(%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 : cos(array_x ), array_tmp1_g : sin(array_x ), 1 1 1 1 array_tmp2 : array_const_2D0 array_x , 1 1 1 array_tmp1 1 array_tmp3 : array_const_1D0 + array_tmp2 , array_tmp4 : -----------, 1 1 1 1 array_tmp3 1 array_tmp5 : array_tmp4 + array_const_0D0 , array_tmp6 : sin(array_x ), 1 1 1 1 1 array_tmp6_g : cos(array_x ), array_tmp7 : array_const_2D0 array_tmp6 , 1 1 1 1 1 array_tmp8 : array_const_2D0 array_x , 1 1 1 array_tmp7 1 array_tmp9 : array_const_1D0 + array_tmp8 , array_tmp10 : -----------, 1 1 1 1 array_tmp9 1 array_tmp11 : array_const_2D0 array_x , 1 1 1 array_tmp10 1 array_tmp12 : array_const_1D0 + array_tmp11 , array_tmp13 : ------------, 1 1 1 1 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp14 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_g array_x array_tmp1 array_x 1 2 1 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 2 1 2 1 array_tmp2 : array_const_2D0 array_x , array_tmp3 : array_tmp2 , 2 1 2 2 2 array_tmp1 - array_tmp4 array_tmp3 2 1 2 array_tmp4 : -------------------------------------, 2 array_tmp3 1 array_tmp6_g array_x 1 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 2 2 2 1 - array_tmp6 array_x 1 2 array_tmp6_g : ----------------------, 2 1 array_tmp7 : array_const_2D0 array_tmp6 , 2 1 2 array_tmp8 : array_const_2D0 array_x , array_tmp9 : array_tmp8 , 2 1 2 2 2 array_tmp7 - array_tmp10 array_tmp9 2 1 2 array_tmp10 : --------------------------------------, 2 array_tmp9 1 array_tmp11 : array_const_2D0 array_x , array_tmp12 : array_tmp11 , 2 1 2 2 2 array_tmp10 - array_tmp13 array_tmp12 2 1 2 array_tmp13 : ----------------------------------------, 2 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 - array_tmp1_g array_x array_tmp1 array_x 2 2 2 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 3 2 3 2 array_tmp1 - array_tmp4 array_tmp3 3 2 2 array_tmp4 : -------------------------------------, 3 array_tmp3 1 array_tmp6_g array_x 2 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 3 3 3 2 - array_tmp6 array_x 2 2 array_tmp6_g : ----------------------, 3 2 array_tmp7 : array_const_2D0 array_tmp6 , 3 1 3 array_tmp7 - array_tmp10 array_tmp9 3 2 2 array_tmp10 : --------------------------------------, 3 array_tmp9 1 array_tmp10 - array_tmp13 array_tmp12 3 2 2 array_tmp13 : ----------------------------------------, 3 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - array_tmp1_g array_x array_tmp1 array_x 3 2 3 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 4 3 4 3 array_tmp1 - array_tmp4 array_tmp3 4 3 2 array_tmp4 : -------------------------------------, 4 array_tmp3 1 array_tmp6_g array_x 3 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 4 4 4 3 - array_tmp6 array_x 3 2 array_tmp6_g : ----------------------, 4 3 array_tmp7 : array_const_2D0 array_tmp6 , 4 1 4 array_tmp7 - array_tmp10 array_tmp9 4 3 2 array_tmp10 : --------------------------------------, 4 array_tmp9 1 array_tmp10 - array_tmp13 array_tmp12 4 3 2 array_tmp13 : ----------------------------------------, 4 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - array_tmp1_g array_x array_tmp1 array_x 4 2 4 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 5 4 5 4 array_tmp1 - array_tmp4 array_tmp3 5 4 2 array_tmp4 : -------------------------------------, 5 array_tmp3 1 array_tmp6_g array_x 4 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 5 5 5 4 - array_tmp6 array_x 4 2 array_tmp6_g : ----------------------, 5 4 array_tmp7 : array_const_2D0 array_tmp6 , 5 1 5 array_tmp7 - array_tmp10 array_tmp9 5 4 2 array_tmp10 : --------------------------------------, 5 array_tmp9 1 array_tmp10 - array_tmp13 array_tmp12 5 4 2 array_tmp13 : ----------------------------------------, 5 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk - array_tmp1_g array_x array_tmp1 array_x kkk - 1 2 kkk - 1 2 ------------------------------, array_tmp1_g : --------------------------, kkk - 1 kkk kkk - 1 - ats(kkk, array_tmp3, array_tmp4, 2) array_tmp4 : -------------------------------------, kkk array_tmp3 1 array_tmp6_g array_x kkk - 1 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------------, kkk kkk kkk kkk - 1 - array_tmp6 array_x kkk - 1 2 array_tmp6_g : ----------------------------, kkk kkk - 1 array_tmp7 : array_const_2D0 array_tmp6 , kkk 1 kkk - ats(kkk, array_tmp9, array_tmp10, 2) array_tmp10 : --------------------------------------, kkk array_tmp9 1 - ats(kkk, array_tmp12, array_tmp13, 2) array_tmp13 : ---------------------------------------, kkk array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp14 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 : cos(array_x ), array_tmp1_g : sin(array_x ), 1 1 1 1 array_tmp2 : array_const_2D0 array_x , 1 1 1 array_tmp1 1 array_tmp3 : array_const_1D0 + array_tmp2 , array_tmp4 : -----------, 1 1 1 1 array_tmp3 1 array_tmp5 : array_tmp4 + array_const_0D0 , array_tmp6 : sin(array_x ), 1 1 1 1 1 array_tmp6_g : cos(array_x ), array_tmp7 : array_const_2D0 array_tmp6 , 1 1 1 1 1 array_tmp8 : array_const_2D0 array_x , 1 1 1 array_tmp7 1 array_tmp9 : array_const_1D0 + array_tmp8 , array_tmp10 : -----------, 1 1 1 1 array_tmp9 1 array_tmp11 : array_const_2D0 array_x , 1 1 1 array_tmp10 1 array_tmp12 : array_const_1D0 + array_tmp11 , array_tmp13 : ------------, 1 1 1 1 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp14 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_g array_x array_tmp1 array_x 1 2 1 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 2 1 2 1 array_tmp2 : array_const_2D0 array_x , array_tmp3 : array_tmp2 , 2 1 2 2 2 array_tmp1 - array_tmp4 array_tmp3 2 1 2 array_tmp4 : -------------------------------------, 2 array_tmp3 1 array_tmp6_g array_x 1 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 2 2 2 1 - array_tmp6 array_x 1 2 array_tmp6_g : ----------------------, 2 1 array_tmp7 : array_const_2D0 array_tmp6 , 2 1 2 array_tmp8 : array_const_2D0 array_x , array_tmp9 : array_tmp8 , 2 1 2 2 2 array_tmp7 - array_tmp10 array_tmp9 2 1 2 array_tmp10 : --------------------------------------, 2 array_tmp9 1 array_tmp11 : array_const_2D0 array_x , array_tmp12 : array_tmp11 , 2 1 2 2 2 array_tmp10 - array_tmp13 array_tmp12 2 1 2 array_tmp13 : ----------------------------------------, 2 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 - array_tmp1_g array_x array_tmp1 array_x 2 2 2 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 3 2 3 2 array_tmp1 - array_tmp4 array_tmp3 3 2 2 array_tmp4 : -------------------------------------, 3 array_tmp3 1 array_tmp6_g array_x 2 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 3 3 3 2 - array_tmp6 array_x 2 2 array_tmp6_g : ----------------------, 3 2 array_tmp7 : array_const_2D0 array_tmp6 , 3 1 3 array_tmp7 - array_tmp10 array_tmp9 3 2 2 array_tmp10 : --------------------------------------, 3 array_tmp9 1 array_tmp10 - array_tmp13 array_tmp12 3 2 2 array_tmp13 : ----------------------------------------, 3 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - array_tmp1_g array_x array_tmp1 array_x 3 2 3 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 4 3 4 3 array_tmp1 - array_tmp4 array_tmp3 4 3 2 array_tmp4 : -------------------------------------, 4 array_tmp3 1 array_tmp6_g array_x 3 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 4 4 4 3 - array_tmp6 array_x 3 2 array_tmp6_g : ----------------------, 4 3 array_tmp7 : array_const_2D0 array_tmp6 , 4 1 4 array_tmp7 - array_tmp10 array_tmp9 4 3 2 array_tmp10 : --------------------------------------, 4 array_tmp9 1 array_tmp10 - array_tmp13 array_tmp12 4 3 2 array_tmp13 : ----------------------------------------, 4 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - array_tmp1_g array_x array_tmp1 array_x 4 2 4 2 array_tmp1 : ------------------------, array_tmp1_g : --------------------, 5 4 5 4 array_tmp1 - array_tmp4 array_tmp3 5 4 2 array_tmp4 : -------------------------------------, 5 array_tmp3 1 array_tmp6_g array_x 4 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------, 5 5 5 4 - array_tmp6 array_x 4 2 array_tmp6_g : ----------------------, 5 4 array_tmp7 : array_const_2D0 array_tmp6 , 5 1 5 array_tmp7 - array_tmp10 array_tmp9 5 4 2 array_tmp10 : --------------------------------------, 5 