110005233685612 " " Order of pole = 0.999999999709317 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.710000000000032 " " y[1] (analytic) = 0.3419854512549199 " " y[1] (numeric) = 0.34198545125492974 " " absolute error = 9.825473767932635000000000000000E-15 " " relative error = 2.8730677670286664000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7100009204823334 " " Order of pole = 0.999999999279849 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.709000000000032 " " y[1] (analytic) = 0.3423857852378186 " " y[1] (numeric) = 0.3423857852378284 " " absolute error = 9.825473767932635000000000000000E-15 " " relative error = 2.86970843754741000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.709000534817963 " " Order of pole = 0.9999999997130811 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7080000000000322 " " y[1] (analytic) = 0.3427868225889531 " " y[1] (numeric) = 0.342786822588963 " " absolute error = 9.880984919163893000000000000000E-15 " " relative error = 2.8825451470205743000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.707999548753027 " " Order of pole = 1.0000000008154615 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7070000000000323 " " y[1] (analytic) = 0.3431885649570027 " " y[1] (numeric) = 0.34318856495701255 " " absolute error = 9.880984919163893000000000000000E-15 " " relative error = 2.8791707906706800000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7069996079020666 " " Order of pole = 1.0000000007436967 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7060000000000324 " " y[1] (analytic) = 0.3435910139954797 " " y[1] (numeric) = 0.3435910139954897 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 2.908110752208981000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7060009762405666 " " Order of pole = 0.9999999992563033 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7050000000000325 " " y[1] (analytic) = 0.3439941713627473 " " y[1] (numeric) = 0.34399417136275734 " " absolute error = 1.004751837285766700000000000000E-14 " " relative error = 2.920839714537604700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7050009733378544 " " Order of pole = 0.9999999992056843 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7040000000000326 " " y[1] (analytic) = 0.3443980387220359 " " y[1] (numeric) = 0.344398038722046 " " absolute error = 1.010302952408892500000000000000E-14 " " relative error = 2.9335328277647640000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7040017467819872 " " Order of pole = 0.9999999984559587 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7030000000000327 " " y[1] (analytic) = 0.34480261774146065 " " y[1] (numeric) = 0.3448026177414708 " " absolute error = 1.015854067532018200000000000000E-14 " " relative error = 2.9461901251971480000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.70300153768895 " " Order of pole = 0.999999998624034 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.7020000000000328 " " y[1] (analytic) = 0.34520791009403856 " " y[1] (numeric) = 0.3452079100940488 " " absolute error = 1.02140518265514400000000000000E-14 " " relative error = 2.9588116401414490000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7020001139109278 " " Order of pole = 1.0000000001724612 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.701000000000033 " " y[1] (analytic) = 0.3456139174577059 " " y[1] (numeric) = 0.3456139174577162 " " absolute error = 1.026956297778269800000000000000E-14 " " relative error = 2.9713974059043563000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.701001861826729 " " Order of pole = 0.9999999982301038 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.700000000000033 " " y[1] (analytic) = 0.34602064151533546 " " y[1] (numeric) = 0.3460206415153458 " " absolute error = 1.032507412901395600000000000000E-14 " " relative error = 2.9839474557925627000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.700000206053685 " " Order of pole = 1.0000000000528821 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6990000000000332 " " y[1] (analytic) = 0.34642808395475405 " " y[1] (numeric) = 0.3464280839547644 " " absolute error = 1.032507412901395600000000000000E-14 " " relative error = 2.9804379630961110000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6990002362603334 " " Order of pole = 1.0000000000741114 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6980000000000333 " " y[1] (analytic) = 0.3468362464687599 " " y[1] (numeric) = 0.34683624646877026 " " absolute error = 1.038058528024521400000000000000E-14 " " relative error = 2.9929355382930570000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6979992768167171 " " Order of pole = 1.0000000011156214 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6970000000000334 " " y[1] (analytic) = 0.34724513075514035 " " y[1] (numeric) = 0.34724513075515073 " " absolute error = 1.038058528024521400000000000000E-14 " " relative error = 2.9894113295904146000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6970002649726206 " " Order of pole = 1.0000000000276277 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6960000000000335 " " y[1] (analytic) = 0.3476547385166895 " " y[1] (numeric) = 0.3476547385167 " " absolute error = 1.04916075827077300000000000000E-14 " " relative error = 3.017823840823061000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6959987787883497 " " Order of pole = 1.0000000017077877 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6950000000000336 " " y[1] (analytic) = 0.348065071461226 " " y[1] (numeric) = 0.34806507146123655 " " absolute error = 1.054711873393898700000000000000E-14 " " relative error = 3.0302146347694997000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.694999462641104 " " Order of pole = 1.000000000909095 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6940000000000337 " " y[1] (analytic) = 0.3484761313016107 " " y[1] (numeric) = 0.34847613130162125 " " absolute error = 1.054711873393898700000000000000E-14 " " relative error = 3.026640216230568000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6939996073871972 " " Order of pole = 1.0000000007375434 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.6930000000000338 " " y[1] (analytic) = 0.3488879197557645 " " y[1] (numeric) = 0.3488879197557751 " " absolute error = 1.060262988517024500000000000000E-14 " " relative error = 3.038978790837043000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6930021272459626 " " Order of pole = 0.9999999978898444 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.692000000000034 " " y[1] (analytic) = 0.3493004385466866 " " y[1] (numeric) = 0.34930043854669723 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 3.0512818938178815000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.691999406935025 " " Order of pole = 1.0000000009885 " " " " "TOP MAIN SOLVE Loop" x[1] = -1.691000000000034 " " y[1] (analytic) = 0.3497136894024721 " " y[1] (numeric) = 0.3497136894024828 " " absolute error = 1.07136521876327600000000000000E-14 " " relative error = 3.0635495584797734000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6910000706069428 " " Order of pole = 1.000000000225672 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = m1 * 2.0 * x / (x * x + 0.000001) /( x * x + 0.000001);" Iterations = 310 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 1 Minutes 50 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 1 Minutes 49 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 4 Minutes 51 Seconds "Time to Timeout " Unknown Percent Done = 62.19999999999315 "%" (%o58) true (%o58) diffeq.max