(%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_const_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : exp(array_x ), 1 1 1 1 1 array_tmp2 1 array_tmp4 : -----------, array_tmp5 : array_tmp4 + array_const_0D0 , 1 array_tmp3 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 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_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 array_x 1 2 array_tmp3 : --------------------, array_tmp4 : 2 1 2 array_tmp2 - array_tmp4 array_tmp3 2 1 2 -------------------------------------, array_tmp5 : array_tmp4 , array_tmp3 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp5 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_tmp3 array_x 2 2 array_tmp3 : --------------------, array_tmp4 : 3 2 3 - ats(3, array_tmp3, array_tmp4, 2) -----------------------------------, array_tmp5 : array_tmp4 , array_tmp3 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp3 array_x 3 2 array_tmp3 : --------------------, array_tmp4 : 4 3 4 - ats(4, array_tmp3, array_tmp4, 2) -----------------------------------, array_tmp5 : array_tmp4 , array_tmp3 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp3 array_x 4 2 array_tmp3 : --------------------, array_tmp4 : 5 4 5 - ats(5, array_tmp3, array_tmp4, 2) -----------------------------------, array_tmp5 : array_tmp4 , array_tmp3 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp3 array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp3 : --------------------------, kkk kkk - 1 - ats(kkk, array_tmp3, array_tmp4, 2) array_tmp4 : -------------------------------------, kkk array_tmp3 1 array_tmp5 : array_tmp4 , 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_tmp5 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_const_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , array_tmp3 : exp(array_x ), 1 1 1 1 1 array_tmp2 1 array_tmp4 : -----------, array_tmp5 : array_tmp4 + array_const_0D0 , 1 array_tmp3 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 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_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 array_x 1 2 array_tmp3 : --------------------, array_tmp4 : 2 1 2 array_tmp2 - array_tmp4 array_tmp3 2 1 2 -------------------------------------, array_tmp5 : array_tmp4 , array_tmp3 2 2 1 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp5 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_tmp3 array_x 2 2 array_tmp3 : --------------------, array_tmp4 : 3 2 3 - ats(3, array_tmp3, array_tmp4, 2) -----------------------------------, array_tmp5 : array_tmp4 , array_tmp3 3 3 1 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp3 array_x 3 2 array_tmp3 : --------------------, array_tmp4 : 4 3 4 - ats(4, array_tmp3, array_tmp4, 2) -----------------------------------, array_tmp5 : array_tmp4 , array_tmp3 4 4 1 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp3 array_x 4 2 array_tmp3 : --------------------, array_tmp4 : 5 4 5 - ats(5, array_tmp3, array_tmp4, 2) -----------------------------------, array_tmp5 : array_tmp4 , array_tmp3 5 5 1 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 array_tmp3 array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp3 : --------------------------, kkk kkk - 1 - ats(kkk, array_tmp3, array_tmp4, 2) array_tmp4 : -------------------------------------, kkk array_tmp3 1 array_tmp5 : array_tmp4 , 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_tmp5 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) - 0.1 (2.0 x + 5.0) (%i56) exact_soln_y(x) := block(-------------------) exp(x) - 0.1 (2.0 x + 5.0) (%o56) exact_soln_y(x) := block(-------------------) exp(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/div_lin_exppostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"), 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:1.0,"), omniout_str(ALWAYS, "/* # did poorly with x_start := -5.0; */"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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, " (-(0.1 * (5.0 + 2.0*x))/exp(x)) "), 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_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_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_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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, 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 ) = (0.2 * x + 0.3) / exp(x);"), 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, "2013-01-28T13:08:50-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_exp"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "div_lin_exp diffeq.max"), logitem_str(html_log_file, "div_lin_exp 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/div_lin_exppostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"), 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:1.0,"), omniout_str(ALWAYS, "/* # did poorly with x_start := -5.0; */"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), 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, " (-(0.1 * (5.0 + 2.0*x))/exp(x)) "), 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_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_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_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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 1.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, 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 ) = (0.2 * x + 0.3) / exp(x);"), 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, "2013-01-28T13:08:50-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_lin_exp"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "div_lin_exp diffeq.max"), logitem_str(html_log_file, "div_lin_exp 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/div_lin_exppostode.ode#################" "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:1.0," "/* # did poorly with x_start := -5.0; */" "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* 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(" " (-(0.1 * (5.0 + 2.0*x))/exp(x)) " "));" "/* 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 = 4. "" estimated_steps = 4000. "" step_error = 2.500000000000000E-14 "" est_needed_step_err = 2.500000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 4.104784444604559500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" max_value3 = 4.104784444604559500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" value3 = 4.104784444604559500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 1. " " y[1] (analytic) = -0.2575156088200097 " " y[1] (numeric) = -0.2575156088200097 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.001 " " y[1] (analytic) = -0.2573317242752073 " " y[1] (numeric) = -0.2573317242752073 " " 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 = 2584.980046451877 " " Order of pole = 957402.5316168092 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0019999999999998 " " y[1] (analytic) = -0.25714795005742785 " " y[1] (numeric) = -0.25714795005742785 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0029999999999997 " " y[1] (analytic) = -0.2569642861298284 " " y[1] (numeric) = -0.2569642861298284 " " 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 = 1583.5936609783694 " " Order of pole = 358764.88838214753 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0039999999999996 " " y[1] (analytic) = -0.25678073245552946 " " y[1] (numeric) = -0.2567807324555294 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 2.161811390614033800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0049999999999994 " " y[1] (analytic) = -0.2565972889976149 " " y[1] (numeric) = -0.2565972889976148 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.32671377379780560000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 621.2508558145179 " " Order of pole = 56349.05187709407 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0059999999999993 " " y[1] (analytic) = -0.2564139557191324 " " y[1] (numeric) = -0.2564139557191323 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.32980732858885050000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0069999999999992 " " y[1] (analytic) = -0.2562307325830933 " " y[1] (numeric) = -0.2562307325830932 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.33290344773580700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 330.43895065462794 " " Order of pole = 16760.975568956972 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0079999999999991 " " y[1] (analytic) = -0.25604761955247296 " " y[1] (numeric) = -0.25604761955247285 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.336002133375169700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 541.1684838508837 " " Order of pole = 42863.89773215561 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.008999999999999 " " y[1] (analytic) = -0.2558646165902106 " " y[1] (numeric) = -0.2558646165902105 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.33910338764533100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.009999999999999 " " y[1] (analytic) = -0.2556817236592096 " " y[1] (numeric) = -0.25568172365920944 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.51331081902986700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0109999999999988 " " y[1] (analytic) = -0.2554989407223374 " " y[1] (numeric) = -0.25549894072233725 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.51797041596165100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 195.72534237122898 " " Order of pole = 6608.383615670611 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0119999999999987 " " y[1] (analytic) = -0.25531626774242594 " " y[1] (numeric) = -0.2553162677424258 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.52263387547947400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 416.4373985148586 " " Order of pole = 25842.35195447324 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0129999999999986 " " y[1] (analytic) = -0.2551337046822714 " " y[1] (numeric) = -0.25513370468227126 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.5273012008023200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 395.07181230724825 " " Order of pole = 23350.370658088643 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0139999999999985 " " y[1] (analytic) = -0.25495125150463466 " " y[1] (numeric) = -0.25495125150463444 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.70929652686936800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0149999999999983 " " y[1] (analytic) = -0.25476890817224107 " " y[1] (numeric) = -0.2547689081722408 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.08944124362554730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 581.5916669729907 " " Order of pole = 49310.854508829274 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0159999999999982 " " y[1] (analytic) = -0.2545866746477807 " " y[1] (numeric) = -0.25458667464778045 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 8.72176853844486700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0169999999999981 " " y[1] (analytic) = -0.25440455089390873 " " y[1] (numeric) = -0.25440455089390845 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.09100153743725630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.017999999999998 " " y[1] (analytic) = -0.254222536873245 " " y[1] (numeric) = -0.2542225368732447 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.09178265455937160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 266.24149329021054 " " Order of pole = 11220.979920751288 