(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_2D0 array_x , 1 1 1 array_tmp2 : array_const_1D0 + array_tmp1 , 1 1 1 array_tmp3 : array_const_3D0 array_x , 1 1 1 array_tmp4 : array_const_2D0 + array_tmp3 , 1 1 1 array_tmp5 : expt(array_tmp2 , array_tmp4 ), 1 1 1 array_tmp2 2 array_tmp5_a1 : ln(array_tmp2 ), array_tmp5_a1 : -----------, 1 1 2 array_tmp2 1 array_tmp6 : array_const_2D0 array_x , 1 1 1 array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : ln(array_tmp7 ), 1 1 1 1 1 array_tmp9 : array_const_3D0 array_tmp8 , 1 1 1 array_tmp10 : array_const_3D0 array_x , 1 1 1 array_tmp11 : array_const_2D0 + array_tmp10 , 1 1 1 array_tmp12 : array_const_2D0 array_tmp11 , 1 1 1 array_tmp13 : array_const_2D0 array_x , 1 1 1 array_tmp12 1 array_tmp14 : array_const_1D0 + array_tmp13 , array_tmp15 : ------------, 1 1 1 1 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 1 1 1 array_tmp17 : array_tmp5 array_tmp16 , 1 1 1 array_tmp18 : array_tmp17 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_3D0 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 2 1 1 2 array_tmp5_a2 : -------------------------------------------------------, 1 glob_h array_tmp5 : array_tmp5 array_tmp5_a2 glob_h, 2 1 1 array_tmp6 : array_const_2D0 array_x , array_tmp7 : array_tmp6 , 2 1 2 2 2 array_tmp7 2 array_tmp8 : -----------, array_tmp9 : array_const_3D0 array_tmp8 , 2 array_tmp7 2 1 2 1 array_tmp10 : array_const_3D0 array_x , array_tmp11 : array_tmp10 , 2 1 2 2 2 array_tmp12 : array_const_2D0 array_tmp11 , 2 1 2 array_tmp13 : array_const_2D0 array_x , array_tmp14 : array_tmp13 , 2 1 2 2 2 array_tmp12 - array_tmp15 array_tmp14 2 1 2 array_tmp15 : ----------------------------------------, 2 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 2 2 2 array_tmp17 : ats(2, array_tmp5, array_tmp16, 1), 2 array_tmp18 : array_tmp17 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 - array_tmp5_a1 array_tmp2 1 2 2 ------------------------------ array_tmp2 1 array_tmp5_a1 : ------------------------------, 3 2 (array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 2 3 1 2 2 array_tmp5_a2 : -----------------------------------------------------------, 2 glob_h ats(2, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 3 2 - array_tmp7 array_tmp8 1 2 2 --------------------------- array_tmp7 1 array_tmp8 : ---------------------------, 3 2 array_tmp9 : array_const_3D0 array_tmp8 , 3 1 3 - array_tmp15 array_tmp14 2 2 array_tmp15 : ---------------------------, 3 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 3 3 3 array_tmp17 : ats(3, array_tmp5, array_tmp16, 1), 3 array_tmp18 : array_tmp17 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 - array_tmp5_a1 array_tmp2 2 3 2 ------------------------------ array_tmp2 1 array_tmp5_a1 : ------------------------------, 4 3 (array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 3 4 1 3 2 array_tmp5_a2 : -----------------------------------------------------------, 3 glob_h ats(3, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 4 3 - array_tmp7 array_tmp8 2 2 3 --------------------------- array_tmp7 1 array_tmp8 : ---------------------------, 4 3 array_tmp9 : array_const_3D0 array_tmp8 , 4 1 4 - array_tmp15 array_tmp14 3 2 array_tmp15 : ---------------------------, 4 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 4 4 4 array_tmp17 : ats(4, array_tmp5, array_tmp16, 1), 4 array_tmp18 : array_tmp17 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 - array_tmp5_a1 array_tmp2 3 4 2 ------------------------------ array_tmp2 1 array_tmp5_a1 : ------------------------------, 5 4 (array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 4 5 1 4 2 array_tmp5_a2 : -----------------------------------------------------------, 4 glob_h ats(4, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 5 4 - array_tmp7 array_tmp8 3 2 4 --------------------------- array_tmp7 1 array_tmp8 : ---------------------------, 5 4 array_tmp9 : array_const_3D0 array_tmp8 , 5 1 5 - array_tmp15 array_tmp14 4 2 array_tmp15 : ---------------------------, 5 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 5 5 5 array_tmp17 : ats(5, array_tmp5, array_tmp16, 1), 5 array_tmp18 : array_tmp17 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp5_a1 : kkk - array_tmp5_a1 array_tmp4 (kkk - 2) kkk - 1 2 -------------------------------------------- array_tmp2 1 --------------------------------------------, kkk - 1 array_tmp5_a2 : ((array_tmp5_a1 array_tmp4 kkk - 1 kkk 1 + array_tmp5_a1 array_tmp4 ) (kkk - 1))/glob_h, kkk - 1 2 ats(kkk - 1, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------------, kkk kkk - 1 - array_tmp7 array_tmp8 (kkk - 2) 2 kkk - 1 ----------------------------------------- array_tmp7 1 array_tmp8 : -----------------------------------------, kkk kkk - 1 array_tmp9 : array_const_3D0 array_tmp8 , kkk 1 kkk - array_tmp15 array_tmp14 kkk - 1 2 array_tmp15 : ---------------------------------, kkk array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , kkk kkk kkk array_tmp17 : ats(kkk, array_tmp5, array_tmp16, 1), kkk array_tmp18 : array_tmp17 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp18 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_2D0 array_x , 1 1 1 array_tmp2 : array_const_1D0 + array_tmp1 , 1 1 1 array_tmp3 : array_const_3D0 array_x , 1 1 1 array_tmp4 : array_const_2D0 + array_tmp3 , 1 1 1 array_tmp5 : expt(array_tmp2 , array_tmp4 ), 1 1 1 array_tmp2 2 array_tmp5_a1 : ln(array_tmp2 ), array_tmp5_a1 : -----------, 1 1 2 