array_tmp9 1 array_tmp10 - array_tmp13 array_tmp12 5 4 2 array_tmp13 : ----------------------------------------, 5 array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp14 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : kkk - array_tmp1_g array_x array_tmp1 array_x kkk - 1 2 kkk - 1 2 ------------------------------, array_tmp1_g : --------------------------, kkk - 1 kkk kkk - 1 - ats(kkk, array_tmp3, array_tmp4, 2) array_tmp4 : -------------------------------------, kkk array_tmp3 1 array_tmp6_g array_x kkk - 1 2 array_tmp5 : array_tmp4 , array_tmp6 : ----------------------------, kkk kkk kkk kkk - 1 - array_tmp6 array_x kkk - 1 2 array_tmp6_g : ----------------------------, kkk kkk - 1 array_tmp7 : array_const_2D0 array_tmp6 , kkk 1 kkk - ats(kkk, array_tmp9, array_tmp10, 2) array_tmp10 : --------------------------------------, kkk array_tmp9 1 - ats(kkk, array_tmp12, array_tmp13, 2) array_tmp13 : ---------------------------------------, kkk array_tmp12 1 array_tmp14 : array_tmp5 - array_tmp13 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp14 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) sin(x) (%i56) exact_soln_y(x) := block(-------) 1 + 2 x sin(x) (%o56) exact_soln_y(x) := block(-------) 1 + 2 x (%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/div_sin_lin_newpostode.ode#################"), omniout_str(ALWAYS, "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 *\ sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), 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, " (sin(x)/(2*x+1)) "), 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6_g, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms), array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms), array(array_tmp14, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp6_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp6 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp7 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp8 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp9 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp11 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp12 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp14 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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_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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6_g : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_tmp10, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term), term array(array_tmp11, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term), term array(array_tmp12, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term), term array(array_tmp13, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term), term array(array_tmp14, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp14 : 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_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, 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 ) \ = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 \ * x + 1.0 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T13:36:53-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_sin_lin_new"), logitem_str(html_log_file, "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) \ - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "div_sin_lin_new diffeq.max"), logitem_str(html_log_file, "div_sin_\ lin_new maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/div_sin_lin_newpostode.ode#################"), omniout_str(ALWAYS, "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 *\ sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), 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, " (sin(x)/(2*x+1)) "), 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_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6_g, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_tmp10, 1 + max_terms), array(array_tmp11, 1 + max_terms), array(array_tmp12, 1 + max_terms), array(array_tmp13, 1 + max_terms), array(array_tmp14, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp6_g : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp6 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp7 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp8 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp9 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp11 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp12 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp14 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 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_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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6_g : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_tmp10, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp10 : 0.0, term : 1 + term), term array(array_tmp11, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp11 : 0.0, term : 1 + term), term array(array_tmp12, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp12 : 0.0, term : 1 + term), term array(array_tmp13, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp13 : 0.0, term : 1 + term), term array(array_tmp14, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp14 : 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_1D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1D0 : 0.0, term : 1 + term), term array_const_1D0 : 1.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, 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 ) \ = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 \ * x + 1.0 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T13:36:53-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "div_sin_lin_new"), logitem_str(html_log_file, "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) \ - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "div_sin_lin_new diffeq.max"), logitem_str(html_log_file, "div_sin_\ lin_new maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) main() "##############ECHO OF PROBLEM#################" "##############temp/div_sin_lin_newpostode.ode#################" "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:1.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "/* 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(" " (sin(x)/(2*x+1)) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 0.9 "" estimated_steps = 900. "" step_error = 1.11111111111111100000000000000E-13 "" est_needed_step_err = 1.11111111111111100000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 4.50043875866446800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" max_value3 = 4.50043875866446800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" value3 = 4.50043875866446800000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 8.3194513872356790E-2 " " y[1] (numeric) = 8.3194513872356790E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.6430721440880085 " " Order of pole = 5.29247756730910600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.101 " " y[1] (analytic) = 8.38838358815041700E-2 " " y[1] (numeric) = 8.38838358815041700E-2 " " 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] = 0.10200000000000001 " " y[1] (analytic) = 8.45707840398218700E-2 " " y[1] (numeric) = 8.45707840398218700E-2 " " 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] = 0.10300000000000001 " " y[1] (analytic) = 8.52553693325933100E-2 " " y[1] (numeric) = 8.52553693325933200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.627790474248634600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000001 " " y[1] (analytic) = 8.59376026724360200E-2 " " y[1] (numeric) = 8.59376026724360200E-2 " " 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] = 0.10500000000000001 " " y[1] (analytic) = 8.66174948999028900E-2 " " y[1] (numeric) = 8.6617494899902900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.60219223886028300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = 8.72950567840777300E-2 " " y[1] (numeric) = 8.72950567840777300E-2 " " 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] = 0.10700000000000001 " " y[1] (analytic) = 8.79702990231646600E-2 " " y[1] (numeric) = 