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.018999999999998 " " y[1] (analytic) = -0.25404063254837456 " " y[1] (numeric) = -0.2540406325483742 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.31107730305357440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 308.1928906600172 " " Order of pole = 14630.885756155238 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0199999999999978 " " y[1] (analytic) = -0.25385883788184754 " " y[1] (numeric) = -0.2538588378818472 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.31201619831949640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0209999999999977 " " y[1] (analytic) = -0.2536771528361795 " " y[1] (numeric) = -0.25367715283617914 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.31295587191738980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1773.7900552176113 " " Order of pole = 447797.8419675849 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0219999999999976 " " y[1] (analytic) = -0.2534955773738512 " " y[1] (numeric) = -0.2534955773738508 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.53287904524557480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0229999999999975 " " y[1] (analytic) = -0.25331411145730903 " " y[1] (numeric) = -0.2533141114573086 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.75311674227396880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0239999999999974 " " y[1] (analytic) = -0.2531327550489649 " " y[1] (numeric) = -0.25313275504896443 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.75437275892706970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0249999999999972 " " y[1] (analytic) = -0.2529515081111964 " " y[1] (numeric) = -0.25295150811119593 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.75562981682181930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 398.9749511339777 " " Order of pole = 23689.352203977563 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0259999999999971 " " y[1] (analytic) = -0.25277037060634705 " " y[1] (numeric) = -0.25277037060634655 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.976498906429880200000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 438.8966754962064 " " Order of pole = 28462.141090574587 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.026999999999997 " " y[1] (analytic) = -0.2525893424967261 " " y[1] (numeric) = -0.2525893424967256 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.97791544228670680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.027999999999997 " " y[1] (analytic) = -0.25240842374460903 " " y[1] (numeric) = -0.25240842374460853 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.97933315247364430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0289999999999968 " " y[1] (analytic) = -0.2522276143122373 " " y[1] (numeric) = -0.2522276143122368 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 1.98075203797017960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0299999999999967 " " y[1] (analytic) = -0.2520469141618187 " " y[1] (numeric) = -0.2520469141618181 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.2024134441740740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 168.92886358231857 " " Order of pole = 5189.179875460920 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0309999999999966 " " y[1] (analytic) = -0.25186632325552716 " " y[1] (numeric) = -0.2518663232555266 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.2039925986825890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 373.9885542857254 " " Order of pole = 20960.87094483776 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0319999999999965 " " y[1] (analytic) = -0.2516858415555033 " " y[1] (numeric) = -0.2516858415555027 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.20557306236140300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 544.3905367109838 " " Order of pole = 43089.18379494258 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0329999999999964 " " y[1] (analytic) = -0.25150546902385407 " " y[1] (numeric) = -0.2515054690238535 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.20715483630269970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0339999999999963 " " y[1] (analytic) = -0.2513252056226533 " " y[1] (numeric) = -0.2513252056226527 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.429611713759590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 433.57090328314706 " " Order of pole = 27686.44382554479 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0349999999999961 " " y[1] (analytic) = -0.25114505131394144 " " y[1] (numeric) = -0.25114505131394077 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.6523867832155680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.035999999999996 " " y[1] (analytic) = -0.2509650060597257 " " y[1] (numeric) = -0.25096500605972505 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.6542896367653930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.036999999999996 " " y[1] (analytic) = -0.2507850698219805 " " y[1] (numeric) = -0.2507850698219798 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.8775435735413220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 172.0835670570065 " " Order of pole = 5329.409527715810 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0379999999999958 " " y[1] (analytic) = -0.2506052425626471 " " y[1] (numeric) = -0.2506052425626464 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.87960841771278060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 280.7535543107115 " " Order of pole = 12305.936958008035 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0389999999999957 " " y[1] (analytic) = -0.25042552424363407 " " y[1] (numeric) = -0.2504255242436333 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 3.10334227944564330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0399999999999956 " " y[1] (analytic) = -0.2502459148268172 " " y[1] (numeric) = -0.2502459148268164 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 3.10556964646332370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 273.1986674108162 " " Order of pole = 11672.228214819737 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0409999999999955 " " y[1] (analytic) = -0.2500664142740396 " " y[1] (numeric) = -0.2500664142740388 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 3.1077988601298120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0419999999999954 " " y[1] (analytic) = -0.24988702254711204 " " y[1] (numeric) = -0.24988702254711123 " " absolute error = 8.0491169285323850000000000000000E-16 " " relative error = 3.2211024192002036000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0429999999999953 " " y[1] (analytic) = -0.24970773960781273 " " y[1] (numeric) = -0.2497077396078119 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 3.33456732168831540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0439999999999952 " " y[1] (analytic) = -0.24952856541788757 " " y[1] (numeric) = -0.24952856541788673 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 3.3369617104734790000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.044999999999995 " " y[1] (analytic) = -0.24934949993905034 " " y[1] (numeric) = -0.24934949993904948 " " absolute error = 8.6042284408449630000000000000000E-16 " " relative error = 3.45067002057278470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 621.1056207710026 " " Order of pole = 55516.60143893475 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.045999999999995 " " y[1] (analytic) = -0.2491705431329826 " " y[1] (numeric) = -0.24917054313298173 " " absolute error = 8.6042284408449630000000000000000E-16 " " relative error = 3.4531483267076546000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 238.226988035644 " " Order of pole = 9147.435027007707 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0469999999999948 " " y[1] (analytic) = -0.24899169496133403 " " y[1] (numeric) = -0.24899169496133314 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.5671005807565210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0479999999999947 " " y[1] (analytic) = -0.2488129553857223 " " y[1] (numeric) = -0.24881295538572137 " " absolute error = 9.1593399531575410000000000000000E-16 " " relative error = 3.6812150472463440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 860.0587235302867 " " Order of pole = 105314.0782924654 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0489999999999946 " " y[1] (analytic) = -0.2486343243677333 " " y[1] (numeric) = -0.2486343243677324 " " absolute error = 9.1593399531575410000000000000000E-16 " " relative error = 3.6838598115724210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0499999999999945 " " y[1] (analytic) = -0.24845580186892133 " " y[1] (numeric) = -0.24845580186892038 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 3.7982190950374690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0509999999999944 " " y[1] (analytic) = -0.2482773878508089 " " y[1] (numeric) = -0.24827738785080797 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 3.8009485241501360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0519999999999943 " " y[1] (analytic) = -0.24809908227488725 " " y[1] (numeric) = -0.24809908227488628 " " absolute error = 9.714451465470120000000000000000E-16 " " relative error = 3.91555316383910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 843.9743694985625 " " Order of pole = 101182.63640144165 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0529999999999942 " " y[1] (analytic) = -0.24792088510261603 " " y[1] (numeric) = -0.24792088510261504 " " absolute error = 9.9920072216264090000000000000000E-16 " " relative error = 4.0303208894606250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 247.8924631375327 " " Order of pole = 9793.609224953967 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.053999999999994 " " y[1] (analytic) = -0.24774279629542373 " " y[1] (numeric) = -0.2477427962954227 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.14525190291976900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.054999999999994 " " y[1] (analytic) = -0.24756481581470755 " " y[1] (numeric) = -0.24756481581470652 " " absolute error = 1.0269562977782698000000000000000E-15 " " relative error = 4.14823202723163140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0559999999999938 " " y[1] (analytic) = -0.24738694362183372 " " y[1] (numeric) = -0.24738694362183264 " " absolute error = 1.0824674490095276000000000000000E-15 " " relative error = 4.37560460209344640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1138.5097844721056 " " Order of pole = 183420.16379026466 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0569999999999937 " " y[1] (analytic) = -0.24720917967813733 " " y[1] (numeric) = -0.24720917967813624 " " absolute error = 1.0824674490095276000000000000000E-15 " " relative error = 4.37875102542261640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 269.362717596599 " " Order of pole = 11331.202657342274 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0579999999999936 " " y[1] (analytic) = -0.24703152394492273 " " y[1] (numeric) = -0.24703152394492162 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 4.4942564693593030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 617.4452497532014 " " Order of pole = 54757.64643921354 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0589999999999935 " " y[1] (analytic) = -0.24685397638346337 " " y[1] (numeric) = -0.24685397638346224 " " absolute error = 1.1379786002407855000000000000000E-15 " " relative error = 4.6099261470799550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 253.83119630144196 " " Order of pole = 10176.183440676563 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0599999999999934 " " y[1] (analytic) = -0.2466765369550021 " " y[1] (numeric) = -0.24667653695500094 " " absolute error = 1.1657341758564144000000000000000E-15 " " relative error = 4.7257602617838906000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 203.86235794990958 " " Order of pole = 6968.089867163128 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0609999999999933 " " y[1] (analytic) = -0.24649920562075112 " " y[1] (numeric) = -0.24649920562074992 " " absolute error = 1.1934897514720433000000000000000E-15 " " relative error = 4.8417590168962860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 550.858524615862 " " Order of pole = 43762.00128613715 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0619999999999932 " " y[1] (analytic) = -0.2463219823418921 " " y[1] (numeric) = -0.2463219823418909 " " absolute error = 1.1934897514720433000000000000000E-15 " " relative error = 4.8452425566123175000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 249.6882670928183 " " Order of pole = 9867.642561740511 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.062999999999993 " " y[1] (analytic) = -0.24614486707957647 " " y[1] (numeric) = -0.24614486707957525 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 4.9614901239961840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 440.6822730163017 " " Order of pole = 28359.36377886301 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.063999999999993 " " y[1] (analytic) = -0.24596785979492522 " " y[1] (numeric) = -0.245967859794924 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 4.9650605900538430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0649999999999928 " " y[1] (analytic) = -0.24579096044902926 " " y[1] (numeric) = -0.245790960449028 " " absolute error = 1.2490009027033011000000000000000E-15 " " relative error = 5.0815575170931150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0659999999999927 " " y[1] (analytic) = -0.24561416900294933 " " y[1] (numeric) = -0.24561416900294808 " " absolute error = 1.2490009027033011000000000000000E-15 " " relative error = 5.0852151884132670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 322.9374467202483 " " Order of pole = 15731.002554900211 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0669999999999926 " " y[1] (analytic) = -0.24543748541771626 " " y[1] (numeric) = -0.24543748541771496 " " absolute error = 1.304512053934559000000000000000E-15 " " relative error = 5.3150481545815090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0679999999999925 " " y[1] (analytic) = -0.2452609096543309 " " y[1] (numeric) = -0.24526090965432956 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.4320422746041220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1337.2584945666483 " " Order of pole = 251375.45774499414 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0689999999999924 " " y[1] (analytic) = -0.2450844416737643 " " y[1] (numeric) = -0.24508444167376298 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.4359535042358590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 316.1355052317592 " " Order of pole = 15128.501935391452 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0699999999999923 " " y[1] (analytic) = -0.24490808143695794 " " y[1] (numeric) = -0.24490808143695658 " " absolute error = 1.3600232051658168000000000000000E-15 " " relative error = 5.5531985599907700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 416.90332542356697 " " Order of pole = 25443.293499698113 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0709999999999922 " " y[1] (analytic) = -0.2447318289048236 " " y[1] (numeric) = -0.2447318289048222 " " absolute error = 1.3877787807814457000000000000000E-15 " " relative error = 5.6706101000093200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.071999999999992 " " y[1] (analytic) = -0.24455568403824357 " " y[1] (numeric) = -0.24455568403824215 " " absolute error = 1.4155343563970746000000000000000E-15 " " relative error = 5.788188330048030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 257.0378169414354 " " Order of pole = 10392.571963206645 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.072999999999992 " " y[1] (analytic) = -0.24437964679807073 " " y[1] (numeric) = -0.2443796467980693 " " absolute error = 1.4155343563970746000000000000000E-15 " " relative error = 5.7923578127057420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 323.6105574186354 " " Order of pole = 15781.913015852526 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0739999999999919 " " y[1] (analytic) = -0.24420371714512876 " " y[1] (numeric) = -0.24420371714512729 " " absolute error = 1.4710455076283324000000000000000E-15 " " relative error = 6.0238456843558160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0749999999999917 " " y[1] (analytic) = -0.24402789504021197 " " y[1] (numeric) = -0.2440278950402105 " " absolute error = 1.4710455076283324000000000000000E-15 " " relative error = 6.0281858653328440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 267.434283579832 " " Order of pole = 11131.923795775874 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0759999999999916 " " y[1] (analytic) = -0.2438521804440857 " " y[1] (numeric) = -0.2438521804440842 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 6.1463509594806780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1732.7519968362226 " " Order of pole = 420534.68434212555 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0769999999999915 " " y[1] (analytic) = -0.24367657331748616 " " y[1] (numeric) = -0.24367657331748466 " " absolute error = 1.4988010832439613000000000000000E-15 " " relative error = 6.1507803677589210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0779999999999914 " " y[1] (analytic) = -0.2435010736211208 " " y[1] (numeric) = -0.24350107362111928 " " absolute error = 1.5265566588595902000000000000000E-15 " " relative error = 6.269198883430220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0789999999999913 " " y[1] (analytic) = -0.24332568131566815 " " y[1] (numeric) = -0.2433256813156666 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 6.3877853996792010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1521.7161795898085 " " Order of pole = 324446.2033442578 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0799999999999912 " " y[1] (analytic) = -0.243150396361778 " " y[1] (numeric) = -0.24315039636177643 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 6.3923902972487570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.080999999999991 " " y[1] (analytic) = -0.24297521872007158 " " y[1] (numeric) = -0.24297521872007 " " absolute error = 1.582067810090848000000000000000E-15 " " relative error = 6.5112311388163690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.081999999999991 " " y[1] (analytic) = -0.24280014835114155 " " y[1] (numeric) = -0.24280014835113997 " " absolute error = 1.582067810090848000000000000000E-15 " " relative error = 6.5159260438458870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0829999999999909 " " y[1] (analytic) = -0.2426251852155522 " " y[1] (numeric) = -0.2426251852155506 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 6.6350217693859080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0839999999999907 " " y[1] (analytic) = -0.24245032927383944 " " y[1] (numeric) = -0.2424503292738378 " " absolute error = 1.6375789613221060000000000000000E-15 " " relative error = 6.7542863984833610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 268.84954649864477 " " Order of pole = 11204.451618177858 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0849999999999906 " " y[1] (analytic) = -0.24227558048651088 " " y[1] (numeric) = -0.24227558048650927 " " absolute error = 1.609823385706477000000000000000E-15 " " relative error = 6.6445961350038200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0859999999999905 " " y[1] (analytic) = -0.24210093881404615 " " y[1] (numeric) = -0.24210093881404451 " " absolute error = 1.6375789613221060000000000000000E-15 " " relative error = 6.7640339163653730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 337.6658474879605 " " Order of pole = 16981.16086334652 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0869999999999904 " " y[1] (analytic) = -0.24192640421689673 " " y[1] (numeric) = -0.24192640421689504 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 6.9983684419805640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 990.1458104866032 " " Order of pole = 137975.6023720942 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0879999999999903 " " y[1] (analytic) = -0.2417519766554861 " " y[1] (numeric) = -0.2417519766554844 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.0034178664281970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0889999999999902 " " y[1] (analytic) = -0.24157765609020995 " " y[1] (numeric) = -0.24157765609020826 " " absolute error = 1.6930901125533637000000000000000E-15 " " relative error = 7.0084714785092950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.08999999999999 " " y[1] (analytic) = -0.24140344248143628 " " y[1] (numeric) = -0.24140344248143455 " " absolute error = 1.7208456881689926000000000000000E-15 " " relative error = 7.1285051715918430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.09099999999999 " " y[1] (analytic) = -0.2412293357895053 " " y[1] (numeric) = -0.24122933578950356 " " absolute error = 1.7486012637846216000000000000000E-15 " " relative error = 7.2487090264611780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 284.587466846051 " " Order of pole = 12366.549648777576 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0919999999999899 " " y[1] (analytic) = -0.24105533597472975 " " y[1] (numeric) = -0.24105533597472797 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 7.3690832530936760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 292.9439812595266 " " Order of pole = 13071.84068619382 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0929999999999898 " " y[1] (analytic) = -0.24088144299739478 " " y[1] (numeric) = -0.24088144299739297 " " absolute error = 1.8041124150158794000000000000000E-15 " " relative error = 7.489628061699181000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 418.2547351999399 " " Order of pole = 25467.34350793274 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0939999999999896 " " y[1] (analytic) = -0.24070765681775824 " " y[1] (numeric) = -0.24070765681775644 " " absolute error = 1.8041124150158794000000000000000E-15 " " relative error = 7.4950354254072930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 241.40255399386888 " " Order of pole = 9226.128420779363 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0949999999999895 " " y[1] (analytic) = -0.2405339773960507 " " y[1] (numeric) = -0.2405339773960489 " " absolute error = 1.8041124150158794000000000000000E-15 " " relative error = 7.5004472737975060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 556.7240422445539 " " Order of pole = 44281.45743611406 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.0959999999999894 " " y[1] (analytic) = -0.24036040469247555 " " y[1] (numeric) = -0.24036040469247372 " " absolute error = 1.8318679906315083000000000000000E-15 " " relative error = 7.6213384354018550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0969999999999893 " " y[1] (analytic) = -0.240186938667209 " " y[1] (numeric) = -0.24018693866720714 " " absolute error = 1.8596235662471372000000000000000E-15 " " relative error = 7.7424008839370670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.0979999999999892 " " y[1] (analytic) = -0.24001357928040035 " " y[1] (numeric) = -0.24001357928039846 " " absolute error = 1.887379141862766000000000000000E-15 " " relative error = 7.8636348306684780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.098999999999989 " " y[1] (analytic) = -0.2398403264921719 " " y[1] (numeric) = -0.23984032649217 " " absolute error = 1.915134717478395000000000000000E-15 " " relative error = 7.985040487096330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.099999999999989 " " y[1] (analytic) = -0.2396671802626192 " " y[1] (numeric) = -0.2396671802626173 " " absolute error = 1.915134717478395000000000000000E-15 " " relative error = 7.9908092354566650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1009999999999889 " " y[1] (analytic) = -0.2394941405518111 " " y[1] (numeric) = -0.23949414055180915 " " absolute error = 1.942890293094024000000000000000E-15 " " relative error = 8.1124752723280410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 404.43127921214636 " " Order of pole = 23793.472748652406 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1019999999999888 " " y[1] (analytic) = -0.23932120731978973 " " y[1] (numeric) = -0.23932120731978776 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 8.2343135854082660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 348.82669249449617 " " Order of pole = 18041.827459744847 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1029999999999887 " " y[1] (analytic) = -0.23914838052657073 " " y[1] (numeric) = -0.23914838052656875 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 8.2402643261500290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 468.8661530180847 " " Order of pole = 31607.852342477476 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1039999999999885 " " y[1] (analytic) = -0.2389756601321433 " " y[1] (numeric) = -0.23897566013214133 " " absolute error = 1.970645868709652900000000000000E-15 " " relative error = 8.2462200025725220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1049999999999884 " " y[1] (analytic) = -0.23880304609647032 " " y[1] (numeric) = -0.23880304609646832 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 8.3684085148477490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1059999999999883 " " y[1] (analytic) = -0.23863053837948836 " " y[1] (numeric) = -0.23863053837948633 " " absolute error = 2.0261570199409107000000000000000E-15 " " relative error = 8.4907700150211370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 374.7144253182248 " " Order of pole = 20580.179170473213 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1069999999999882 " " y[1] (analytic) = -0.23845813694110782 " " y[1] (numeric) = -0.2384581369411058 " " absolute error = 2.0261570199409107000000000000000E-15 " " relative error = 8.4969087066268250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.107999999999988 " " y[1] (analytic) = -0.23828584174121312 " " y[1] (numeric) = -0.23828584174121104 " " absolute error = 2.0816681711721685000000000000000E-15 " " relative error = 8.7360128321553150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1103.6101488972015 " " Order of pole = 170144.17930053113 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.108999999999988 " " y[1] (analytic) = -0.23811365273966253 " " y[1] (numeric) = -0.23811365273966045 " " absolute error = 2.0816681711721685000000000000000E-15 " " relative error = 8.7423301739364120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 377.3555540239958 " " Order of pole = 20842.158478309226 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1099999999999879 " " y[1] (analytic) = -0.2379415698962886 " " y[1] (numeric) = -0.2379415698962865 " " absolute error = 2.0816681711721685000000000000000E-15 " " relative error = 8.748652755714370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 357.2892198688981 " " Order of pole = 18775.096388748985 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1109999999999878 " " y[1] (analytic) = -0.23776959317089802 " " y[1] (numeric) = -0.23776959317089588 " " absolute error = 2.1371793224034263000000000000000E-15 " " relative error = 8.9884467307277540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 195.76967199634962 " " Order of pole = 6401.8496536571265 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1119999999999877 " " y[1] (analytic) = -0.2375977225232717 " " y[1] (numeric) = -0.23759772252326955 " " absolute error = 2.1371793224034263000000000000000E-15 " " relative error = 8.9949486876672350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 711.7914316598626 " " Order of pole = 71195.067462476 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1129999999999876 " " y[1] (analytic) = -0.2374259579131651 " " y[1] (numeric) = -0.2374259579131629 " " absolute error = 2.192690473634684200000000000000E-15 " " relative error = 9.2352600907969250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1139999999999874 " " y[1] (analytic) = -0.23725429930030795 " " y[1] (numeric) = -0.23725429930030575 " " absolute error = 2.192690473634684200000000000000E-15 " " relative error = 9.241942001056240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1149999999999873 " " y[1] (analytic) = -0.2370827466444047 " " y[1] (numeric) = -0.23708274664440251 " " absolute error = 2.192690473634684200000000000000E-15 " " relative error = 9.248629453932610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1159999999999872 " " y[1] (analytic) = -0.2369112999051345 " " y[1] (numeric) = -0.23691129990513227 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 9.372478434500330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1169999999999871 " " y[1] (analytic) = -0.23673995904215106 " " y[1] (numeric) = -0.2367399590421488 " " absolute error = 2.248201624865942000000000000000E-15 " " relative error = 9.496502550571340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1346.8256467307224 " " Order of pole = 251603.26875160838 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.117999999999987 " " y[1] (analytic) = -0.23656872401508305 " " y[1] (numeric) = -0.2365687240150808 " " absolute error = 2.248201624865942000000000000000E-15 " " relative error = 9.5033763834419720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 241.60492202987274 " " Order of pole = 9159.926170464485 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.118999999999987 " " y[1] (analytic) = -0.23639759478353414 " " y[1] (numeric) = -0.23639759478353187 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 9.6276664852095140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 214.23151210141972 " " Order of pole = 7441.339346871766 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1199999999999868 " " y[1] (analytic) = -0.23622657130708286 " " y[1] (numeric) = -0.23622657130708058 " " absolute error = 2.275957200481571000000000000000E-15 " " relative error = 9.634636729849240000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 280.26389629617347 " " Order of pole = 11965.477130722338 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1209999999999867 " " y[1] (analytic) = -0.236055653545283 " " y[1] (numeric) = -0.23605565354528069 " " absolute error = 2.3037127760971998000000000000E-15 " " relative error = 9.7591933999380980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1219999999999866 " " y[1] (analytic) = -0.23588484145766342 " " y[1] (numeric) = -0.23588484145766112 " " absolute error = 2.3037127760971998000000000000E-15 " " relative error = 9.7662603576443470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1229999999999865 " " y[1] (analytic) = -0.23571413500372843 " " y[1] (numeric) = -0.2357141350037261 " " absolute error = 2.3314683517128287000000000000000E-15 " " relative error = 9.891084179894221000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1239999999999863 " " y[1] (analytic) = -0.23554353414295756 " " y[1] (numeric) = -0.2355435341429552 " " absolute error = 2.3592239273284576000000000000000E-15 " " relative error = 1.0016084440240175000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1249999999999862 " " y[1] (analytic) = -0.23537303883480593 " " y[1] (numeric) = -0.23537303883480354 " " absolute error = 2.3869795029440866000000000000000E-15 " " relative error = 1.0141261355848676000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 363.8693133409897 " " Order of pole = 19360.490872506438 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1259999999999861 " " y[1] (analytic) = -0.23520264903870416 " " y[1] (numeric) = -0.23520264903870175 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.0266615144127712000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.126999999999986 " " y[1] (analytic) = -0.23503236471405853 " " y[1] (numeric) = -0.2350323647140561 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.0274053454287002000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.127999999999986 " " y[1] (analytic) = -0.23486218582025106 " " y[1] (numeric) = -0.23486218582024865 " " absolute error = 2.4147350785597155000000000000000E-15 " " relative error = 1.0281497935166982000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1289999999999858 " " y[1] (analytic) = -0.23469211231663967 " " y[1] (numeric) = -0.23469211231663722 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 1.0407212368858856000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1299999999999857 " " y[1] (analytic) = -0.2345221441625581 " " y[1] (numeric) = -0.23452214416255562 " " absolute error = 2.4702462297909733000000000000000E-15 " " relative error = 1.0533104405180314000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1309999999999856 " " y[1] (analytic) = -0.2343522813173161 " " y[1] (numeric) = -0.23435228131731362 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 1.065917426263188000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 313.67025955911464 " " Order of pole = 14649.103946589143 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1319999999999855 " " y[1] (analytic) = -0.2341825237401996 " " y[1] (numeric) = -0.2341825237401971 " " absolute error = 2.4980018054066022000000000000000E-15 " " relative error = 1.066690103732022000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1329999999999854 " " y[1] (analytic) = -0.23401287139047064 " " y[1] (numeric) = -0.2340128713904681 " " absolute error = 2.525757381022231000000000000000E-15 " " relative error = 1.0793241269228251000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1339999999999852 " " y[1] (analytic) = -0.23384332422736756 " " y[1] (numeric) = -0.233843324227365 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 1.091975990794187100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 490.14820052105136 " " Order of pole = 34166.7741770829 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1349999999999851 " " y[1] (analytic) = -0.23367388221010504 " " y[1] (numeric) = -0.2336738822101025 " " absolute error = 2.55351295663786000000000000000E-15 " " relative error = 1.092767806348978000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.135999999999985 " " y[1] (analytic) = -0.23350454529787426 " " y[1] (numeric) = -0.23350454529787168 " " absolute error = 2.581268532253489000000000000000E-15 " " relative error = 1.1054468035988967000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 