(%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_2D0 array_x , 1 1 1 array_tmp2 : array_const_3D0 + array_tmp1 , 1 1 1 array_tmp3_a1 : sin(array_tmp2 ), array_tmp3_a2 : cos(array_tmp2 ), 1 1 1 1 array_tmp3_a1 1 array_tmp3 : --------------, array_tmp4 : array_tmp3 + array_const_0D0 , 1 array_tmp3_a2 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 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_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_a2 array_tmp2 1 2 array_tmp3_a1 : --------------------------, 2 1 - array_tmp3_a1 array_tmp2 1 2 array_tmp3_a2 : ----------------------------, 2 1 array_tmp3_a1 - ats(2, array_tmp3_a2, array_tmp3, 2) 2 array_tmp3 : -----------------------------------------------------, 2 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp3_a2 array_tmp2 2 2 array_tmp3_a1 : --------------------------, 3 2 - array_tmp3_a1 array_tmp2 2 2 array_tmp3_a2 : ----------------------------, 3 2 array_tmp3_a1 - ats(3, array_tmp3_a2, array_tmp3, 2) 3 array_tmp3 : -----------------------------------------------------, 3 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3_a2 array_tmp2 3 2 array_tmp3_a1 : --------------------------, 4 3 - array_tmp3_a1 array_tmp2 3 2 array_tmp3_a2 : ----------------------------, 4 3 array_tmp3_a1 - ats(4, array_tmp3_a2, array_tmp3, 2) 4 array_tmp3 : -----------------------------------------------------, 4 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3_a2 array_tmp2 4 2 array_tmp3_a1 : --------------------------, 5 4 - array_tmp3_a1 array_tmp2 4 2 array_tmp3_a2 : ----------------------------, 5 4 array_tmp3_a1 - ats(5, array_tmp3_a2, array_tmp3, 2) 5 array_tmp3 : -----------------------------------------------------, 5 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3_a1 : kkk array_tmp3_a2 array_tmp2 kkk - 1 2 --------------------------------, array_tmp3_a2 : kkk - 1 kkk - array_tmp3_a1 array_tmp2 kkk - 1 2 ----------------------------------, array_tmp3 : kkk - 1 kkk array_tmp3_a1 - ats(kkk, array_tmp3_a2, array_tmp3, 2) kkk ---------------------------------------------------------, array_tmp3_a2 1 array_tmp4 : array_tmp3 , 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_tmp4 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_2D0 array_x , 1 1 1 array_tmp2 : array_const_3D0 + array_tmp1 , 1 1 1 array_tmp3_a1 : sin(array_tmp2 ), array_tmp3_a2 : cos(array_tmp2 ), 1 1 1 1 array_tmp3_a1 1 array_tmp3 : --------------, array_tmp4 : array_tmp3 + array_const_0D0 , 1 array_tmp3_a2 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 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_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_a2 array_tmp2 1 2 array_tmp3_a1 : --------------------------, 2 1 - array_tmp3_a1 array_tmp2 1 2 array_tmp3_a2 : ----------------------------, 2 1 array_tmp3_a1 - ats(2, array_tmp3_a2, array_tmp3, 2) 2 array_tmp3 : -----------------------------------------------------, 2 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp3_a2 array_tmp2 2 2 array_tmp3_a1 : --------------------------, 3 2 - array_tmp3_a1 array_tmp2 2 2 array_tmp3_a2 : ----------------------------, 3 2 array_tmp3_a1 - ats(3, array_tmp3_a2, array_tmp3, 2) 3 array_tmp3 : -----------------------------------------------------, 3 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_tmp3_a2 array_tmp2 3 2 array_tmp3_a1 : --------------------------, 4 3 - array_tmp3_a1 array_tmp2 3 2 array_tmp3_a2 : ----------------------------, 4 3 array_tmp3_a1 - ats(4, array_tmp3_a2, array_tmp3, 2) 4 array_tmp3 : -----------------------------------------------------, 4 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_tmp3_a2 array_tmp2 4 2 array_tmp3_a1 : --------------------------, 5 4 - array_tmp3_a1 array_tmp2 4 2 array_tmp3_a2 : ----------------------------, 5 4 array_tmp3_a1 - ats(5, array_tmp3_a2, array_tmp3, 2) 5 array_tmp3 : -----------------------------------------------------, 5 array_tmp3_a2 1 array_tmp4 : array_tmp3 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp3_a1 : kkk array_tmp3_a2 array_tmp2 kkk - 1 2 --------------------------------, array_tmp3_a2 : kkk - 1 kkk - array_tmp3_a1 array_tmp2 kkk - 1 2 ----------------------------------, array_tmp3 : kkk - 1 kkk array_tmp3_a1 - ats(kkk, array_tmp3_a2, array_tmp3, 2) kkk ---------------------------------------------------------, array_tmp3_a2 1 array_tmp4 : array_tmp3 , 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_tmp4 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) ln(expt(tan(3.0 + 2.0 x), 2) + 1.0) (%i56) exact_soln_y(x) := block(-----------------------------------) 4.0 ln(expt(tan(3.0 + 2.0 x), 2) + 1.0) (%o56) exact_soln_y(x) := block(-----------------------------------) 4.0 (%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/lin_tanpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.0,"), 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: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, " (ln(1.0 + expt(tan(2.0 * x + 3.0),2))/4.0) "), 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_g, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a2 : 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_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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 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_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_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 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 ) = tan (2.0 * x + 3.0 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T16:05:56-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_tan"), logitem_str(html_log_file, "diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "lin_tan diffeq.max"), logitem_str(html_log_file, "lin_tan 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/lin_tanpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.0,"), 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: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, " (ln(1.0 + expt(tan(2.0 * x + 3.0),2))/4.0) "), 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_g, 1 + max_terms), array(array_tmp3_a1, 1 + max_terms), array(array_tmp3_a2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_a2 : 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_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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 0.0, term : 1 + term), term array(array_tmp3_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a1 : 0.0, term : 1 + term), term array(array_tmp3_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_a2 : 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_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_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 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 ) = tan (2.0 * x + 3.0 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T16:05:56-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_tan"), logitem_str(html_log_file, "diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "lin_tan diffeq.max"), logitem_str(html_log_file, "lin_tan 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/lin_tanpostode.ode#################" "diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter: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(" " (ln(1.0 + expt(tan(2.0 * x + 3.0),2))/4.0) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 5. "" estimated_steps = 5000. "" step_error = 2.00000000000000E-14 "" est_needed_step_err = 2.00000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.20774024197146150000000000000000000000000000000000000000000000000000000000000000000000000000E-76 "" max_value3 = 1.20774024197146150000000000000000000000000000000000000000000000000000000000000000000000000000E-76 "" value3 = 1.20774024197146150000000000000000000000000000000000000000000000000000000000000000000000000000E-76 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.0 " " y[1] (analytic) = 5.028957536846423000E-3 " " y[1] (numeric) = 5.028957536846423000E-3 " " 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] = 1.000E-3 " " y[1] (analytic) = 4.887431120086471000E-3 " " y[1] (numeric) = 4.88743112008642000E-3 " " absolute error = 5.11743425413158100000000000000000E-17 " " relative error = 1.0470601279882671000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.000E-3 " " y[1] (analytic) = 4.747944188910092000E-3 " " y[1] (numeric) = 4.747944188910091000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.82681536150809200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.000E-3 " " y[1] (analytic) = 4.610495605706182400E-3 " " y[1] (numeric) = 4.610495605706169000E-3 " " absolute error = 1.301042606982605300000000000000000E-17 " " relative error = 2.8219148617609990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.000E-3 " " y[1] (analytic) = 4.475084250108221000E-3 " " y[1] (numeric) = 4.475084250108221000E-3 " " 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] = 5.000E-3 " " y[1] (analytic) = 4.341709018957837000E-3 " " y[1] (numeric) = 4.3417090189577817000E-3 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 1.2785553105671382000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.000E-3 " " y[1] (analytic) = 4.210368826268111000E-3 " " y[1] (numeric) = 4.2103688262680766000E-3 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 8.2402447270368520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.000E-3 " " y[1] (analytic) = 4.081062603188379500E-3 " " y[1] (numeric) = 4.081062603188349000E-3 " " absolute error = 3.035766082959412400000000000000000E-17 " " relative error = 7.4386658038219830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.000E-3 " " y[1] (analytic) = 3.953789297968784400E-3 " " y[1] (numeric) = 3.953789297968766000E-3 " " absolute error = 1.821459649775647400000000000000000E-17 " " relative error = 4.6068708079902043000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.000000000000001000E-3 " " y[1] (analytic) = 3.828547875925971000E-3 " " y[1] (numeric) = 3.828547875925921000E-3 " " absolute error = 4.987329993433320400000000000000000E-17 " " relative error = 1.302668832951994000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000000200E-2 " " y[1] (analytic) = 3.7053373194089680000E-3 " " y[1] (numeric) = 3.705337319408918000E-3 " " absolute error = 4.943961906533900000000000000000E-17 " " relative error = 1.334281195030984000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.100000000000000300E-2 " " y[1] (analytic) = 3.5841566277660664000E-3 " " y[1] (numeric) = 3.5841566277660414000E-3 " " absolute error = 2.4719809532669500000000000000000E-17 " " relative error = 6.8969668739272890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.200000000000000400E-2 " " y[1] (analytic) = 3.465004817312010700E-3 " " y[1] (numeric) = 3.465004817312004000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.00256399911446560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000000600E-2 " " y[1] (analytic) = 3.3478809212958077000E-3 " " y[1] (numeric) = 3.3478809212957755000E-3 " " absolute error = 3.20923843055709300000000000000000E-17 " " relative error = 9.5858798625219550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000000700E-2 " " y[1] (analytic) = 3.2327839898690197000E-3 " " y[1] (numeric) = 3.2327839898689880000E-3 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 9.65886451598259900000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000000800E-2 " " y[1] (analytic) = 3.119713090054961000E-3 " " y[1] (numeric) = 3.1197130900549170000E-3 " " absolute error = 4.42354486374085800000000000000000E-17 " " relative error = 1.4179332316943694000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.600000000000001000E-2 " " y[1] (analytic) = 3.0086673057180563000E-3 " " y[1] (numeric) = 3.008667305718027000E-3 " " absolute error = 2.94902990916057200000000000000000E-17 " " relative error = 9.801781352015421000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.700000000000001000E-2 " " y[1] (analytic) = 2.8996457375341560000E-3 " " y[1] (numeric) = 2.8996457375340995000E-3 " " absolute error = 5.68121938382404300000000000000000E-17 " " relative error = 1.959280511506665300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.80000000000000100E-2 " " y[1] (analytic) = 2.792647502960914000E-3 " " y[1] (numeric) = 2.7926475029609166000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 9.3176285628828600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.90000000000000100E-2 " " y[1] (analytic) = 2.68767173620956000E-3 " " y[1] (numeric) = 2.687671736209519000E-3 " " absolute error = 4.076600168545496700000000000000000E-17 " " relative error = 1.5167775564343103000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000000120E-2 " " y[1] (analytic) = 2.584717588216024000E-3 " " y[1] (numeric) = 2.5847175882160234000E-3 " " absolute error = 4.3368086899420180000000000000000000E-19 " " relative error = 1.677865585669377000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.10000000000000130E-2 " " y[1] (analytic) = 2.4837842266140592000E-3 " " y[1] (numeric) = 2.4837842266140034000E-3 " " absolute error = 5.59448321002520300000000000000000E-17 " " relative error = 2.252403067093999000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.200000000000001400E-2 " " y[1] (analytic) = 2.3848708357074386000E-3 " " y[1] (numeric) = 2.384870835707428900E-3 " " absolute error = 9.540979117872439000000000000000000E-18 " " relative error = 4.0006271933139060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.300000000000001500E-2 " " y[1] (analytic) = 2.2879766164442053000E-3 " " y[1] (numeric) = 2.287976616444167300E-3 " " absolute error = 3.816391647148975600000000000000000E-17 " " relative error = 1.6680203895965134000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.400000000000001600E-2 " " y[1] (analytic) = 2.1931007863900462000E-3 " " y[1] (numeric) = 2.1931007863900345000E-3 " " absolute error = 1.170938346284344800000000000000000E-17 " " relative error = 5.3391907638306390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.500000000000001700E-2 " " y[1] (analytic) = 2.1002425797034435000E-3 " " y[1] (numeric) = 2.1002425797034094000E-3 " " absolute error = 3.42607886505419400000000000000000E-17 " " relative error = 1.6312776905694196000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.600000000000002000E-2 " " y[1] (analytic) = 2.0094012471104333000E-3 " " y[1] (numeric) = 2.0094012471103895000E-3 " " absolute error = 4.38017677684143800000000000000000E-17 " " relative error = 2.1798417728366776000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.700000000000002000E-2 " " y[1] (analytic) = 1.9205760558805332000E-3 " " y[1] (numeric) = 1.920576055880509000E-3 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 1.2645231408209323000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.800000000000002000E-2 " " y[1] (analytic) = 1.8337662898030388000E-3 " " y[1] (numeric) = 1.833766289802998000E-3 " " absolute error = 4.076600168545496700000000000000000E-17 " " relative error = 2.2230750948003067000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.90000000000000200E-2 " " y[1] (analytic) = 1.7489712491636533000E-3 " " y[1] (numeric) = 1.7489712491635936000E-3 " " absolute error = 5.98479599211998400000000000000000E-17 " " relative error = 3.4218950111283275000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00000000000000200E-2 " " y[1] (analytic) = 1.666190250721917800E-3 " " y[1] (numeric) = 1.6661902507218950000E-3 " " absolute error = 2.276824562219559300000000000000000E-17 " " relative error = 1.3664853465761603000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.10000000000000200E-2 " " y[1] (analytic) = 1.5854226276892924000E-3 " " y[1] (numeric) = 1.5854226276892652000E-3 " " absolute error = 2.71050543121376100000000000000000E-17 " " relative error = 1.7096422013127466000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.20000000000000230E-2 " " y[1] (analytic) = 1.5066677297073083000E-3 " " y[1] (numeric) = 1.5066677297072714000E-3 " " absolute error = 3.68628738645071500000000000000000E-17 " " relative error = 2.446649193957867200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.30000000000000240E-2 " " y[1] (analytic) = 1.4299249228266897000E-3 " " y[1] (numeric) = 1.4299249228266725000E-3 " " absolute error = 1.71303943252709700000000000000000E-17 " " relative error = 1.1979925695264783000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.40000000000000250E-2 " " y[1] (analytic) = 1.3551935894869713000E-3 " " y[1] (numeric) = 1.355193589486942000E-3 " " absolute error = 2.90566182226115200000000000000000E-17 " " relative error = 2.144093541175274800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.500000000000002600E-2 " " y[1] (analytic) = 1.282473128496354200E-3 " " y[1] (numeric) = 1.2824731284963328000E-3 " " absolute error = 2.125036258071588700000000000000000E-17 " " relative error = 1.6569830672110100000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.600000000000002600E-2 " " y[1] (analytic) = 1.2117629550124805000E-3 " " y[1] (numeric) = 1.2117629550124757000E-3 " " absolute error = 4.7704895589362195000000000000000000E-18 " " relative error = 3.9368174602161250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.700000000000003000E-2 " " y[1] (analytic) = 1.1430625005235384000E-3 " " y[1] (numeric) = 1.143062500523518000E-3 " " absolute error = 2.038300084272748300000000000000000E-17 " " relative error = 1.7831921555813252000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.80000000000000300E-2 " " y[1] (analytic) = 1.0763712128298267000E-3 " " y[1] (numeric) = 1.0763712128297924000E-3 " " absolute error = 3.42607886505419400000000000000000E-17 " " relative error = 3.1829900541903977000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.90000000000000300E-2 " " y[1] (analytic) = 1.0116885560260698000E-3 " " y[1] (numeric) = 1.0116885560260233000E-3 " " absolute error = 4.64038529823795900000000000000000E-17 " " relative error = 4.586772550304882000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.00000000000000300E-2 " " y[1] (analytic) = 9.4901401048406130000E-4 " " y[1] (numeric) = 9.4901401048406160000E-4 " " absolute error = 3.25260651745651330000000000000000000E-19 " " relative error = 3.427353528529535300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.10000000000000300E-2 " " y[1] (analytic) = 8.8834707283620210000E-4 " " y[1] (numeric) = 8.8834707283615330000E-4 " " absolute error = 4.8789097761847700000000000000000E-17 " " relative error = 5.492121182555377000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.20000000000000300E-2 " " y[1] (analytic) = 8.296872559587339000E-4 " " y[1] (numeric) = 8.2968725595873540000E-4 " " absolute error = 1.4094628242311558000000000000000000E-18 " " relative error = 1.69878808443606840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.30000000000000300E-2 " " y[1] (analytic) = 7.7303408895678470000E-4 " " y[1] (numeric) = 7.7303408895676330000E-4 " " absolute error = 2.135878279796443700000000000000000E-17 " " relative error = 2.762980714962813300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.40000000000000340E-2 " " y[1] (analytic) = 7.1838711714858440000E-4 " " y[1] (numeric) = 7.1838711714856250000E-4 " " absolute error = 2.17924636669586400000000000000000E-17 " " relative error = 3.0335265133173720000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.50000000000000340E-2 " " y[1] (analytic) = 6.6574590205124670000E-4 " " y[1] (numeric) = 6.6574590205121050000E-4 " " absolute error = 3.62123525610158500000000000000000E-17 " " relative error = 5.4393654470032850000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.600000000000003500E-2 " " y[1] (analytic) = 6.1511002136646830000E-4 " " y[1] (numeric) = 6.1511002136644020000E-4 " " absolute error = 2.808083626737456500000000000000000E-17 " " relative error = 4.5651729433692084000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.700000000000003600E-2 " " y[1] (analytic) = 5.664790689670990000E-4 " " y[1] (numeric) = 5.664790689670720000E-4 " " absolute error = 2.69966340948890600000000000000000E-17 " " relative error = 4.76568960334473000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.800000000000003700E-2 " " y[1] (analytic) = 5.1985265488399050000E-4 " " y[1] (numeric) = 5.1985265488396600000E-4 " " absolute error = 2.43945488809238500000000000000000E-17 " " relative error = 4.692589073411137500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90000000000000400E-2 " " y[1] (analytic) = 4.7523040529351734000E-4 " " y[1] (numeric) = 4.7523040529350040000E-4 " " absolute error = 1.69135538907738700000000000000000E-17 " " relative error = 3.559021834961827000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000000300E-2 " " y[1] (analytic) = 4.32611962505566800000E-4 " " y[1] (numeric) = 4.3261196250556780000E-4 " " absolute error = 9.757819552369540000000000000000000E-19 " " relative error = 2.25555934603726470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.10000000000000300E-2 " " y[1] (analytic) = 3.91996984952114900000E-4 " " y[1] (numeric) = 3.9199698495209706000E-4 " " absolute error = 1.778091562876227300000000000000000E-17 " " relative error = 4.535982752758757600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.20000000000000400E-2 " " y[1] (analytic) = 3.5338514717612330000E-4 " " y[1] (numeric) = 3.5338514717609120000E-4 " " absolute error = 3.20923843055709300000000000000000E-17 " " relative error = 9.081418549143617000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.30000000000000400E-2 " " y[1] (analytic) = 3.16776139821213050000E-4 " " y[1] (numeric) = 3.1677613982118870000E-4 " " absolute error = 2.434033877229957500000000000000000E-17 " " relative error = 7.683766456033319000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.40000000000000400E-2 " " y[1] (analytic) = 2.8216966962178850000E-4 " " y[1] (numeric) = 2.82169669621740200000E-4 " " absolute error = 4.82469966756049500000000000000000E-17 " " relative error = 1.709857644879895500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.50000000000000400E-2 " " y[1] (analytic) = 2.4956545939345728000E-4 " " y[1] (numeric) = 2.4956545939340688000E-4 " " absolute error = 5.041540102057596000000000000000000E-17 " " relative error = 2.020127350279373700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.60000000000000400E-2 " " y[1] (analytic) = 2.18963248024308250000E-4 " " y[1] (numeric) = 2.1896324802427228000E-4 " " absolute error = 3.59684070722066100000000000000000E-17 " " relative error = 1.642668685121695400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.700000000000004000E-2 " " y[1] (analytic) = 1.90362790466501170000E-4 " " y[1] (numeric) = 1.9036279046647570000E-4 " " absolute error = 2.547875105340935400000000000000000E-17 " " relative error = 1.33843126542594700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.800000000000004000E-2 " " y[1] (analytic) = 1.63763857728398020000E-4 " " y[1] (numeric) = 1.63763857728357360000E-4 " " absolute error = 4.065758146820641600000000000000000E-17 " " relative error = 2.482695634566506300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.900000000000004000E-2 " " y[1] (analytic) = 1.39166236867132170000E-4 " " y[1] (numeric) = 1.39166236867123680000E-4 " " absolute error = 8.483881999699072000000000000000000E-18 " " relative error = 6.096221461962064000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.000000000000004000E-2 " " y[1] (analytic) = 1.16569730982065910000E-4 " " y[1] (numeric) = 1.16569730982023790000E-4 " " absolute error = 4.21212544010618500000000000000000E-17 " " relative error = 3.61339552268008100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.10000000000000400E-2 " " y[1] (analytic) = 9.59741592080887400000E-5 " " y[1] (numeric) = 9.59741592080448400000E-5 " " absolute error = 4.38966354585068600000000000000000E-17 " " relative error = 4.573797345109456600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.20000000000000400E-2 " " y[1] (analytic) = 7.73793567101491900000E-5 " " y[1] (numeric) = 7.73793567101180300000E-5 " " absolute error = 3.115725993180218400000000000000000E-17 " " relative error = 4.02655969970289900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.30000000000000400E-2 " " y[1] (analytic) = 6.07851746778603700000E-5 " " y[1] (numeric) = 6.0785174677842200000E-5 " " absolute error = 1.8160386389132200000000000000000E-17 " " relative error = 2.98763415345530200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.40000000000000500E-2 " " y[1] (analytic) = 4.61914803207390200000E-5 " " y[1] (numeric) = 4.61914803207176600000E-5 " " absolute error = 2.135878279796443700000000000000000E-17 " " relative error = 4.62396585899733260000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.50000000000000500E-2 " " y[1] (analytic) = 3.3598156863916100000E-5 " " y[1] (numeric) = 3.359815686389686600000E-5 " " absolute error = 1.92378122980396700000000000000000E-17 " " relative error = 5.72585346748612300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.60000000000000500E-2 " " y[1] (analytic) = 2.30051035444890720000E-5 " " y[1] (numeric) = 2.300510354444458600000E-5 " " absolute error = 4.448617038979585400000000000000000E-17 " " relative error = 1.93375223474934630000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.70000000000000500E-2 " " y[1] (analytic) = 1.441223560813110800000E-5 " " y[1] (numeric) = 1.44122356081144900000E-5 " " absolute error = 1.661709235923486400000000000000000E-17 " " relative error = 1.15298506151674470000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.80000000000000500E-2 " " y[1] (analytic) = 7.81948430668165000000E-6 " " y[1] (numeric) = 7.819484306634744000000E-6 " " absolute error = 4.690529648715413600000000000000000E-17 " " relative error = 5.9985153301061240000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.90000000000000500E-2 " " y[1] (analytic) = 3.226796895555149000000E-6 " " y[1] (numeric) = 3.2267968955095744000000E-6 " " absolute error = 4.557418421054400000000000000000E-17 " " relative error = 1.4123660610099623000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000000500E-2 " " y[1] (analytic) = 6.3413663235778240000000E-7 " " y[1] (numeric) = 6.3413663232954020000000E-7 " " absolute error = 2.82421960438265060000000000000000E-17 " " relative error = 4.453645256041942000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.10000000000000500E-2 " " y[1] (analytic) = 4.14827756035017700000000E-8 " " y[1] (numeric) = 4.14827755975059660000000E-8 " " absolute error = 5.99580212647837000000000000000000E-18 " " relative error = 1.445371491962614600000000E-8 "%" Correct digits = 10 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.20000000000000500E-2 " " y[1] (analytic) = 1.448830584085602000000E-6 " " y[1] (numeric) = 1.4488305840631244000000E-6 " " absolute error = 2.247750156305055600000000000000000E-17 " " relative error = 1.5514237351109442000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.30000000000000500E-2 " " y[1] (analytic) = 4.8561913166268680000000E-6 " " y[1] (numeric) = 4.85619131657289040000E-6 " " absolute error = 5.39771745637802800000000000000000E-17 " " relative error = 1.1115125217363364000000000E-9 "%" Correct digits = 11 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.40000000000000500E-2 " " y[1] (analytic) = 1.026359223243048800000E-5 " " y[1] (numeric) = 1.026359223242864900000E-5 " " absolute error = 1.8397555614363403000000000000000000E-18 " " relative error = 1.792506482889250000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.50000000000000600E-2 " " y[1] (analytic) = 1.767107659230894600000E-5 " " y[1] (numeric) = 1.767107659226170300000E-5 " " absolute error = 4.724410966605585600000000000000000E-17 " " relative error = 2.67352752500762200000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.60000000000000600E-2 " " y[1] (analytic) = 2.70787036594578400000E-5 " " y[1] (numeric) = 2.70787036594154300000E-5 " " absolute error = 4.24092456031283100000000000000000E-17 " " relative error = 1.56614755774381160000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.70000000000000600E-2 " " y[1] (analytic) = 3.848654870188275600000E-5 " " y[1] (numeric) = 3.8486548701843700000E-5 " " absolute error = 3.9058383263790300000000000000000E-17 " " relative error = 1.01485803692965500000000000E-10 "%" Correct digits = 12 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.80000000000000600E-2 " " y[1] (analytic) = 5.18947029945345300000E-5 " " y[1] (numeric) = 5.18947029945179700000E-5 " " absolute error = 1.65611881847160800000000000000000E-17 " " relative error = 3.191306092735568500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.90000000000000600E-2 " " y[1] (analytic) = 6.73032738223719700000E-5 " " y[1] (numeric) = 6.7303273822350500000E-5 " " absolute error = 2.146720301521298800000000000000000E-17 " " relative error = 3.189622405571179700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000000600E-2 " " y[1] (analytic) = 8.4712384483627700000E-5 " " y[1] (numeric) = 8.47123844836266300000E-5 " " absolute error = 1.0706496453294356000000000000000000E-18 " " relative error = 1.2638643710192804000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.10000000000000600E-2 " " y[1] (analytic) = 1.04122174293995420000E-4 " " y[1] (numeric) = 1.04122174293953550000E-4 " " absolute error = 4.18637563850965400000000000000000E-17 " " relative error = 4.02063793509455800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.20000000000000600E-2 " " y[1] (analytic) = 1.2553279859073610000E-4 " " y[1] (numeric) = 1.2553279859071870000E-4 " " absolute error = 1.740144486839234600000000000000000E-17 " " relative error = 1.386207036228419800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.30000000000000600E-2 " " y[1] (analytic) = 1.4894442873808630000E-4 " " y[1] (numeric) = 1.48944428738065240000E-4 " " absolute error = 2.106062720053092400000000000000000E-17 " " relative error = 1.413992277453044000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.40000000000000600E-2 " " y[1] (analytic) = 1.74357252132410020000E-4 " " y[1] (numeric) = 1.74357252132377650000E-4 " " absolute error = 3.23634348486923100000000000000000E-17 " " relative error = 1.85615650928674520000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.50000000000000600E-2 " " y[1] (analytic) = 2.0177147220831018000E-4 " " y[1] (numeric) = 2.01771472208285290000E-4 " " absolute error = 2.490954491285446400000000000000000E-17 " " relative error = 1.23454245737661490000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.60000000000000700E-2 " " y[1] (analytic) = 2.31187308445194600000E-4 " " y[1] (numeric) = 2.31187308445176880000E-4 " " absolute error = 1.775381057445013500000000000000000E-17 " " relative error = 7.679405367816229000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.70000000000000700E-2 " " y[1] (analytic) = 2.6260499637423470000E-4 " " y[1] (numeric) = 2.6260499637423350000E-4 " " absolute error = 1.1926223897340549000000000000000000E-18 " " relative error = 4.5415068494525730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.80000000000000700E-2 " " y[1] (analytic) = 2.96024787585988050000E-4 " " y[1] (numeric) = 2.96024787585973840000E-4 " " absolute error = 1.420304845956010800000000000000000E-17 " " relative error = 4.7979253951611955000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.90000000000000700E-2 " " y[1] (analytic) = 3.31446949738345400000E-4 " " y[1] (numeric) = 3.3144694973831880000E-4 " " absolute error = 2.65629532258948600000000000000000E-17 " " relative error = 8.014239758991444000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000000700E-2 " " y[1] (analytic) = 3.68871766565181670000E-4 " " y[1] (numeric) = 3.68871766565169100000E-4 " " absolute error = 1.252253509220757600000000000000000E-17 " " relative error = 3.394820701192043000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.10000000000000700E-2 " " y[1] (analytic) = 4.0829953788553830000E-4 " " y[1] (numeric) = 4.08299537885504050000E-4 " " absolute error = 3.42607886505419400000000000000000E-17 " " relative error = 8.391091703891795000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.20000000000000700E-2 " " y[1] (analytic) = 4.4973057961304940000E-4 " " y[1] (numeric) = 4.49730579612993600000E-4 " " absolute error = 5.5782201774379200000000000000000E-17 " " relative error = 1.240347094528784500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.30000000000000700E-2 " " y[1] (analytic) = 4.9316522376615907000E-4 " " y[1] (numeric) = 4.9316522376613390000E-4 " " absolute error = 2.515349040166370300000000000000000E-17 " " relative error = 5.1004185188837580000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.40000000000000700E-2 " " y[1] (analytic) = 5.3860381847895260000E-4 " " y[1] (numeric) = 5.3860381847889670000E-4 " " absolute error = 5.58364118830034800000000000000000E-17 " " relative error = 1.036688006421652200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.50000000000000700E-2 " " y[1] (analytic) = 5.860467280119270000E-4 " " y[1] (numeric) = 5.8604672801190390000E-4 " " absolute error = 2.309350627394124400000000000000000E-17 " " relative error = 3.940557155277088500000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.60000000000000700E-2 " " y[1] (analytic) = 6.3549433276413240000E-4 " " y[1] (numeric) = 6.3549433276411750000E-4 " " absolute error = 1.48535697630514100000000000000000E-17 " " relative error = 2.3373252910761055000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.70000000000000800E-2 " " y[1] (analytic) = 6.8694702928506480000E-4 " " y[1] (numeric) = 6.8694702928505590000E-4 " " absolute error = 8.890457814381136000000000000000000E-18 " " relative error = 1.2941984513178284000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.80000000000000800E-2 " " y[1] (analytic) = 7.4040523028757390000E-4 " " y[1] (numeric) = 7.4040523028752820000E-4 " " absolute error = 4.564491146163973700000000000000000E-17 " " relative error = 6.164855351428463000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.90000000000000800E-2 " " y[1] (analytic) = 7.9586936466094400000E-4 " " y[1] (numeric) = 7.9586936466089590000E-4 " " absolute error = 4.82469966756049500000000000000000E-17 " " relative error = 6.062175379267063000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000007 " " y[1] (analytic) = 8.5333987748490940000E-4 " " y[1] (numeric) = 8.5333987748485310000E-4 " " absolute error = 5.62700927519976800000000000000000E-17 " " relative error = 6.5941009246919650000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10100000000000008 " " y[1] (analytic) = 9.1281723004376100000E-4 " " y[1] (numeric) = 9.1281723004373850000E-4 " " absolute error = 2.255140518769849200000000000000000E-17 " " relative error = 2.4705279924018703000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000008 " " y[1] (analytic) = 9.7430189984141920000E-4 " " y[1] (numeric) = 9.743018998413671000E-4 " " absolute error = 5.225854471380131000000000000000000E-17 " " relative error = 5.363691143608269000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000008 " " y[1] (analytic) = 1.0377943806164033000E-3 " " y[1] (numeric) = 1.0377943806163926000E-3 " " absolute error = 1.062518129035794300000000000000000E-17 " " relative error = 1.0238233593100651000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000008 " " y[1] (analytic) = 1.1032951823582353000E-3 " " y[1] (numeric) = 1.1032951823581971000E-3 " " absolute error = 3.816391647148975600000000000000000E-17 " " relative error = 3.459084847077497000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000008 " " y[1] (analytic) = 1.170804831323326900E-3 " " y[1] (numeric) = 1.1708048313233091000E-3 " " absolute error = 1.778091562876227300000000000000000E-17 " " relative error = 1.5186916856727536000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000008 " " y[1] (analytic) = 1.2403238700523796000E-3 " " y[1] (numeric) = 1.2403238700523518000E-3 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.237768399511394000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000008 " " y[1] (analytic) = 1.3118528573875674000E-3 " " y[1] (numeric) = 1.3118528573875250000E-3 " " absolute error = 4.250072516143177400000000000000000E-17 " " relative error = 3.2397478819437114000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000008 " " y[1] (analytic) = 1.3853923684906486000E-3 " " y[1] (numeric) = 1.385392368490615000E-3 " " absolute error = 3.36102673470506400000000000000000E-17 " " relative error = 2.426046808938915000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000008 " " y[1] (analytic) = 1.4609429948615474000E-3 " " y[1] (numeric) = 1.460942994861545000E-3 " " absolute error = 2.3852447794681098000000000000000000E-18 " " relative error = 1.6326747777685590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000008 " " y[1] (analytic) = 1.5385053443574934000E-3 " " y[1] (numeric) = 1.538505344357453000E-3 " " absolute error = 4.033232081646076500000000000000000E-17 " " relative error = 2.621526208172143000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000008 " " y[1] (analytic) = 1.6180800412123236000E-3 " " y[1] (numeric) = 1.6180800412123134000E-3 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.4325253329634670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000009 " " y[1] (analytic) = 1.6996677260571344000E-3 " " y[1] (numeric) = 1.6996677260570894000E-3 " " absolute error = 4.510281037539698400000000000000000E-17 " " relative error = 2.6536251576668960000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000009 " " y[1] (analytic) = 1.783269055940447000E-3 " " y[1] (numeric) = 1.7832690559404318000E-3 " " absolute error = 1.517883041479706200000000000000000E-17 " " relative error = 8.5118004847519570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000009 " " y[1] (analytic) = 1.8688847043499637000E-3 " " y[1] (numeric) = 1.8688847043499118000E-3 " " absolute error = 5.18248638448071100000000000000000E-17 " " relative error = 2.773036973558669000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000009 " " y[1] (analytic) = 1.9565153612337988000E-3 " " y[1] (numeric) = 1.9565153612338004000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 8.8663933355620210000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000009 " " y[1] (analytic) = 2.046161733023422000E-3 " " y[1] (numeric) = 2.0461617330233892000E-3 " " absolute error = 3.25260651745651330000000000000000E-17 " " relative error = 1.5896135994345084000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000009 " " y[1] (analytic) = 2.1378245426558695000E-3 " " y[1] (numeric) = 2.137824542655856800E-3 " " absolute error = 1.257674520083185100000000000000000E-17 " " relative error = 5.8829641768484260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000009 " " y[1] (analytic) = 2.2315045295977365000E-3 " " y[1] (numeric) = 2.2315045295976818000E-3 " " absolute error = 5.464378949326942000000000000000000E-17 " " relative error = 2.448742037871633700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000009 " " y[1] (analytic) = 2.327202449868615000E-3 " " y[1] (numeric) = 2.327202449868604200E-3 " " absolute error = 1.084202172485504400000000000000000E-17 " " relative error = 4.6588218938438913000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000009 " " y[1] (analytic) = 2.4249190760661543000E-3 " " y[1] (numeric) = 2.4249190760661377000E-3 " " absolute error = 1.69135538907738700000000000000000E-17 " " relative error = 6.9748941553183820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1210000000000001 " " y[1] (analytic) = 2.5246551973906310000E-3 " " y[1] (numeric) = 2.5246551973906310000E-3 " " 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] = 0.1220000000000001 " " y[1] (analytic) = 2.626411619670933000E-3 " " y[1] (numeric) = 2.6264116196708864000E-3 " " absolute error = 4.64038529823795900000000000000000E-17 " " relative error = 1.7668157053079744000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1230000000000001 " " y[1] (analytic) = 2.73018916539033000E-3 " " y[1] (numeric) = 2.7301891653903290000E-3 " " absolute error = 1.3010426069826053000000000000000000E-18 " " relative error = 4.76539363453446900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1240000000000001 " " y[1] (analytic) = 2.835988673713775700E-3 " " y[1] (numeric) = 2.835988673713735000E-3 " " absolute error = 4.076600168545496700000000000000000E-17 " " relative error = 1.437452908867622200000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000008 " " y[1] (analytic) = 2.9438110005145646000E-3 " " y[1] (numeric) = 2.943811000514524000E-3 " " absolute error = 4.076600168545496700000000000000000E-17 " " relative error = 1.3848036330569202000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000008 " " y[1] (analytic) = 3.0536570184026235000E-3 " " y[1] (numeric) = 3.0536570184026000E-3 " " absolute error = 2.341876692568689600000000000000000E-17 " " relative error = 7.66908882842950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000009 " " y[1] (analytic) = 3.165527616752773000E-3 " " y[1] (numeric) = 3.165527616752768000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 1.64401359204343500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000009 " " y[1] (analytic) = 3.2794237017337435000E-3 " " y[1] (numeric) = 3.2794237017337047000E-3 " " absolute error = 3.90312782094781600000000000000000E-17 " " relative error = 1.1901871108891288000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1290000000000001 " " y[1] (analytic) = 3.3953461963375420000E-3 " " y[1] (numeric) = 3.3953461963375053000E-3 " " absolute error = 3.64291929955129500000000000000000E-17 " " relative error = 1.072915422727969000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1300000000000001 " " y[1] (analytic) = 3.5132960404098496000E-3 " " y[1] (numeric) = 3.51329604040979000E-3 " " absolute error = 5.94142790522056400000000000000000E-17 " " relative