array_tmp2 1 array_tmp6 : array_const_2D0 array_x , 1 1 1 array_tmp7 : array_const_1D0 + array_tmp6 , array_tmp8 : ln(array_tmp7 ), 1 1 1 1 1 array_tmp9 : array_const_3D0 array_tmp8 , 1 1 1 array_tmp10 : array_const_3D0 array_x , 1 1 1 array_tmp11 : array_const_2D0 + array_tmp10 , 1 1 1 array_tmp12 : array_const_2D0 array_tmp11 , 1 1 1 array_tmp13 : array_const_2D0 array_x , 1 1 1 array_tmp12 1 array_tmp14 : array_const_1D0 + array_tmp13 , array_tmp15 : ------------, 1 1 1 1 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 1 1 1 array_tmp17 : array_tmp5 array_tmp16 , 1 1 1 array_tmp18 : array_tmp17 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_3D0 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 2 1 1 2 array_tmp5_a2 : -------------------------------------------------------, 1 glob_h array_tmp5 : array_tmp5 array_tmp5_a2 glob_h, 2 1 1 array_tmp6 : array_const_2D0 array_x , array_tmp7 : array_tmp6 , 2 1 2 2 2 array_tmp7 2 array_tmp8 : -----------, array_tmp9 : array_const_3D0 array_tmp8 , 2 array_tmp7 2 1 2 1 array_tmp10 : array_const_3D0 array_x , array_tmp11 : array_tmp10 , 2 1 2 2 2 array_tmp12 : array_const_2D0 array_tmp11 , 2 1 2 array_tmp13 : array_const_2D0 array_x , array_tmp14 : array_tmp13 , 2 1 2 2 2 array_tmp12 - array_tmp15 array_tmp14 2 1 2 array_tmp15 : ----------------------------------------, 2 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 2 2 2 array_tmp17 : ats(2, array_tmp5, array_tmp16, 1), 2 array_tmp18 : array_tmp17 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 - array_tmp5_a1 array_tmp2 1 2 2 ------------------------------ array_tmp2 1 array_tmp5_a1 : ------------------------------, 3 2 (array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 2 3 1 2 2 array_tmp5_a2 : -----------------------------------------------------------, 2 glob_h ats(2, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 3 2 - array_tmp7 array_tmp8 1 2 2 --------------------------- array_tmp7 1 array_tmp8 : ---------------------------, 3 2 array_tmp9 : array_const_3D0 array_tmp8 , 3 1 3 - array_tmp15 array_tmp14 2 2 array_tmp15 : ---------------------------, 3 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 3 3 3 array_tmp17 : ats(3, array_tmp5, array_tmp16, 1), 3 array_tmp18 : array_tmp17 , if not array_y_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 - array_tmp5_a1 array_tmp2 2 3 2 ------------------------------ array_tmp2 1 array_tmp5_a1 : ------------------------------, 4 3 (array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 3 4 1 3 2 array_tmp5_a2 : -----------------------------------------------------------, 3 glob_h ats(3, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 4 3 - array_tmp7 array_tmp8 2 2 3 --------------------------- array_tmp7 1 array_tmp8 : ---------------------------, 4 3 array_tmp9 : array_const_3D0 array_tmp8 , 4 1 4 - array_tmp15 array_tmp14 3 2 array_tmp15 : ---------------------------, 4 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 4 4 4 array_tmp17 : ats(4, array_tmp5, array_tmp16, 1), 4 array_tmp18 : array_tmp17 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 - array_tmp5_a1 array_tmp2 3 4 2 ------------------------------ array_tmp2 1 array_tmp5_a1 : ------------------------------, 5 4 (array_tmp5_a1 array_tmp4 + array_tmp5_a1 array_tmp4 ) 4 5 1 4 2 array_tmp5_a2 : -----------------------------------------------------------, 4 glob_h ats(4, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------, 5 4 - array_tmp7 array_tmp8 3 2 4 --------------------------- array_tmp7 1 array_tmp8 : ---------------------------, 5 4 array_tmp9 : array_const_3D0 array_tmp8 , 5 1 5 - array_tmp15 array_tmp14 4 2 array_tmp15 : ---------------------------, 5 array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , 5 5 5 array_tmp17 : ats(5, array_tmp5, array_tmp16, 1), 5 array_tmp18 : array_tmp17 , if not array_y_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp18 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 while kkk <= glob_max_terms do (array_tmp5_a1 : kkk - array_tmp5_a1 array_tmp4 (kkk - 2) kkk - 1 2 -------------------------------------------- array_tmp2 1 --------------------------------------------, kkk - 1 array_tmp5_a2 : ((array_tmp5_a1 array_tmp4 kkk - 1 kkk 1 + array_tmp5_a1 array_tmp4 ) (kkk - 1))/glob_h, kkk - 1 2 ats(kkk - 1, array_tmp5, array_tmp5_a2, 1) glob_h array_tmp5 : -------------------------------------------------, kkk kkk - 1 - array_tmp7 array_tmp8 (kkk - 2) 2 kkk - 1 ----------------------------------------- array_tmp7 1 array_tmp8 : -----------------------------------------, kkk kkk - 1 array_tmp9 : array_const_3D0 array_tmp8 , kkk 1 kkk - array_tmp15 array_tmp14 kkk - 1 2 array_tmp15 : ---------------------------------, kkk array_tmp14 1 array_tmp16 : array_tmp15 + array_tmp9 , kkk kkk kkk array_tmp17 : ats(kkk, array_tmp5, array_tmp16, 1), kkk array_tmp18 : array_tmp17 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp18 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) (%i56) exact_soln_y(x) := block(expt(1.0 + 2.0 x, 2.0 + 3.0 x)) (%o56) exact_soln_y(x) := block(expt(1.0 + 2.0 x, 2.0 + 3.0 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/expt_lin_lin_newpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 \ ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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, " (expt(2.0*x+1.0,3.0*x+2.