672.5055030701665 " " Order of pole = 63358.03040016488 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.136999999999985 " " y[1] (analytic) = -0.2333353134498429 " " y[1] (numeric) = -0.2333353134498403 " " absolute error = 2.609024107869118000000000000000E-15 " " relative error = 1.1181437002804749000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 217.8174787972589 " " Order of pole = 7606.299665256467 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1379999999999848 " " y[1] (analytic) = -0.2331661866251552 " " y[1] (numeric) = -0.2331661866251526 " " absolute error = 2.609024107869118000000000000000E-15 " " relative error = 1.11895474452454000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1389999999999847 " " y[1] (analytic) = -0.23299716478293225 " " y[1] (numeric) = -0.23299716478292962 " " absolute error = 2.6367796834847470000000000000000E-15 " " relative error = 1.1316788708314354000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1289.883513226377 " " Order of pole = 229941.13824601422 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1399999999999846 " " y[1] (analytic) = -0.23282824788227188 " " y[1] (numeric) = -0.2328282478822692 " " absolute error = 2.6922908347160046000000000000000E-15 " " relative error = 1.1563420071250738000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1409999999999845 " " y[1] (analytic) = -0.2326594358822487 " " y[1] (numeric) = -0.232659435882246 " " absolute error = 2.6922908347160046000000000000000E-15 " " relative error = 1.1571810206221768000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 224.87010586098532 " " Order of pole = 8039.330781312778 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1419999999999844 " " y[1] (analytic) = -0.2324907287419144 " " y[1] (numeric) = -0.2324907287419117 " " absolute error = 2.6922908347160046000000000000000E-15 " " relative error = 1.1580207302393934000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 391.68167986060024 " " Order of pole = 22151.094609539494 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1429999999999843 " " y[1] (analytic) = -0.2323221264202978 " " y[1] (numeric) = -0.23232212642029507 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.1708081585869926000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 196.08877948825256 " " Order of pole = 6348.794581656536 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1439999999999841 " " y[1] (analytic) = -0.23215362887640467 " " y[1] (numeric) = -0.23215362887640195 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.1716579333677994000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.144999999999984 " " y[1] (analytic) = -0.2319852360692182 " " y[1] (numeric) = -0.23198523606921548 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 1.1725084132164533000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 190.49773655639962 " " Order of pole = 6071.992795591716 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.145999999999984 " " y[1] (analytic) = -0.23181694795769883 " " y[1] (numeric) = -0.23181694795769606 " " absolute error = 2.7755575615628914000000000000000E-15 " " relative error = 1.1973057129840937000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 619.7291870116044 " " Order of pole = 53750.27780144300 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1469999999999838 " " y[1] (analytic) = -0.23164876450078437 " " y[1] (numeric) = -0.23164876450078156 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.210156740192339000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1479999999999837 " " y[1] (analytic) = -0.2314806856573901 " " y[1] (numeric) = -0.2314806856573873 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.2110354387526084000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 191.99016390023266 " " Order of pole = 6146.667424243136 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1489999999999836 " " y[1] (analytic) = -0.23131271138640902 " " y[1] (numeric) = -0.2313127113864062 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.2239140234990524000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1499999999999835 " " y[1] (analytic) = -0.23114484164671162 " " y[1] (numeric) = -0.23114484164670882 " " absolute error = 2.8033131371785200000000000000000E-15 " " relative error = 1.2127950237640105000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1509999999999834 " " y[1] (analytic) = -0.23097707639714632 " " y[1] (numeric) = -0.2309770763971435 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.2256925046216952000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 304.5120199472081 " " Order of pole = 13767.97311777758 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1519999999999833 " " y[1] (analytic) = -0.2308094155965392 " " y[1] (numeric) = -0.23080941559653637 " " absolute error = 2.831068712794149000000000000000E-15 " " relative error = 1.2265828521237324000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 248.35284726786617 " " Order of pole = 9523.97585250803 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1529999999999831 " " y[1] (analytic) = -0.23064185920369437 " " y[1] (numeric) = -0.2306418592036915 " " absolute error = 2.858824288409778000000000000000E-15 " " relative error = 1.2395079966316824000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 331.91741992802645 " " Order of pole = 16142.346520948484 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.153999999999983 " " y[1] (analytic) = -0.23047440717739393 " " y[1] (numeric) = -0.23047440717739104 " " absolute error = 2.886579864025407000000000000000E-15 " " relative error = 1.25245136732411000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 276.9329935939071 " " Order of pole = 11576.807234089194 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.154999999999983 " " y[1] (analytic) = -0.23030705947639804 " " y[1] (numeric) = -0.23030705947639513 " " absolute error = 2.914335439641036000000000000000E-15 " " relative error = 1.2654129865870212000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1559999999999828 " " y[1] (analytic) = -0.23013981605944503 " " y[1] (numeric) = -0.23013981605944211 " " absolute error = 2.914335439641036000000000000000E-15 " " relative error = 1.2663325666725414000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1569999999999827 " " y[1] (analytic) = -0.22997267688525155 " " y[1] (numeric) = -0.2299726768852486 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.279321985161162000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1579999999999826 " " y[1] (analytic) = -0.22980564191251254 " " y[1] (numeric) = -0.2298056419125096 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.2802518644762972000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 448.2907109473057 " " Order of pole = 28539.950209091872 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1589999999999825 " " y[1] (analytic) = -0.2296387110999014 " " y[1] (numeric) = -0.22963871109989845 " " absolute error = 2.942091015256665000000000000000E-15 " " relative error = 1.2811825154238676000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1599999999999824 " " y[1] (analytic) = -0.22947188440607003 " " y[1] (numeric) = -0.22947188440606706 " " absolute error = 2.9698465908722940000000000000000E-15 " " relative error = 1.2942093531671606000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 529.1281068080965 " " Order of pole = 39385.881372541655 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1609999999999823 " " y[1] (analytic) = -0.22930516178964896 " " y[1] (numeric) = -0.22930516178964594 " " absolute error = 3.0253577421035516000000000000000E-15 " " relative error = 1.3193587612645355000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 379.4046215372672 " " Order of pole = 20749.95177840056 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1619999999999822 " " y[1] (analytic) = -0.22913854320924731 " " y[1] (numeric) = -0.2291385432092443 " " absolute error = 3.0253577421035516000000000000000E-15 " " relative error = 1.3203181358017196000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 361.8090647378165 " " Order of pole = 18927.993992115025 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.162999999999982 " " y[1] (analytic) = -0.22897202862345312 " " y[1] (numeric) = -0.22897202862345006 " " absolute error = 3.0531133177191805000000000000000E-15 " " relative error = 1.333400125803163900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.163999999999982 " " y[1] (analytic) = -0.22880561799083313 " " y[1] (numeric) = -0.22880561799083005 " " absolute error = 3.0808688933348094000000000000000E-15 " " relative error = 1.3465005450426665000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1649999999999818 " " y[1] (analytic) = -0.22863931126993312 " " y[1] (numeric) = -0.22863931126993 " " absolute error = 3.1086244689504383000000000000000E-15 " " relative error = 1.3596194161381003000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1659999999999817 " " y[1] (analytic) = -0.22847310841927781 " " y[1] (numeric) = -0.22847310841927468 " " absolute error = 3.1363800445660670000000000000000E-15 " " relative error = 1.3727567617325023000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1669999999999816 " " y[1] (analytic) = -0.22830700939737106 " " y[1] (numeric) = -0.22830700939736792 " " absolute error = 3.1363800445660670000000000000000E-15 " " relative error = 1.3737554763845033000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1679999999999815 " " y[1] (analytic) = -0.22814101416269592 " " y[1] (numeric) = -0.22814101416269278 " " absolute error = 3.1363800445660670000000000000000E-15 " " relative error = 1.3747550198621442000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 400.3052456262196 " " Order of pole = 22901.304514924726 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1689999999999814 " " y[1] (analytic) = -0.22797512267371475 " " y[1] (numeric) = -0.22797512267371156 " " absolute error = 3.191891195797325000000000000000E-15 " " relative error = 1.400105045832418000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 220.1577553576728 " " Order of pole = 7677.3137778281125 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1699999999999813 " " y[1] (analytic) = -0.22780933488886912 " " y[1] (numeric) = -0.22780933488886593 " " absolute error = 3.191891195797325000000000000000E-15 " " relative error = 1.401123969460868200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1709999999999812 " " y[1] (analytic) = -0.2276436507665802 " " y[1] (numeric) = -0.22764365076657697 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 1.4143362929609202000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1532.140648441675 " " Order of pole = 320753.96908031125 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.171999999999981 " " y[1] (analytic) = -0.22747807026524852 " " y[1] (numeric) = -0.2274780702652453 " " absolute error = 3.219646771412954000000000000000E-15 " " relative error = 1.4153657834615518000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 351.167666145726 " " Order of pole = 17870.784344060954 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.172999999999981 " " y[1] (analytic) = -0.22731259334325432 " " y[1] (numeric) = -0.22731259334325113 " " absolute error = 3.191891195797325000000000000000E-15 " " relative error = 1.4041858169192573000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 465.03967156166647 " " Order of pole = 30529.8124126423 