error = 1.6911264626955425000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1310000000000001 " " y[1] (analytic) = 3.6332741906804356000E-3 " " y[1] (numeric) = 3.6332741906803890000E-3 " " absolute error = 4.68375338513737900000000000000000E-17 " " relative error = 1.2891274204274167000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1320000000000001 " " y[1] (analytic) = 3.755281620794654000E-3 " " y[1] (numeric) = 3.7552816207945930000E-3 " " absolute error = 6.07153216591882500000000000000000E-17 " " relative error = 1.61679809372966000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1330000000000001 " " y[1] (analytic) = 3.879319321345006000E-3 " " y[1] (numeric) = 3.8793193213449895000E-3 " " absolute error = 1.69135538907738700000000000000000E-17 " " relative error = 4.3599282476467390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1340000000000001 " " y[1] (analytic) = 4.005388299903887000E-3 " " y[1] (numeric) = 4.005388299903861500E-3 " " absolute error = 2.515349040166370300000000000000000E-17 " " relative error = 6.2799130866456280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1350000000000001 " " y[1] (analytic) = 4.133489581056227000E-3 " " y[1] (numeric) = 4.133489581056182000E-3 " " absolute error = 4.510281037539698400000000000000000E-17 " " relative error = 1.0911557774840672000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1360000000000001 " " y[1] (analytic) = 4.263624206433201000E-3 " " y[1] (numeric) = 4.263624206433176400E-3 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 5.6961231777957810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1370000000000001 " " y[1] (analytic) = 4.395793234746528000E-3 " " y[1] (numeric) = 4.395793234746481000E-3 " " absolute error = 4.68375338513737900000000000000000E-17 " " relative error = 1.0655081199258125000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1380000000000001 " " y[1] (analytic) = 4.529997741822899000E-3 " " y[1] (numeric) = 4.529997741822879300E-3 " " absolute error = 1.994931997373328200000000000000000E-17 " " relative error = 4.40382558904004100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1390000000000001 " " y[1] (analytic) = 4.666238820639647000E-3 " " y[1] (numeric) = 4.6662388206396305000E-3 " " absolute error = 1.647987302177966700000000000000000E-17 " " relative error = 3.5317251549333710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1400000000000001 " " y[1] (analytic) = 4.8045175813604060000E-3 " " y[1] (numeric) = 4.804517581360393500E-3 " " absolute error = 1.21430643318376500000000000000000E-17 " " relative error = 2.52742634951485100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1410000000000001 " " y[1] (analytic) = 4.944835151371783000E-3 " " y[1] (numeric) = 4.944835151371738000E-3 " " absolute error = 4.510281037539698400000000000000000E-17 " " relative error = 9.1211959539004420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1420000000000001 " " y[1] (analytic) = 5.08719267532029000E-3 " " y[1] (numeric) = 5.087192675320257000E-3 " " absolute error = 3.295974604355933500000000000000000E-17 " " relative error = 6.4789655409472350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 12.559206357365387 " " Order of pole = 11238.693380003087 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1430000000000001 " " y[1] (analytic) = 5.231591315150308000E-3 " " y[1] (numeric) = 5.231591315150280000E-3 " " absolute error = 2.68882138776405100000000000000000E-17 " " relative error = 5.1395860758033980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 6.056191028802021 " " Order of pole = 5419.870202731336 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1440000000000001 " " y[1] (analytic) = 5.378032250142234000E-3 " " y[1] (numeric) = 5.3780322501421840000E-3 " " absolute error = 5.030698080332741000000000000000000E-17 " " relative error = 9.3541612365743860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 4.075743160907307 " " Order of pole = 3648.117488247297 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1450000000000001 " " y[1] (analytic) = 5.526516676951327000E-3 " " y[1] (numeric) = 5.526516676951307000E-3 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 3.45280026301690970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 3.118600675683534 " " Order of pole = 2792.0885501690823 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1460000000000001 " " y[1] (analytic) = 5.677045809647528000E-3 " " y[1] (numeric) = 5.677045809647485000E-3 " " absolute error = 4.33680868994201800000000000000000E-17 " " relative error = 7.6391997446490180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 2.555325308616981 " " Order of pole = 2288.5247972936245 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1470000000000001 " " y[1] (analytic) = 5.829620879755184000E-3 " " y[1] (numeric) = 5.829620879755171000E-3 " " absolute error = 1.301042606982605300000000000000000E-17 " " relative error = 2.23177910505432870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 2.184862395097448 " " Order of pole = 1957.5106131360055 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1480000000000001 " " y[1] (analytic) = 5.984243136294214000E-3 " " y[1] (numeric) = 5.9842431362942010E-3 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.3190548063874922000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.923094160847095 " " Order of pole = 1723.7724175444482 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1490000000000001 " " y[1] (analytic) = 6.140913845821157000E-3 " " y[1] (numeric) = 6.140913845821142000E-3 " " absolute error = 1.47451495458028600000000000000000E-17 " " relative error = 2.4011327818638620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.7286159387846545 " " Order of pole = 1550.2588352629548 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1500000000000001 " " y[1] (analytic) = 6.299634292471308000E-3 " " y[1] (numeric) = 6.299634292471291000E-3 " " absolute error = 1.647987302177966700000000000000000E-17 " " relative error = 2.6160047165713670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.5786787479901148 " " Order of pole = 1416.612692790954 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1510000000000001 " " y[1] (analytic) = 6.460405778001298000E-3 " " y[1] (numeric) = 6.460405778001271000E-3 " " absolute error = 2.602085213965210600000000000000000E-17 " " relative error = 4.0277426888969137000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.459745612251916 " " Order of pole = 1310.7202538800577 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1520000000000001 " " y[1] (analytic) = 6.623229621832297000E-3 " " y[1] (numeric) = 6.623229621832265000E-3 " " absolute error = 3.20923843055709300000000000000000E-17 " " relative error = 4.8454283088395583000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.363257077102597 " " Order of pole = 1224.9219539931594 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1530000000000001 " " y[1] (analytic) = 6.788107161093907000E-3 " " y[1] (numeric) = 6.7881071610938730000E-3 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 5.1110668550413850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.2835358389437532 " " Order of pole = 1154.1373388114869 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1540000000000001 " " y[1] (analytic) = 6.955039750668637000E-3 " " y[1] (numeric) = 6.955039750668603000E-3 " " absolute error = 3.38271077815477400000000000000000E-17 " " relative error = 4.8636828823725564000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.2166676830603287 " " Order of pole = 1094.8636617024351 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1550000000000001 " " y[1] (analytic) = 7.124028763237032000E-3 " " y[1] (numeric) = 7.1240287632370010000E-3 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 4.38305677943310660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.1598662604574144 " " Order of pole = 1044.607448800449 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1560000000000001 " " y[1] (analytic) = 7.295075589323465000E-3 " " y[1] (numeric) = 7.295075589323405000E-3 " " absolute error = 6.07153216591882500000000000000000E-17 " " relative error = 8.3227817060657620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.111094050035956 " " Order of pole = 1001.5453138962772 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1570000000000001 " " y[1] (analytic) = 7.468181637342370000E-3 " " y[1] (numeric) = 7.468181637342352000E-3 " " absolute error = 1.908195823574487800000000000000000E-17 " " relative error = 2.55510098205583900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.0688265588996178 " " Order of pole = 964.3129512907119 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1580000000000001 " " y[1] (analytic) = 7.6433483336456960000E-3 " " y[1] (numeric) = 7.643348333645626000E-3 " " absolute error = 7.02563007770606900000000000000000E-17 " " relative error = 9.1918224461647810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 1.0319003515688399 " " Order of pole = 931.8691437236118 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1590000000000001 " " y[1] (analytic) = 7.820577122569956000E-3 " " y[1] (numeric) = 7.820577122569955000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.21815276390593480000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.9994120841760403 " " Order of pole = 903.4054125861015 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000011 " " y[1] (analytic) = 7.99986946648542000E-3 " " y[1] (numeric) = 7.999869466485352000E-3 " " absolute error = 6.76542155630954800000000000000000E-17 " " relative error = 8.4569149342405450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.9706496301342001 " " Order of pole = 878.2843854889328 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000012 " " y[1] (analytic) = 8.181226845844156000E-3 " " y[1] (numeric) = 8.181226845844124000E-3 " " absolute error = 3.295974604355933500000000000000000E-17 " " relative error = 4.02870457751724640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.9450439958682926 " " Order of pole = 855.9967680148104 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000012 " " y[1] (analytic) = 8.364650759230551000E-3 " " y[1] (numeric) = 8.364650759230522000E-3 " " absolute error = 2.94902990916057200000000000000000E-17 " " relative error = 3.5255864160332834000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.9221350557979322 " " Order of pole = 836.1306817585521 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000012 " " y[1] (analytic) = 8.550142723411109000E-3 " " y[1] (numeric) = 8.550142723411073000E-3 " " absolute error = 3.64291929955129500000000000000000E-17 " " relative error = 4.260653204743160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.9015466848153578 " " Order of pole = 818.3494118047779 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000012 " " y[1] (analytic) = 8.737704273385607000E-3 " " y[1] (numeric) = 8.737704273385556000E-3 " " absolute error = 5.030698080332741000000000000000000E-17 " " relative error = 5.757459766240740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.8829684127557561 " " Order of pole = 802.3749904714468 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000012 " " y[1] (analytic) = 8.927336962438664000E-3 " " y[1] (numeric) = 8.927336962438664000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.8661416887823034 " " Order of pole = 787.9759062775082 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000012 " " y[1] (analytic) = 9.119042362192397000E-3 " " y[1] (numeric) = 9.119042362192332000E-3 " " absolute error = 6.41847686111418600000000000000000E-17 " " relative error = 7.0385426519403270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.8508494584935398 " " Order of pole = 774.9577773287203 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000012 " " y[1] (analytic) = 9.312822062658778000E-3 " " y[1] (numeric) = 9.312822062658741000E-3 " " absolute error = 3.64291929955129500000000000000000E-17 " " relative error = 3.91172436780270000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.8369081575919716 " " Order of pole = 763.1561871822184 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000012 " " y[1] (analytic) = 9.508677672294062000E-3 " " y[1] (numeric) = 9.508677672294004000E-3 " " absolute error = 5.89805981832114400000000000000000E-17 " " relative error = 6.2028181221313590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.82416149269431 " " Order of pole = 752.4311199465391 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000012 " " y[1] (analytic) = 9.706610818052531000E-3 " " y[1] (numeric) = 9.706610818052535000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.57431344161967800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.8124755604940918 " " Order of pole = 742.6625930126135 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000012 " " y[1] (analytic) = 9.906623145442175000E-3 " " y[1] (numeric) = 9.90662314544210900E-3 " " absolute error = 6.59194920871186700000000000000000E-17 " " relative error = 6.6540829422230330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.8017349808181308 " " Order of pole = 733.747197069765 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000012 " " y[1] (analytic) = 1.010871631857965500E-2 " " y[1] (numeric) = 1.010871631857961800E-2 " " absolute error = 3.816391647148975600000000000000000E-17 " " relative error = 3.7753474594341024000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7918398059994018 " " Order of pole = 725.5953308072135 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000013 " " y[1] (analytic) = 1.031289202024755000E-2 " " y[1] (numeric) = 1.031289202024750800E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.03702117133618640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7827030305451285 " " Order of pole = 718.128972785808 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000013 " " y[1] (analytic) = 1.051915195195098200E-2 " " y[1] (numeric) = 1.051915195195093900E-2 " " absolute error = 4.33680868994201800000000000000000E-17 " " relative error = 4.1227740693846254000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7742485692558922 " " Order of pole = 711.279872496977 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000013 " " y[1] (analytic) = 1.07274978339756700E-2 " " y[1] (numeric) = 1.07274978339756300E-2 " " absolute error = 3.989863994746656300000000000000000E-17 " " relative error = 3.71928669340778700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7664096040360777 " " Order of pole = 704.9880713371547 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000013 " " y[1] (analytic) = 1.093793140544645200E-2 " " y[1] (numeric) = 1.09379314054464300E-2 " " absolute error = 2.255140518769849200000000000000000E-17 " " relative error = 2.0617614384077420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7591272231961803 " " Order of pole = 699.2006853090506 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000013 " " y[1] (analytic) = 1.11504544243866300E-2 " " y[1] (numeric) = 1.115045442438658300E-2 " " absolute error = 4.8572257327350600000000000000000E-17 " " relative error = 4.35607872815663160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.752349294527813 " " Order of pole = 693.8708969036671 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000013 " " y[1] (analytic) = 1.136506866777778200E-2 " " y[1] (numeric) = 1.136506866777773100E-2 " " absolute error = 5.030698080332741000000000000000000E-17 " " relative error = 4.42645638789298750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7460295265287694 " " Order of pole = 688.9571153366189 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000013 " " y[1] (analytic) = 1.158177593162066900E-2 " " y[1] (numeric) = 1.158177593162063200E-2 " " absolute error = 3.64291929955129500000000000000000E-17 " " relative error = 3.14538920547181740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7401266820539247 " " Order of pole = 684.422273170073 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000013 " " y[1] (analytic) = 1.180057803099660700E-2 " " y[1] (numeric) = 1.180057803099659700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 8.82019578068229300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7346039162154854 " " Order of pole = 680.2332341058878 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000013 " " y[1] (analytic) = 1.202147680012969000E-2 " " y[1] (numeric) = 1.202147680012966300E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.30883244023142640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7294282161571194 " " Order of pole = 676.360291926774 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000013 " " y[1] (analytic) = 1.224447409244954800E-2 " " y[1] (numeric) = 1.224447409244951700E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 2.5501317844951116000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7245699248145356 " " Order of pole = 672.7767445784116 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000013 " " y[1] (analytic) = 1.246957178065519200E-2 " " y[1] (numeric) = 1.246957178065513100E-2 " " absolute error = 6.07153216591882500000000000000000E-17 " " relative error = 4.8690783233935614000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7200023342812599 " " Order of pole = 669.4585305232854 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000013 " " y[1] (analytic) = 1.269677175677921800E-2 " " y[1] (numeric) = 1.269677175677917000E-2 " " absolute error = 4.68375338513737900000000000000000E-17 " " relative error = 3.68893248997452570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7157013371432887 " " Order of pole = 666.3839169531886 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000014 " " y[1] (analytic) = 1.29260759322532110E-2 " " y[1] (numeric) = 1.292607593225314200E-2 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 5.3681364245998770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7116451263223443 " " Order of pole = 663.5332313948868 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000014 " " y[1] (analytic) = 1.31574862379733100E-2 " " y[1] (numeric) = 1.315748623797328200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.10948923780931830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.707813935690683 " " Order of pole = 660.8886297853633 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000014 " " y[1] (analytic) = 1.339100462436731400E-2 " " y[1] (numeric) = 1.33910046243672400E-2 " " absolute error = 7.4593109467002700000000000000000E-17 " " relative error = 5.5703893441472850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7041898151031373 " " Order of pole = 658.4338953306504 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000014 " " y[1] (analytic) = 1.36266330614615300E-2 " " y[1] (numeric) = 1.36266330614614900E-2 " " absolute error = 3.989863994746656300000000000000000E-17 " " relative error = 2.92798960443917800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.7007564345997529 " " Order of pole = 656.1542634534161 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000014 " " y[1] (analytic) = 1.386437353894959500E-2 " " y[1] (numeric) = 1.386437353894953400E-2 " " absolute error = 6.07153216591882500000000000000000E-17 " " relative error = 4.3792329663232810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6974989134288485 " " Order of pole = 654.036268936781 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000014 " " y[1] (analytic) = 1.410422806626090700E-2 " " y[1] (numeric) = 1.410422806626088500E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 1.47591783215118430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6944036702687487 " " Order of pole = 652.0676120237597 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000014 " " y[1] (analytic) = 1.434619867263085000E-2 " " y[1] (numeric) = 1.434619867263080300E-2 " " absolute error = 4.8572257327350600000000000000000E-17 " " relative error = 3.38572317557646550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6914582916192072 " " Order of pole = 650.2370407621704 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19100000000000014 " " y[1] (analytic) = 1.459028740717085700E-2 " " y[1] (numeric) = 1.459028740717084600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 7.13374628298640300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6886514158200232 " " Order of pole = 648.5342473202395 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19200000000000014 " " y[1] (analytic) = 1.483649633894026400E-2 " " y[1] (numeric) = 1.483649633894020300E-2 " " absolute error = 5.89805981832114400000000000000000E-17 " " relative error = 3.97537240840409200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6859726305550448 " " Order of pole = 646.9497763567571 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19300000000000014 " " y[1] (analytic) = 1.508482755701784400E-2 " " y[1] (numeric) = 1.508482755701781600E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.83996638415109460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6834123820298549 " " Order of pole = 645.4749438250169 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19400000000000014 " " y[1] (analytic) = 1.533528317057534800E-2 " " y[1] (numeric) = 1.53352831705753120E-2 " " absolute error = 3.64291929955129500000000000000000E-17 " " relative error = 2.37551485618548250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6809618942860943 " " Order of pole = 644.1017648356079 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19500000000000015 " " y[1] (analytic) = 1.558786530895079300E-2 " " y[1] (numeric) = 1.55878653089507380E-2 " " absolute error = 5.37764277552810200000000000000000E-17 " " relative error = 3.4498904557766330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6786130973445675 " " Order of pole = 642.8228894082898 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19600000000000015 " " y[1] (analytic) = 1.584257612172315600E-2 " " y[1] (numeric) = 1.584257612172312600E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.97095613287078600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6763585630581538 " " Order of pole = 641.6315451120765 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19700000000000015 " " y[1] (analytic) = 1.609941777878788300E-2 " " y[1] (numeric) = 1.609941777878784000E-2 " " absolute error = 4.510281037539698400000000000000000E-17 " " relative error = 2.80151810426480850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6741914477180815 " " Order of pole = 640.521485738273 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19800000000000015 " " y[1] (analytic) = 1.635839247043283400E-2 " " y[1] (numeric) = 1.635839247043278700E-2 " " absolute error = 4.8572257327350600000000000000000E-17 " " relative error = 2.9692561426890257000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6721054405903825 " " Order of pole = 639.4869452703819 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19900000000000015 " " y[1] (analytic) = 1.66195024074154930E-2 " " y[1] (numeric) = 1.66195024074154400E-2 " " absolute error = 5.20417042793042100000000000000000E-17 " " relative error = 3.13136356333289570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6700947176730462 " " Order of pole = 638.5225965165191 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000015 " " y[1] (analytic) = 1.688274982104073800E-2 " " y[1] (numeric) = 1.688274982104069600E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 2.46602975609792440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6681539000617034 " " Order of pole = 637.6235138571661 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20100000000000015 " " y[1] (analytic) = 1.7148136963239602E-2 " " y[1] (numeric) = 1.714813696323958200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 1.01161046223011140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6662780163921583 " " Order of pole = 636.785139632977 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20200000000000015 " " y[1] (analytic) = 1.741566610664889700E-2 " " y[1] (numeric) = 1.741566610664882000E-2 " " absolute error = 7.97972798949331300000000000000000E-17 " " relative error = 4.581925227911229400000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6644624688986588 " " Order of pole = 636.0032537606073 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20300000000000015 " " y[1] (analytic) = 1.768533954469122500E-2 " " y[1] (numeric) = 1.768533954469120600E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 9.80882199967450200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Real estimate of pole used for equation 1" Radius of convergence = 0.6627030026860733 " " Order of pole = 635.2739462175258 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = tan (2.0 * x + 3.0 ) ;" Iterations = 204 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 10 Minutes 44 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 10 Minutes 5 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 13 Minutes 6 Seconds "Time to Timeout " Unknown Percent Done = 4.100000000000003 "%" (%o58) true (%o58) diffeq.max