8.79702990231646700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.577553783710580500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 3.122257551261073 " " Order of pole = 7.2499162229178180000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000001 " " y[1] (analytic) = 8.86432322450719300E-2 " " y[1] (numeric) = 8.86432322450719600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.565577817542408400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = 8.93138670079898300E-2 " " y[1] (numeric) = 8.93138670079898400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.553822298005860200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = 8.99822138009629600E-2 " " y[1] (numeric) = 8.99822138009629800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.54228121554239200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = 9.0648283044456910E-2 " " y[1] (numeric) = 9.06482830444569200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.530948777155363400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = 9.13120850909192800E-2 " " y[1] (numeric) = 9.1312085090919300E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.519819396742103400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000002 " " y[1] (analytic) = 9.19736302253354200E-2 " " y[1] (numeric) = 9.19736302253354500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.017775371878629300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000002 " " y[1] (analytic) = 9.26329286657784900E-2 " " y[1] (numeric) = 9.26329286657785200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.996296890900600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.4025496239533535 " " Order of pole = 1.91763049883775240000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000002 " " y[1] (analytic) = 9.32899905639543500E-2 " " y[1] (numeric) = 9.32899905639543600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.487596656824681500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = 9.39448260057409400E-2 " " y[1] (numeric) = 9.39448260057409700E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.95445494932661600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000002 " " y[1] (analytic) = 9.45974450117227400E-2 " " y[1] (numeric) = 9.45974450117227600E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.93407243844581400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.6394994395821114 " " Order of pole = 1.902122903629788200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000002 " " y[1] (analytic) = 9.52478575377196400E-2 " " y[1] (numeric) = 9.52478575377196500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.457018369396774800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000002 " " y[1] (analytic) = 9.58960734753109500E-2 " " y[1] (numeric) = 9.58960734753109700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.44716955604938080000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (analytic) = 9.65421026523543400E-2 " " y[1] (numeric) = 9.65421026523543600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.437485555684240300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = 9.7185954833499590E-2 " " y[1] (numeric) = 9.71859548334996100E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.42796228442577800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12200000000000003 " " y[1] (analytic) = 9.78276397206975700E-2 " " y[1] (numeric) = 9.78276397206975800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.41859579229716480000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12300000000000003 " " y[1] (analytic) = 9.84671669537041400E-2 " " y[1] (numeric) = 9.84671669537041700E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.818764515554573000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12400000000000003 " " y[1] (analytic) = 9.91045461105794500E-2 " " y[1] (numeric) = 9.91045461105794800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.800635965242163000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000003 " " y[1] (analytic) = 9.97397867081821800E-2 " " y[1] (numeric) = 9.9739786708182200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.782798773857011000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000003 " " y[1] (analytic) = 0.10037289820265917 " " y[1] (numeric) = 0.1003728982026592 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.765246008896611300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.639294463401939 " " Order of pole = 4.187583613202150400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = 0.10100388998993044 " " y[1] (numeric) = 0.10100388998993046 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.373985478103665000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = 0.1016327714061694 " " y[1] (numeric) = 0.10163277140616941 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.365483555727580500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = 0.10225955172827862 " " y[1] (numeric) = 0.10225955172827864 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.357114085996597000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = 0.10288424017436101 " " y[1] (numeric) = 0.10288424017436104 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.69774802910442900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = 0.10350684590418659 " " y[1] (numeric) = 0.1035068459041866 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.340760380299940700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.8252983952110928 " " Order of pole = 2.93045587795859300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = 0.10412737801965458 " " y[1] (numeric) = 0.1041273780196546 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.66554062375314100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13300000000000003 " " y[1] (analytic) = 0.10474584556525154 " " y[1] (numeric) = 0.10474584556525157 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.649802048553663000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13400000000000004 " " y[1] (analytic) = 0.10536225752850482 " " y[1] (numeric) = 0.10536225752850484 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.317149815631080700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.58267463665141 " " Order of pole = 2.0268231537556858000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = 0.10597662284043176 " " y[1] (numeric) = 0.10597662284043179 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.619028128252424700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = 0.1065889503759849 " " y[1] (numeric) = 0.10658895037598491 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.30199122506240600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = 0.10719924895449266 " " y[1] (numeric) = 0.10719924895449268 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.294578828038780400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = 0.10780752734009617 " " y[1] (numeric) = 0.10780752734009619 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.28727447426140700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = 0.10841379424218182 " " y[1] (numeric) = 0.10841379424218184 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.28007583396752500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (analytic) = 0.10901805831580978 " " y[1] (numeric) = 0.1090180583158098 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.272980643960148800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14100000000000004 " " y[1] (analytic) = 0.10962032816213857 " " y[1] (numeric) = 0.1096203281621386 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.531973410495164700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14200000000000004 " " y[1] (analytic) = 0.11022061232884564 " " y[1] (numeric) = 0.11022061232884565 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.259091880782676800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.8997499552837517 " " Order of pole = 8.40909564203684600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = 0.11081891931054394 " " y[1] (numeric) = 0.11081891931054395 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.252294093296941700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = 0.11141525754919476 " " y[1] (numeric) = 0.11141525754919478 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.245591323224900400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.1448791264995763 " " Order of pole = 8.03943578375765400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = 0.11200963543451663 " " y[1] (numeric) = 0.11200963543451664 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.238981606714337200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14600000000000005 " " y[1] (analytic) = 0.11260206130439038 " " y[1] (numeric) = 0.11260206130439039 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.232463033718314300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14700000000000005 " " y[1] (analytic) = 0.11319254344526058 " " y[1] (numeric) = 0.1131925434452606 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.226033746165063900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14800000000000005 " " y[1] (analytic) = 0.1137810900925332 " " y[1] (numeric) = 0.1137810900925332 " " 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] = 0.14900000000000005 " " y[1] (analytic) = 0.11436770943096947 " " y[1] (numeric) = 0.11436770943096948 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.213435844510890500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (analytic) = 0.11495240959507635 " " y[1] (numeric) = 0.11495240959507635 " " 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] = 0.15100000000000005 " " y[1] (analytic) = 0.11553519866949319 " " y[1] (numeric) = 0.11553519866949319 " " 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] = 0.15200000000000005 " " y[1] (analytic) = 0.11611608468937488 " " y[1] (numeric) = 0.1161160846893749 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.195164980367645300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15300000000000005 " " y[1] (analytic) = 0.11669507564077165 " " y[1] (numeric) = 0.11669507564077165 " " 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] = 0.15400000000000005 " " y[1] (analytic) = 0.11727217946100503 " " y[1] (numeric) = 0.11727217946100504 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.183382782821824800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = 0.1178474040390408 " " y[1] (numeric) = 0.11784740403904082 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.177606576994855700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.14332769265197315 " " Order of pole = 1.422861828359600600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = 0.11842075721585817 " " y[1] (numeric) = 0.11842075721585817 " " 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] = 0.15700000000000006 " " y[1] (analytic) = 0.1189922467848157 " " y[1] (numeric) = 0.11899224678481571 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.1662766426211700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = 0.11956188049201409 " " y[1] (numeric) = 0.11956188049201408 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.160720101649906500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.7903697419393475 " " Order of pole = 8.13713540992466700000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = 0.12012966603665523 " " y[1] (numeric) = 0.12012966603665523 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 3.6964687451839495 " " Order of pole = 4.5826986649899480000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = 0.1206956110713985 " " y[1] (numeric) = 0.12069561107139849 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.149817104749975800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = 0.12125972320271339 " " y[1] (numeric) = 0.12125972320271339 " " 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] = 0.16200000000000006 " " y[1] (analytic) = 0.1218220099912292 " " y[1] (numeric) = 0.1218220099912292 " " 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] = 0.16300000000000006 " " y[1] (analytic) = 0.12238247895208149 " " y[1] (numeric) = 0.12238247895208149 " " 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] = 0.16400000000000006 " " y[1] (analytic) = 0.12294113755525532 " " y[1] (numeric) = 0.12294113755525532 " " 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] = 0.16500000000000006 " " y[1] (analytic) = 0.12349799322592558 " " y[1] (numeric) = 0.12349799322592557 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.123725774428303200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.466554093843765 " " Order of pole = 2.11935358152004480000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = 0.12405305334479405 " " y[1] (numeric) = 0.12405305334479404 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.118697801757641800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = 0.12460632524842355 " " y[1] (numeric) = 0.12460632524842355 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "Complex estimate of poles used for equation 1" Radius of convergence = 6.25294413415497900E-2 " " Order of pole = 1.190159082398167800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16825058882683105 " " y[1] (analytic) = 0.12529573550470652 " " y[1] (numeric) = 0.12529573550470652 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.8622851073940613 " " Order of pole = 8.59419202470235200000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.16950117765366204 " " y[1] (analytic) = 0.12598237461235137 " " y[1] (numeric) = 0.12598237461235134 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.203131644488604800000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17012647206707754 " " y[1] (analytic) = 0.12632465938415907 " " y[1] (numeric) = 0.12632465938415907 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17137706089390853 " " y[1] (analytic) = 0.12700716810400686 " " y[1] (numeric) = 0.12700716810400686 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200235530732402 " " y[1] (analytic) = 0.1273473955286908 " " y[1] (numeric) = 0.12734739552869082 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.17951655001658100000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.173252944134155 " " y[1] (analytic) = 0.12802580515089884 " " y[1] (numeric) = 0.12802580515089887 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.167967276824741600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.3658084078550272 " " Order of pole = 3.846878371405182400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.174503532960986 " " y[1] (analytic) = 0.1287014992534281 " " y[1] (numeric) = 0.12870149925342814 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.156585259428484300000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1751288273744015 " " y[1] (analytic) = 0.12903833225472622 " " y[1] (numeric) = 0.12903833225472625 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.15095585402006180000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1763794162012325 " " y[1] (analytic) = 0.12970997864212305 " " y[1] (numeric) = 0.12970997864212308 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.139818069988899700000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700471061464798 " " y[1] (analytic) = 0.13004479540336628 " " y[1] (numeric) = 0.1300447954033663 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.1343088379306602000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17825529944147897 " " y[1] (analytic) = 0.1307124244522778 " " y[1] (numeric) = 0.13071242445227785 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.24681521009692300000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17950588826830996 " " y[1] (analytic) = 0.13137739198636417 " " y[1] (numeric) = 0.1313773919863642 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.112659963482126400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18013118268172545 " " y[1] (analytic) = 0.13170888183115487 " " y[1] (numeric) = 0.13170888183115492 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.214685483581945300000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18138177150855644 " " y[1] (analytic) = 0.13236988191475685 " " y[1] (numeric) = 0.1323698819147569 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.1936390988854800000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200706592197194 " " y[1] (analytic) = 0.13269939543091022 " " y[1] (numeric) = 0.13269939543091028 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.18322563196300600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18325765474880293 " " y[1] (analytic) = 0.1333564575604387 " " y[1] (numeric) = 0.1333564575604388 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 6.24392161955481500000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18450824357563392 " " y[1] (analytic) = 0.13401091061504775 " " y[1] (numeric) = 0.13401091061504786 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.28457190186791000000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1851335379890494 " " y[1] (analytic) = 0.13433716276545973 " " y[1] (numeric) = 0.13433716276545984 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.26445193400059600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1863841268158804 " " y[1] (analytic) = 0.13498772631373168 " " y[1] (numeric) = 0.1349877263137318 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.22462200781745100000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1870094212292959 " " y[1] (analytic) = 0.13531204089466836 " " y[1] (numeric) = 0.13531204089466847 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.20490931394193600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1882600100561269 " " y[1] (analytic) = 0.1359587435846112 " " y[1] (numeric) = 0.13595874358461132 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.16588176202313400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18951059888295788 " " y[1] (analytic) = 0.13660288813118945 " " y[1] (numeric) = 0.13660288813118954 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 6.09553194562912900000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19013589329637337 " " y[1] (analytic) = 0.13692400501162152 " " y[1] (numeric) = 0.13692400501162164 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.10831544498662200000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19138648212320436 " " y[1] (analytic) = 0.13756433575924448 " " y[1] (numeric) = 0.1375643357592446 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.07057307766303400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19201177653661985 " " y[1] (analytic) = 0.13788355271863162 " " y[1] (numeric) = 0.13788355271863173 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 8.05188873317402400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19326236536345084 " " y[1] (analytic) = 0.13852009749736954 " " y[1] (numeric) = 0.13852009749736968 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.00186096158920130000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.6858440629937033 " " Order of pole = 3.78026498992767300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.19451295419028183 " " y[1] (analytic) = 0.13915413361011084 " " y[1] (numeric) = 0.13915413361011097 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.97296123929595400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19513824860369733 " " y[1] (analytic) = 0.1394702147164628 " " y[1] (numeric) = 0.13947021471646293 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.95035953449087900000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19638883743052832 " " y[1] (analytic) = 0.14010051058100936 " " y[1] (numeric) = 0.1401005105810095 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.90559402693254200000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970141318439438 " " y[1] (analytic) = 0.14041472834376026 " " y[1] (numeric) = 0.1404147283437604 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.8834274520256600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1982647206707748 " " y[1] (analytic) = 0.1410413110014095 " " y[1] (numeric) = 0.14104131100140968 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.37753278050188280000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1995153094976058 " " y[1] (analytic) = 0.14166543306809576 " " y[1] (numeric) = 0.14166543306809593 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.17554049768601050000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2001406039110213 " " y[1] (analytic) = 0.14197657507233077 " " y[1] (numeric) = 0.14197657507233094 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.17296429787049070000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20139119273785228 " " y[1] (analytic) = 0.1425970283616929 " " y[1] (numeric) = 0.14259702836169308 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.1678606181845990000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20201648715126777 " " y[1] (analytic) = 0.14290634256683946 " " y[1] (numeric) = 0.14290634256683965 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.3595549771944548000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20326707597809876 " " y[1] (analytic) = 0.14352315335933105 " " y[1] (numeric) = 0.14352315335933127 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.54709954267176930000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20451766480492975 " " y[1] (analytic) = 0.1441375502832141 " " y[1] (numeric) = 0.14413755028321432 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.54050491692649560000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20514295921834524 " " y[1] (analytic) = 0.14444384713348443 " " y[1] (numeric) = 0.14444384713348465 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.53723823708346640000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.2527036951448391 " " Order of pole = 1.286259987409721400000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20639354804517623 " " y[1] (analytic) = 0.14505464474451082 " " y[1] (numeric) = 0.14505464474451105 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.53076521828118820000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 2.2638275315904326 " " Order of pole = 1.22213350550737230000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.20701884245859173 " " y[1] (analytic) = 0.14535914834372204 " " y[1] (numeric) = 0.14535914834372227 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.52755851595921420000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20826943128542272 " " y[1] (analytic) = 0.14596637218825534 " " y[1] (numeric) = 0.14596637218825562 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.90150479179081540000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2095200201122537 " " y[1] (analytic) = 0.146571227581421 " " y[1] (numeric) = 0.14657122758142124 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.7042920678404980000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2101453145256692 " " y[1] (analytic) = 0.1468727705979746 " " y[1] (numeric) = 0.14687277059797485 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.7007930028393228000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2113959033525002 " " y[1] (analytic) = 0.14747409420674917 " " y[1] (numeric) = 0.1474740942067494 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.505651593382490000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120211977659157 " " y[1] (analytic) = 0.1477738775587094 " " y[1] (numeric) = 0.14777387755870963 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.5025971341708530000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 4.611741495488442 " " Order of pole = 5.3044857395434520000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.21327178659274668 " " y[1] (analytic) = 0.1483716942210024 " " y[1] (numeric) = 0.14837169422100263 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.49654289580525870000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21452237541957767 " " y[1] (analytic) = 0.14896718658963307 " " y[1] (numeric) = 0.14896718658963326 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.30424044218959120000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21514766983299316 " " y[1] (analytic) = 0.1492640645567072 " " y[1] (numeric) = 0.1492640645567074 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.30164638010101670000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21639825865982415 " " y[1] (analytic) = 