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1739999999999808 " " y[1] (analytic) = -0.22714721995895756 " " y[1] (numeric) = -0.22714721995895432 " " absolute error = 3.247402347028583000000000000000E-15 " " relative error = 1.4296465295130378000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1749999999999807 " " y[1] (analytic) = -0.2269819500706978 " " y[1] (numeric) = -0.22698195007069455 " " absolute error = 3.247402347028583000000000000000E-15 " " relative error = 1.4306874824262980000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 460.8231894257885 " " Order of pole = 29937.578518269605 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1759999999999806 " " y[1] (analytic) = -0.22681678363679456 " " y[1] (numeric) = -0.22681678363679128 " " absolute error = 3.2751579226442120000000000000000E-15 " " relative error = 1.4439663018450943000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1633.5337980852473 " " Order of pole = 363693.30026279704 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1769999999999805 " " y[1] (analytic) = -0.22665172061554725 " " y[1] (numeric) = -0.22665172061554398 " " absolute error = 3.2751579226442120000000000000000E-15 " " relative error = 1.4450178951871373000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 481.27011382644747 " " Order of pole = 32597.157718495764 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1779999999999804 " " y[1] (analytic) = -0.22648676096523532 " " y[1] (numeric) = -0.22648676096523204 " " absolute error = 3.2751579226442120000000000000000E-15 " " relative error = 1.446070361325417000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1789999999999803 " " y[1] (analytic) = -0.2263219046441183 " " y[1] (numeric) = -0.226321904644115 " " absolute error = 3.3029134982598407000000000000000E-15 " " relative error = 1.4593874611710844000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1799999999999802 " " y[1] (analytic) = -0.22615715161043587 " " y[1] (numeric) = -0.22615715161043254 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.4727233033128537000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.18099999999998 " " y[1] (analytic) = -0.22599250182240796 " " y[1] (numeric) = -0.2259925018224046 " " absolute error = 3.3584246494910985000000000000000E-15 " " relative error = 1.486077910730974000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.18199999999998 " " y[1] (analytic) = -0.22582795523823487 " " y[1] (numeric) = -0.2258279552382315 " " absolute error = 3.3861802251067274000000000000000E-15 " " relative error = 1.499451306431266000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1829999999999798 " " y[1] (analytic) = -0.22566351181609728 " " y[1] (numeric) = -0.22566351181609387 " " absolute error = 3.4139358007223564000000000000000E-15 " " relative error = 1.5128435134451496000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1839999999999797 " " y[1] (analytic) = -0.22549917151415635 " " y[1] (numeric) = -0.22549917151415294 " " absolute error = 3.4139358007223564000000000000000E-15 " " relative error = 1.5139460503552390000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1849999999999796 " " y[1] (analytic) = -0.22533493429055393 " " y[1] (numeric) = -0.2253349342905505 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 1.5273669780381946000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1859999999999795 " " y[1] (analytic) = -0.22517080010341237 " " y[1] (numeric) = -0.22517080010340892 " " absolute error = 3.4416913763379850000000000000000E-15 " " relative error = 1.5284803246057427000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 408.58859281484644 " " Order of pole = 23716.123314077082 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1869999999999794 " " y[1] (analytic) = -0.22500676891083488 " " y[1] (numeric) = -0.2250067689108314 " " absolute error = 3.469446951953614000000000000000E-15 " " relative error = 1.5419300355930526000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1879999999999793 " " y[1] (analytic) = -0.2248428406709054 " " y[1] (numeric) = -0.2248428406709019 " " absolute error = 3.497202527569243000000000000000E-15 " " relative error = 1.5553986585180962000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1889999999999792 " " y[1] (analytic) = -0.22467901534168885 " " y[1] (numeric) = -0.22467901534168533 " " absolute error = 3.524958103184872000000000000000E-15 " " relative error = 1.5688862165539416000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.189999999999979 " " y[1] (analytic) = -0.22451529288123104 " " y[1] (numeric) = -0.2245152928812275 " " absolute error = 3.524958103184872000000000000000E-15 " " relative error = 1.5700302896736665000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.190999999999979 " " y[1] (analytic) = -0.2243516732475589 " " y[1] (numeric) = -0.22435167324755537 " " absolute error = 3.524958103184872000000000000000E-15 " " relative error = 1.5711753124726144000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1458.4346544930956 " " Order of pole = 289534.4612908976 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1919999999999789 " " y[1] (analytic) = -0.22418815639868053 " " y[1] (numeric) = -0.22418815639867698 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.5847017683140244000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.1929999999999787 " " y[1] (analytic) = -0.22402474229258518 " " y[1] (numeric) = -0.2240247422925816 " " absolute error = 3.58046925441613000000000000000E-15 " " relative error = 1.598247237235918800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 422.7247123798763 " " Order of pole = 25262.567930365312 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1939999999999786 " " y[1] (analytic) = -0.22386143088724336 " " y[1] (numeric) = -0.22386143088723978 " " absolute error = 3.58046925441613000000000000000E-15 " " relative error = 1.5994131906623854000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 327.0388579396765 " " Order of pole = 15528.498425065696 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1949999999999785 " " y[1] (analytic) = -0.2236982221406071 " " y[1] (numeric) = -0.2236982221406035 " " absolute error = 3.608224830031759000000000000000E-15 " " relative error = 1.6129877097386064000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 15497.913496751802 " " Order of pole = 32524180.36223346 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1959999999999784 " " y[1] (analytic) = -0.2235351160106098 " " y[1] (numeric) = -0.22353511601060616 " " absolute error = 3.635980405647387700000000000000E-15 " " relative error = 1.6265813043328775000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 279.87212073383904 " " Order of pole = 11656.84103138126 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1969999999999783 " " y[1] (analytic) = -0.2233721124551663 " " y[1] (numeric) = -0.22337211245516267 " " absolute error = 3.635980405647387700000000000000E-15 " " relative error = 1.6277682857018136000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 281.0038600784268 " " Order of pole = 11739.799101755423 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.1979999999999782 " " y[1] (analytic) = -0.22320921143217326 " " y[1] (numeric) = -0.2232092114321696 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 1.6413910329934203000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 547.0403635265893 " " Order of pole = 41474.99364700444 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.198999999999978 " " y[1] (analytic) = -0.22304641289950886 " " y[1] (numeric) = -0.2230464128995052 " " absolute error = 3.6637359812630166000000000000000E-15 " " relative error = 1.6425890619068925000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.199999999999978 " " y[1] (analytic) = -0.22288371681503316 " " y[1] (numeric) = -0.22288371681502947 " " absolute error = 3.6914915568786455000000000000000E-15 " " relative error = 1.6562410254231996000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 461.07311709194596 " " Order of pole = 29752.52180579859 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2009999999999779 " " y[1] (analytic) = -0.22272112313658798 " " y[1] (numeric) = -0.2227211231365843 " " absolute error = 3.6914915568786455000000000000000E-15 " " relative error = 1.6574501353492040000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2019999999999778 " " y[1] (analytic) = -0.22255863182199717 " " y[1] (numeric) = -0.22255863182199345 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.6711313787500884000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 409.78837163953307 " " Order of pole = 23721.378138723176 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2029999999999776 " " y[1] (analytic) = -0.22239624282906648 " " y[1] (numeric) = -0.22239624282906276 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.6723516032385870000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 470.37400458785845 " " Order of pole = 31008.8210775469 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2039999999999775 " " y[1] (analytic) = -0.2222339561155838 " " y[1] (numeric) = -0.22223395611558008 " " absolute error = 3.7192471324942744000000000000000E-15 " " relative error = 1.673572840758815200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 455.28688177341303 " " Order of pole = 29095.602604629174 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2049999999999774 " " y[1] (analytic) = -0.2220717716393192 " " y[1] (numeric) = -0.22207177163931546 " " absolute error = 3.747002708109903300000000000000E-15 " " relative error = 1.6872935629998248000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2059999999999773 " " y[1] (analytic) = -0.22190968935802496 " " y[1] (numeric) = -0.22190968935802122 " " absolute error = 3.747002708109903300000000000000E-15 " " relative error = 1.6885259579921086000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 543.953174166445 " " Order of pole = 40901.97683791719 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2069999999999772 " " y[1] (analytic) = -0.2217477092294357 " " y[1] (numeric) = -0.22174770922943193 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 1.7022761122731161000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.207999999999977 " " y[1] (analytic) = -0.22158583121126843 " " y[1] (numeric) = -0.22158583121126463 " " absolute error = 3.802513859341161000000000000000E-15 " " relative error = 1.7160455786163054000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 217.61591405201838 " " Order of pole = 7435.756736353326 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.208999999999977 " " y[1] (analytic) = -0.22142405526122258 " " y[1] (numeric) = -0.22142405526121875 " " absolute error = 3.83026943495679000000000000000E-15 " " relative error = 1.7298343806584485000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2099999999999769 " " y[1] (analytic) = -0.2212623813369802 " " y[1] (numeric) = -0.22126238133697634 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.7436425420626242000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2109999999999768 " " y[1] (analytic) = -0.22110080939620594 " " y[1] (numeric) = -0.22110080939620208 " " absolute error = 3.858025010572419000000000000000E-15 " " relative error = 1.7449167287574036000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2119999999999767 " " y[1] (analytic) = -0.22093933939654717 " " y[1] (numeric) = -0.22093933939654328 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 1.7587545055585402000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2129999999999765 " " y[1] (analytic) = -0.220777971295634 " " y[1] (numeric) = -0.22077797129563012 " " absolute error = 3.885780586188048000000000000000E-15 " " relative error = 1.7600399910300701000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2139999999999764 " " y[1] (analytic) = -0.22061670505107947 " " y[1] (numeric) = -0.22061670505107556 " " absolute error = 3.913536161803677000000000000000E-15 " " relative error = 1.7739074477146120000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2149999999999763 " " y[1] (analytic) = -0.22045554062047948 " " y[1] (numeric) = -0.22045554062047557 " " absolute error = 3.913536161803677000000000000000E-15 " " relative error = 1.7752042660342757000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 614.6330558091347 " " Order of pole = 51863.96572397496 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2159999999999762 " " y[1] (analytic) = -0.220294477961413 " " y[1] (numeric) = -0.22029447796140905 " " absolute error = 3.941291737419305700000000000000E-15 " " relative error = 1.7891014672231895000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.216999999999976 " " y[1] (analytic) = -0.22013351703144202 " " y[1] (numeric) = -0.22013351703143808 " " absolute error = 3.941291737419305700000000000000E-15 " " relative error = 1.790409652545716000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 241.7901691467945 " " Order of pole = 8915.509106668173 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.217999999999976 " " y[1] (analytic) = -0.2199726577881118 " " y[1] (numeric) = -0.21997265778810782 " " absolute error = 3.969047313034934600000000000000E-15 " " relative error = 1.804336662994776000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 301.8593586403547 " " Order of pole = 13311.834514212956 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2189999999999759 " " y[1] (analytic) = -0.21981190018895067 " " y[1] (numeric) = -0.2198119001889467 " " absolute error = 3.969047313034934600000000000000E-15 " " relative error = 1.8056562495584338000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2199999999999758 " " y[1] (analytic) = -0.21965124419147047 " " y[1] (numeric) = -0.21965124419146648 " " absolute error = 3.9968028886505635000000000000000E-15 " " relative error = 1.8196131341585034000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 419.412778404368 " " Order of pole = 24672.222664997575 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2209999999999757 " " y[1] (analytic) = -0.21949068975316635 " " y[1] (numeric) = -0.2194906897531623 " " absolute error = 4.052314039881821400000000000000E-15 " " relative error = 1.8462350473448105000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 195.99777216002246 " " Order of pole = 6213.336636285448 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2219999999999756 " " y[1] (analytic) = -0.21933023683151684 " " y[1] (numeric) = -0.2193302368315128 " " absolute error = 4.052314039881821400000000000000E-15 " " relative error = 1.8475856764768334000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 287.00888958641826 " " Order of pole = 12123.284277373483 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2229999999999754 " " y[1] (analytic) = -0.21916988538398413 " " y[1] (numeric) = -0.21916988538398008 " " absolute error = 4.052314039881821400000000000000E-15 " " relative error = 1.8489374271388587000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2239999999999753 " " y[1] (analytic) = -0.21900963536801402 " " y[1] (numeric) = -0.21900963536800994 " " absolute error = 4.08006961549745030000000000000E-15 " " relative error = 1.862963521509673800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2249999999999752 " " y[1] (analytic) = -0.21884948674103594 " " y[1] (numeric) = -0.21884948674103183 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.8770092871973965000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2546.621754370428 " " Order of pole = 871445.2800918521 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.225999999999975 " " y[1] (analytic) = -0.21868943946046313 " " y[1] (numeric) = -0.218689439460459 " " absolute error = 4.135580766728708000000000000000E-15 " " relative error = 1.891074748251106200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.226999999999975 " " y[1] (analytic) = -0.21852949348369263 " " y[1] (numeric) = -0.2185294934836885 " " absolute error = 4.135580766728708000000000000000E-15 " " relative error = 1.892458862555007000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.227999999999975 " " y[1] (analytic) = -0.2183696487681055 " " y[1] (numeric) = -0.21836964876810133 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 1.90655448952319000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 350.3576618336114 " " Order of pole = 17508.66488261897 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2289999999999748 " " y[1] (analytic) = -0.21820990527106665 " " y[1] (numeric) = -0.2182099052710625 " " absolute error = 4.163336342344337000000000000000E-15 " " relative error = 1.907950208388808000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 264.32759524579905 " " Order of pole = 10419.591881689043 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2299999999999747 " " y[1] (analytic) = -0.2180502629499252 " " y[1] (numeric) = -0.218050262949921 " " absolute error = 4.191091917959966000000000000000E-15 " " relative error = 1.922076066894008700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2309999999999746 " " y[1] (analytic) = -0.21789072176201427 " " y[1] (numeric) = -0.21789072176201008 " " absolute error = 4.191091917959966000000000000000E-15 " " relative error = 1.923483425116918000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2319999999999744 " " y[1] (analytic) = -0.21773128166465133 " " y[1] (numeric) = -0.2177312816646471 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 1.9376395809185762000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 607.9387876781454 " " Order of pole = 50546.52241308802 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2329999999999743 " " y[1] (analytic) = -0.21757194261513807 " " y[1] (numeric) = -0.21757194261513382 " " absolute error = 4.246603069191224000000000000000E-15 " " relative error = 1.9518155779410487000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2339999999999742 " " y[1] (analytic) = -0.21741270457076056 " " y[1] (numeric) = -0.2174127045707563 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.9660114404288143000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 950.9892134091413 " " Order of pole = 122137.43696857363 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2349999999999741 " " y[1] (analytic) = -0.21725356748878927 " " y[1] (numeric) = -0.217253567488785 " " absolute error = 4.274358644806852700000000000000E-15 " " relative error = 1.9674515333458995000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.235999999999974 " " y[1] (analytic) = -0.21709453132647927 " " y[1] (numeric) = -0.21709453132647497 " " absolute error = 4.3021142204224816000000000000000E-15 " " relative error = 1.9816778405867416000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 329.6749805429855 " " Order of pole = 15610.424091568899 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.236999999999974 " " y[1] (analytic) = -0.2169355960410701 " " y[1] (numeric) = -0.21693559604106577 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 1.995924078415596800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 348.96051835911436 " " Order of pole = 17354.506663550488 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2379999999999738 " " y[1] (analytic) = -0.21677676158978604 " " y[1] (numeric) = -0.2167767615897817 " " absolute error = 4.3298697960381105000000000000000E-15 " " relative error = 1.9973865114894873000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2389999999999737 " " y[1] (analytic) = -0.21661802792983612 " " y[1] (numeric) = -0.21661802792983176 " " absolute error = 4.3576253716537394000000000000000E-15 " " relative error = 2.0116633012027976000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 559.9634165483088 " " Order of pole = 42998.01521109832 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2399999999999736 " " y[1] (analytic) = -0.21645939501841407 " " y[1] (numeric) = -0.21645939501840972 " " absolute error = 4.3576253716537394000000000000000E-15 " " relative error = 2.0131375546360733000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 360.57344184451875 " " Order of pole = 18429.83049249409 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2409999999999735 " " y[1] (analytic) = -0.21630086281269867 " " y[1] (numeric) = -0.21630086281269426 " " absolute error = 4.413136522884997000000000000000E-15 " " relative error = 2.040276892795597800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2419999999999733 " " y[1] (analytic) = -0.21614243126985344 " " y[1] (numeric) = -0.21614243126984903 " " absolute error = 4.413136522884997000000000000000E-15 " " relative error = 2.0417724076468835000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 225.0074712898217 " " Order of pole = 7812.516982848499 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2429999999999732 " " y[1] (analytic) = -0.2159841003470271 " " y[1] (numeric) = -0.21598410034702267 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.056119914088737000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 702.1902086291681 " " Order of pole = 66818.78483132392 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2439999999999731 " " y[1] (analytic) = -0.2158258700013534 " " y[1] (numeric) = -0.21582587000134895 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.057627335626067000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 852.2894365923711 " " Order of pole = 98140.4089333686 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.244999999999973 " " y[1] (analytic) = -0.21566774018995122 " " y[1] (numeric) = -0.21566774018994678 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 2.0591360092099414000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 575.0485392402404 " " Order of pole = 45313.612105528526 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.245999999999973 " " y[1] (analytic) = -0.21550971086992476 " " y[1] (numeric) = -0.2155097108699203 " " absolute error = 4.468647674116255000000000000000E-15 " " relative error = 2.073524972994557000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 537.2938166492463 " " Order of pole = 39543.000048442234 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2469999999999728 " " y[1] (analytic) = -0.2153517819983635 " " y[1] (numeric) = -0.21535178199835903 " " absolute error = 4.468647674116255000000000000000E-15 " " relative error = 2.0750455987172714000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 259.5917554771841 " " Order of pole = 10036.89661842903 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2479999999999727 " " y[1] (analytic) = -0.2151939535323423 " " y[1] (numeric) = -0.2151939535323378 " " absolute error = 4.496403249731884000000000000000E-15 " " relative error = 2.0894654222039294000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 438.43917154969415 " " Order of pole = 26687.78211043583 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2489999999999726 " " y[1] (analytic) = -0.21503622542892148 " " y[1] (numeric) = -0.21503622542891698 " " absolute error = 4.496403249731884000000000000000E-15 " " relative error = 