0.1498560908008763 " " y[1] (numeric) = 0.1498560908008765 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.29650405446360580000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21702355307323964 " " y[1] (analytic) = 0.1501512417617248 " " y[1] (numeric) = 0.150151241761725 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.29395552797172270000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21827414190007063 " " y[1] (analytic) = 0.15073982603545977 " " y[1] (numeric) = 0.15073982603546 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.4730321160964980000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21952473072690162 " " y[1] (analytic) = 0.15132612895738878 " " y[1] (numeric) = 0.15132612895738898 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.28390933309416340000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22015002514031712 " " y[1] (analytic) = 0.15161842821128516 " " y[1] (numeric) = 0.15161842821128535 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.2814341343695660000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.39275640398957445 " " Order of pole = 9.57633972120675000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2214006139671481 " " y[1] (analytic) = 0.15220132886481813 " " y[1] (numeric) = 0.1522013288648183 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.09416556961657560000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.6019092681290201 " " Order of pole = 2.90789614609821000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2220259083805636 " " y[1] (analytic) = 0.15249193287484022 " " y[1] (numeric) = 0.15249193287484036 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.10067014443631900000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2232764972073946 " " y[1] (analytic) = 0.15307145475368186 " " y[1] (numeric) = 0.15307145475368203 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.08794584830825760000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22452708603422558 " " y[1] (analytic) = 0.15364873704861118 " " y[1] (numeric) = 0.15364873704861132 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.03215221575418400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22515238044764108 " " y[1] (analytic) = 0.1539365415621365 " " y[1] (numeric) = 0.15393654156213663 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 9.01526542494959700000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22640296927447207 " " y[1] (analytic) = 0.15451048370288367 " " y[1] (numeric) = 0.1545104837028838 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.98177746598786400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.1423652851369774 " " Order of pole = 4.98712182661620300000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.22702826368788756 " " y[1] (analytic) = 0.15479662386963344 " " y[1] (numeric) = 0.1547966238696336 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.07582096773650940000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22827885251471855 " " y[1] (analytic) = 0.1553672487121756 " " y[1] (numeric) = 0.15536724871217578 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.07186974780176320000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22952944134154954 " " y[1] (analytic) = 0.15593567460490784 " " y[1] (numeric) = 0.155935674604908 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.06796250515295550000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.3447760123155135 " " Order of pole = 8.499867476530198000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.23015473575496503 " " y[1] (analytic) = 0.15621906606835337 " " y[1] (numeric) = 0.15621906606835353 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.06602515227499240000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23140532458179602 " " y[1] (analytic) = 0.1567842122387453 " " y[1] (numeric) = 0.15678421223874545 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.85152121482861200000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23203061899521152 " " y[1] (analytic) = 0.1570659694167705 " " y[1] (numeric) = 0.15706596941677067 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.06027711993984670000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2332812078220425 " " y[1] (analytic) = 0.15762785810474803 " " y[1] (numeric) = 0.15762785810474822 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.23258053268916480000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2345317966488735 " " y[1] (analytic) = 0.15818758738176536 " " y[1] (numeric) = 0.15818758738176555 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.22821918283961730000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.235157091062289 " " y[1] (analytic) = 0.15846664528059007 " " y[1] (numeric) = 0.15846664528059026 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.22605630330208080000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23640767988911998 " " y[1] (analytic) = 0.15902315364180322 " " y[1] (numeric) = 0.1590231536418034 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.04722771420372580000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23703297430253548 " " y[1] (analytic) = 0.1593006065091325 " " y[1] (numeric) = 0.1593006065091327 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.219637724971650000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23828356312936647 " " y[1] (analytic) = 0.1598539155992173 " " y[1] (numeric) = 0.1598539155992175 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.21541614155089040000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23953415195619746 " " y[1] (analytic) = 0.16040510375892103 " " y[1] (numeric) = 0.16040510375892122 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.21123969721940280000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24015944636961295 " " y[1] (analytic) = 0.16067990544829366 " " y[1] (numeric) = 0.16067990544829383 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.0364298711101960000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24141003519644394 " " y[1] (analytic) = 0.16122792992819038 " " y[1] (numeric) = 0.16122792992819054 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.03290697689876770000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 5.8858972180621745 " " Order of pole = 8.4418161350185980000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.24203532960985943 " " y[1] (analytic) = 0.1615011550597359 " " y[1] (numeric) = 0.16150115505973608 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.20301944117699320000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24328591843669042 " " y[1] (analytic) = 0.16204603692921823 " " y[1] (numeric) = 0.1620460369292184 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.02769223394531610000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2445365072635214 " " y[1] (analytic) = 0.16258883532612672 " " y[1] (numeric) = 0.16258883532612692 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.1949715299927591000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2451618016769369 " " y[1] (analytic) = 0.16285945610247385 " " y[1] (numeric) = 0.16285945610247407 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.36341241852924500000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2464123905037679 " " y[1] (analytic) = 0.16339914653760815 " " y[1] (numeric) = 0.16339914653760834 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.18904555761975530000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.6718627944932363 " " Order of pole = 3.6912695122737205000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2470376849171834 " " y[1] (analytic) = 0.16366821847562738 " " y[1] (numeric) = 0.16366821847562757 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.18709075664763170000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24828827374401438 " " y[1] (analytic) = 0.16420482146226795 " " y[1] (numeric) = 0.16420482146226817 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.3522416878365182000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24953886257084537 " " y[1] (analytic) = 0.16473937744545433 " " y[1] (numeric) = 0.16473937744545453 