2.090998035685914800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1032.546213567382 " " Order of pole = 143337.82114006908 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2499999999999725 " " y[1] (analytic) = -0.21487859764514694 " " y[1] (numeric) = -0.21487859764514242 " " absolute error = 4.524158825347513000000000000000E-15 " " relative error = 2.1054487859320276000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2509999999999724 " " y[1] (analytic) = -0.21472107013805009 " " y[1] (numeric) = -0.21472107013804553 " " absolute error = 4.551914400963142000000000000000E-15 " " relative error = 2.1199197628982522000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 324.8355618680658 " " Order of pole = 15101.20080707129 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2519999999999722 " " y[1] (analytic) = -0.21456364286464807 " " y[1] (numeric) = -0.2145636428646435 " " absolute error = 4.579669976578771000000000000000E-15 " " relative error = 2.134410991272989200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 261.73080095716017 " " Order of pole = 10169.912184005843 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2529999999999721 " " y[1] (analytic) = -0.21440631578194377 " " y[1] (numeric) = -0.2144063157819392 " " absolute error = 4.579669976578771000000000000000E-15 " " relative error = 2.1359771795325290000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 243.5819358236188 " " Order of pole = 8948.270741203141 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.253999999999972 " " y[1] (analytic) = -0.21424908884692592 " " y[1] (numeric) = -0.21424908884692132 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 2.1504994849645576000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.254999999999972 " " y[1] (analytic) = -0.21409196201656905 " " y[1] (numeric) = -0.21409196201656444 " " absolute error = 4.6074255521943996000000000000E-15 " " relative error = 2.1520777841429753000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2559999999999718 " " y[1] (analytic) = -0.21393493524783377 " " y[1] (numeric) = -0.21393493524782914 " " absolute error = 4.6351811278100286000000000000000E-15 " " relative error = 2.1666312341368577000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2569999999999717 " " y[1] (analytic) = -0.21377800849766665 " " y[1] (numeric) = -0.213778008497662 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.1812050435845243000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 495.38512795469745 " " Order of pole = 33693.867044632876 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2579999999999716 " " y[1] (analytic) = -0.21362118172300032 " " y[1] (numeric) = -0.21362118172299566 " " absolute error = 4.6629367034256575000000000000000E-15 " " relative error = 2.1828063424309788000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 287.8078408122493 " " Order of pole = 12058.363390901151 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2589999999999715 " " y[1] (analytic) = -0.2134644548807537 " " y[1] (numeric) = -0.213464454880749 " " absolute error = 4.690692279041286400000000000000E-15 " " relative error = 2.1974114058762706000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 711.3707787148836 " " Order of pole = 68344.91084137146 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2599999999999714 " " y[1] (analytic) = -0.21330782792783182 " " y[1] (numeric) = -0.21330782792782713 " " absolute error = 4.690692279041286400000000000000E-15 " " relative error = 2.199024913716848300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2609999999999713 " " y[1] (analytic) = -0.21315130082112616 " " y[1] (numeric) = -0.21315130082112144 " " absolute error = 4.718447854656915300000000000000E-15 " " relative error = 2.213661299030296000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 481.66089210439657 " " Order of pole = 31836.14680328199 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2619999999999711 " " y[1] (analytic) = -0.2129948735175145 " " y[1] (numeric) = -0.21299487351750976 " " absolute error = 4.746203430272544000000000000000E-15 " " relative error = 2.2283181524001636000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.262999999999971 " " y[1] (analytic) = -0.21283854597386107 " " y[1] (numeric) = -0.21283854597385632 " " absolute error = 4.746203430272544000000000000000E-15 " " relative error = 2.229954827287455000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 382.1045459144968 " " Order of pole = 20401.386023764986 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.263999999999971 " " y[1] (analytic) = -0.21268231814701666 " " y[1] (numeric) = -0.21268231814701188 " " absolute error = 4.773959005888173000000000000000E-15 " " relative error = 2.244643112545056000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2649999999999708 " " y[1] (analytic) = -0.21252618999381864 " " y[1] (numeric) = -0.21252618999381384 " " absolute error = 4.801714581503802000000000000000E-15 " " relative error = 2.2593519328810538000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1627.857343810881 " " Order of pole = 352925.88536761346 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2659999999999707 " " y[1] (analytic) = -0.21237016147109106 " " y[1] (numeric) = -0.21237016147108626 " " absolute error = 4.801714581503802000000000000000E-15 " " relative error = 2.2610118805025425000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2669999999999706 " " y[1] (analytic) = -0.2122142325356447 " " y[1] (numeric) = -0.21221423253563987 " " absolute error = 4.829470157119431000000000000000E-15 " " relative error = 2.2757522431056765000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 382.57641548368065 " " Order of pole = 20503.707923154132 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2679999999999705 " " y[1] (analytic) = -0.21205840314427707 " " y[1] (numeric) = -0.21205840314427227 " " absolute error = 4.801714581503802000000000000000E-15 " " relative error = 2.264335914213635200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 429.08011370097466 " " Order of pole = 25404.994328142497 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2689999999999704 " " y[1] (analytic) = -0.21190267325377274 " " y[1] (numeric) = -0.21190267325376788 " " absolute error = 4.85722573273506000000000000000E-15 " " relative error = 2.2921965344524414000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 271.5668296242682 " " Order of pole = 10804.354355109843 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2699999999999703 " " y[1] (analytic) = -0.21174704282090298 " " y[1] (numeric) = -0.21174704282089812 " " absolute error = 4.85722573273506000000000000000E-15 " " relative error = 2.2938812594626565000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 646.7728361929749 " " Order of pole = 56468.43032052225 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2709999999999702 " " y[1] (analytic) = -0.21159151180242627 " " y[1] (numeric) = -0.21159151180242142 " " absolute error = 4.85722573273506000000000000000E-15 " " relative error = 2.295567384229712200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 341.1332095262064 " " Order of pole = 16513.742813831304 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.27199999999997 " " y[1] (analytic) = -0.2114360801550881 " " y[1] (numeric) = -0.21143608015508322 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 2.3103820808480563000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 875.7900185341047 " " Order of pole = 102637.9934760017 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.27299999999997 " " y[1] (analytic) = -0.2112807478356211 " " y[1] (numeric) = -0.21128074783561618 " " absolute error = 4.912736883966317700000000000000E-15 " " relative error = 2.325217481617627000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 266.3397277414832 " " Order of pole = 10410.554948387215 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2739999999999698 " " y[1] (analytic) = -0.2111255148007451 " " y[1] (numeric) = -0.21112551480074015 " " absolute error = 4.9404924595819466000000000000000E-15 " " relative error = 2.340073611777647000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2749999999999697 " " y[1] (analytic) = -0.21097038100716725 " " y[1] (numeric) = -0.2109703810071623 " " absolute error = 4.9404924595819466000000000000000E-15 " " relative error = 2.3417943485697662000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 380.8195763511166 " " Order of pole = 20247.830166446347 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2759999999999696 " " y[1] (analytic) = -0.2108153464115821 " " y[1] (numeric) = -0.21081534641157712 " " absolute error = 4.9682480351975755000000000000000E-15 " " relative error = 2.356682338247754200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2769999999999695 " " y[1] (analytic) = -0.2106604109706715 " " y[1] (numeric) = -0.21066041097066654 " " absolute error = 4.9682480351975755000000000000000E-15 " " relative error = 2.3584156189124986000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2779999999999694 " " y[1] (analytic) = -0.21050557464110498 " " y[1] (numeric) = -0.21050557464109998 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 2.373335537232678000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 344.48305479109996 " " Order of pole = 16740.302511017177 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2789999999999693 " " y[1] (analytic) = -0.21035083737953944 " " y[1] (numeric) = -0.21035083737953444 " " absolute error = 4.9960036108132044000000000000000E-15 " " relative error = 2.3750813987960664000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.2799999999999692 " " y[1] (analytic) = -0.21019619914261956 " " y[1] (numeric) = -0.21019619914261453 " " absolute error = 5.023759186428833000000000000000E-15 " " relative error = 2.3900333150268707000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 350.3662234264722 " " Order of pole = 17263.376557721855 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.280999999999969 " " y[1] (analytic) = -0.2100416598869776 " " y[1] (numeric) = -0.21004165988697254 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 2.4050061139121914000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.281999999999969 " " y[1] (analytic) = -0.20988721956923365 " " y[1] (numeric) = -0.2098872195692286 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 2.4067757781593574000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 766.3503349834277 " " Order of pole = 78591.32752827751 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2829999999999688 " " y[1] (analytic) = -0.20973287814599564 " " y[1] (numeric) = -0.2097328781459906 " " absolute error = 5.051514762044462000000000000000E-15 " " relative error = 2.408546912958534000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 225.8371880347909 " " Order of pole = 7752.519606774368 " " " " "TOP MAIN SOLVE Loop" x[1] = 1.2839999999999687 " " y[1] (analytic) = -0.20957863557385942 " " y[1] (numeric) = -0.20957863557385434 " " absolute error = 5.079270337660091000000000000000E-15 " " relative error = 2.423563033394242000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = (0.2 * x + 0.3) / exp(x);" Iterations = 285 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 39 Minutes 9 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 39 Minutes 0 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 42 Minutes 1 Seconds "Time to Timeout " Unknown Percent Done = 7.1499999999992125 "%" (%o58) true (%o58) diffeq.max