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.17937212293843980000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25016415698426087 " " y[1] (analytic) = 0.1650058906151541 " " y[1] (numeric) = 0.16500589061515433 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.34567683673129880000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.1724210673853415 " " Order of pole = 5.44595479823328800000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2514147458110919 " " y[1] (analytic) = 0.1655373928871186 " " y[1] (numeric) = 0.16553739288711883 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.34135617972699040000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25204004022450743 " " y[1] (analytic) = 0.1658023842088718 " " y[1] (numeric) = 0.165802384208872 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.17181082911717460000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2532906290513385 " " y[1] (analytic) = 0.16633085274519516 " " y[1] (numeric) = 0.16633085274519532 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.00121805994038080000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2545412178781695 " " y[1] (analytic) = 0.1668573097912313 " " y[1] (numeric) = 0.16685730979123145 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 8.31715902957927400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25516651229158505 " " y[1] (analytic) = 0.16711978673658445 " " y[1] (numeric) = 0.16711978673658456 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.64327693509505800000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.6666329542230742 " " Order of pole = 3.14397397005450330000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2564171011184161 " " y[1] (analytic) = 0.16764324290296026 " " y[1] (numeric) = 0.16764324290296037 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.62253369357574200000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570423955318316 " " y[1] (analytic) = 0.16790422428569318 " " y[1] (numeric) = 0.1679042242856933 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.6122399799547900000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25829298435866266 " " y[1] (analytic) = 0.16842469902797788 " " y[1] (numeric) = 0.168424699027978 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.59180649294633300000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2595435731854937 " " y[1] (analytic) = 0.16894319686863757 " " y[1] (numeric) = 0.16894319686863765 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.928681852257780000000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2601688675989092 " " y[1] (analytic) = 0.1692017071112407 " " y[1] (numeric) = 0.1692017071112408 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.5615355990187900000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.26141945642574027 " " y[1] (analytic) = 0.16971725553139758 " " y[1] (numeric) = 0.16971725553139763 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.27080184377529600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 3.982268867863089 " " Order of pole = 1.1290630652638356000000000E-9 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2620447508391558 " " y[1] (analytic) = 0.16997429581477175 " " y[1] (numeric) = 0.16997429581477186 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.53171127612738500000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.26329533966598684 " " y[1] (analytic) = 0.17048691376698077 " " y[1] (numeric) = 0.1704869137669808 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.628017951780443600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2645459284928179 " " y[1] (analytic) = 0.17099758851194108 " " y[1] (numeric) = 0.1709975885119411 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.623155967120009400000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2651712229062334 " " y[1] (analytic) = 0.17125219977358147 " " y[1] (numeric) = 0.17125219977358147 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.26642181173306445 " " y[1] (analytic) = 0.17175997522956277 " " y[1] (numeric) = 0.17175997522956277 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.26704710614648 " " y[1] (analytic) = 0.17201314147564978 " " y[1] (numeric) = 0.17201314147564978 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.268297694973311 " " y[1] (analytic) = 0.17251803610853025 " " y[1] (numeric) = 0.17251803610853023 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.608850659427169500000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 3.443182145885101 " " Order of pole = 5.5245941155135370000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.26954828380014206 " " y[1] (analytic) = 0.17302102036329886 " " y[1] (numeric) = 0.17302102036329878 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.81252085278704330000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2701735782135576 " " y[1] (analytic) = 0.17327179862448194 " " y[1] (numeric) = 0.17327179862448186 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.805555636168124500000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27142416704038863 " " y[1] (analytic) = 0.17377193243719757 " " y[1] (numeric) = 0.17377193243719746 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.38896632530917600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27204946145380415 " " y[1] (analytic) = 0.17402128998814695 " " y[1] (numeric) = 0.1740212899881468 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 7.97476435714257100000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2733000502806352 " " y[1] (analytic) = 0.17451859135371842 " " y[1] (numeric) = 0.17451859135371828 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 7.95203977992615600000000000000E-14 "%" Correct digits = 16 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 4.225136079253162 " " Order of pole = 4.13995948633783000000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.27455063910746624 " " y[1] (analytic) = 0.175014014333001 " " y[1] (numeric) = 0.17501401433300082 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.11013412297215590000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27517593352088177 " " y[1] (analytic) = 0.17526102388921855 " " y[1] (numeric) = 0.17526102388921833 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.26693659547136040000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2764265223477128 " " y[1] (analytic) = 0.1757536440301561 " " y[1] (numeric) = 0.17575364403015586 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.26338549707073260000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27705181676112833 " " y[1] (analytic) = 0.17599925656364204 " " y[1] (numeric) = 0.17599925656364182 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.26162240261929240000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2783024055879594 " " y[1] (analytic) = 0.17648909140527938 " " y[1] (numeric) = 0.17648909140527916 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.25812084563992070000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 3.1585051344177524 " " Order of pole = 6.9323569107382350000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2795529944147904 " " y[1] (analytic) = 0.17697707904199272 " " y[1] (numeric) = 0.1769770790419925 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.2546517669236990000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28017828882820595 " " y[1] (analytic) = 0.17722038255783137 " " y[1] (numeric) = 0.17722038255783112 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.4095454311478212000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.281428877655037 " " y[1] (analytic) = 0.17770561375648636 " " y[1] (numeric) = 0.1777056137564861 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.40569661959563360000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2820541720684525 " " y[1] (analytic) = 0.17794754333903226 " " y[1] (numeric) = 0.17794754333903198 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.55976166317440850000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28330476089528356 " " y[1] (analytic) = 0.17843003519734008 " " y[1] (numeric) = 0.1784300351973398 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.5555439186531460000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2845553497221146 " " y[1] (analytic) = 0.17891071024746383 " " y[1] (numeric) = 0.17891071024746355 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.55136467667241680000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2851806441355301 " " y[1] (analytic) = 0.1791503688086513 " " y[1] (numeric) = 0.17915036880865104 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.3943604035081240000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28643123296236117 " " y[1] (analytic) = 0.17962833265586667 " " y[1] (numeric) = 0.1796283326558664 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.54516691243820970000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2870565273757767 " " y[1] (analytic) = 0.17986663979414097 " " y[1] (numeric) = 0.1798666397941407 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.54311970509903470000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28830711620260774 " " y[1] (analytic) = 0.180341909108806 " " y[1] (numeric) = 0.18034190910880568 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.69295829949162870000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2895577050294388 " " y[1] (analytic) = 0.1808153912522574 " " y[1] (numeric) = 0.18081539125225712 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.53502284420615670000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2901829994428543 " " y[1] (analytic) = 0.18105146441573683 " " y[1] (numeric) = 0.18105146441573655 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.53302132657129860000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29143358826968535 " " y[1] (analytic) = 0.1815222794631319 " " y[1] (numeric) = 0.18152227946313157 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.83485414778076620000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.4609464812250592 " " Order of pole = 3.295141937087464600000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.2920588826831009 " " y[1] (analytic) = 0.1817570231533058 " " y[1] (numeric) = 0.18175702315330547 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.83248438827376960000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2933094715099319 " " y[1] (analytic) = 0.18222518736110405 " " y[1] (numeric) = 0.1822251873611037 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.82777645731009440000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29456006033676296 " " y[1] (analytic) = 0.18269159329881088 " " y[1] (numeric) = 0.18269159329881052 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.97503605112805370000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2951853547501785 " " y[1] (analytic) = 0.1829241391409298 " " y[1] (numeric) = 0.18292413914092942 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 2.1242579598498670000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29643594357700953 " " y[1] (analytic) = 0.18338792099659043 " " y[1] (numeric) = 0.18338792099659001 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.27023476776408970000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29706123799042505 " " y[1] (analytic) = 0.18361915877184137 " " y[1] (numeric) = 0.18361915877184098 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 2.11621739919655130000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2983118268172561 " " y[1] (analytic) = 0.18408033240096905 " " y[1] (numeric) = 0.18408033240096863 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.2616953631285490000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29956241564408714 " " y[1] (analytic) = 0.184539775948306 " " y[1] (numeric) = 0.18453977594830553 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.55687308083579000000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 4.102072267970005 " " Order of pole = 3.73409747567166050000000000E-10 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30018771005750267 " " y[1] (analytic) = 0.18476885111120261 " " y[1] (numeric) = 0.18476885111120211 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.7039209156560560000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3014382988843337 " " y[1] (analytic) = 0.18522571253179557 " " y[1] (numeric) = 0.1852257125317951 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.5474043480043050000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30206359329774923 " " y[1] (analytic) = 0.18545350050803786 " " y[1] (numeric) = 0.18545350050803736 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.6939386946738540000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3033141821245803 " " y[1] (analytic) = 0.18590779526892479 " " y[1] (numeric) = 0.18590779526892426 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.8366531695677577000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3045647709514113 " " y[1] (analytic) = 0.1863603874456722 " " y[1] (numeric) = 0.18636038744567168 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.8297641141719787000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.6023887332337009 " " Order of pole = 3.7552183584921295000000000000E-12 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30519006536482685 " " y[1] (analytic) = 0.1865860471819369 " " y[1] (numeric) = 0.18658604718193636 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.8263417584635014000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3064406541916579 " " y[1] (analytic) = 0.1870360981614033 " " y[1] (numeric) = 0.18703609816140274 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.9679378353666430000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3070659486050734 " " y[1] (analytic) = 0.18726049108132198 " " y[1] (numeric) = 0.18726049108132142 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.9643813764832483000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 0.955622677129226 " " Order of pole = 4.33200142424539100000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.30831653743190446 " " y[1] (analytic) = 0.1877080159540806 " " y[1] (numeric) = 0.18770801595408004 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.9573138338875010000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3095671262587355 " " y[1] (analytic) = 0.18815386507105503 " " y[1] (numeric) = 0.18815386507105444 " " absolute error = 5.8286708792820720000000000000000E-16 " " relative error = 3.09782149682703230000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "Complex estimate of poles used for equation 1" Radius of convergence = 1.7233706321041822 " " Order of pole = 2.181188563099567500000000000E-11 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.310192420672151 " " y[1] (analytic) = 0.18837616328674153 " " y[1] (numeric) = 0.18837616328674095 " " absolute error = 5.8286708792820720000000000000000E-16 " " relative error = 3.0941658315918740000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31144300949898207 " " y[1] (analytic) = 0.18881951114171622 " " y[1] (numeric) = 0.18881951114171563 " " absolute error = 5.8286708792820720000000000000000E-16 " " relative error = 3.0869007360724670000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3120683039123976 " " y[1] (analytic) = 0.18904056241717804 " " y[1] (numeric) = 0.18904056241717743 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 3.2301145094792050000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31331889273922864 " " y[1] (analytic) = 0.1894814237358318 " " y[1] (numeric) = 0.18948142373583113 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.5155626427200260000000000000E-13 "%" Correct digits = 15 h = 6.2529441341549770000E-4 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff( y , x , 1 ) = cos ( x ) / ( 2.0 * x + 1.0 ) - 2.0 * sin ( x ) / ( 2.0 * x + 1.0 ) / ( 2.0 * x + 1.0 ) ;" Iterations = 302 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 2 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 9 Minutes 43 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 9 Minutes 40 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 12 Minutes 42 Seconds "Time to Timeout " Unknown Percent Done = 23.841053507339964 "%" (%o58) true (%o58) diffeq.max