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5_c1, 1 + max_terms), array(array_tmp5_a1, 1 + max_terms), array(array_tmp5_a2, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_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_tmp15, 1 + max_terms), array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms), array(array_tmp18, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp11 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp14 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp15 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp17 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp18 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term array(array_tmp5_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term), term array(array_tmp5_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_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_tmp15, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term), term array(array_tmp16, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term), term array(array_tmp17, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term), term array(array_tmp18, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp18 : 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_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, 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 )\ = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 \ * ( 3.0 * x + 2.0 ) ) / ( 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, "2013-01-28T14:03:08-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_lin_lin_new"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x\ + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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 ), 1 logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "expt_lin_lin_new diffeq.max"), logitem_str(html_log_file, "expt_li\ n_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/expt_lin_lin_newpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 \ ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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, " (expt(2.0*x+1.0,3.0*x+2.0)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5_c1, 1 + max_terms), array(array_tmp5_a1, 1 + max_terms), array(array_tmp5_a2, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 1 + max_terms), array(array_tmp8, 1 + max_terms), array(array_tmp9, 1 + max_terms), array(array_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_tmp15, 1 + max_terms), array(array_tmp16, 1 + max_terms), array(array_tmp17, 1 + max_terms), array(array_tmp18, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5_a1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp8 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp9 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp10 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp11 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp12 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp13 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp14 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp15 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp16 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp17 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp18 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5_c1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_c1 : 0.0, term : 1 + term), term array(array_tmp5_a1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a1 : 0.0, term : 1 + term), term array(array_tmp5_a2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5_a2 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_tmp8, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp8 : 0.0, term : 1 + term), term array(array_tmp9, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp9 : 0.0, term : 1 + term), term array(array_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_tmp15, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp15 : 0.0, term : 1 + term), term array(array_tmp16, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp16 : 0.0, term : 1 + term), term array(array_tmp17, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp17 : 0.0, term : 1 + term), term array(array_tmp18, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp18 : 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_const_3D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, 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 )\ = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 \ * ( 3.0 * x + 2.0 ) ) / ( 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, "2013-01-28T14:03:08-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "expt_lin_lin_new"), logitem_str(html_log_file, "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x\ + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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 ), 1 logitem_float(html_log_file, glob_h), logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "expt_lin_lin_new diffeq.max"), logitem_str(html_log_file, "expt_li\ n_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/expt_lin_lin_newpostode.ode#################" "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 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(" " (expt(2.0*x+1.0,3.0*x+2.0)) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 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 = 1.058672991960640700000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" max_value3 = 1.058672991960640700000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" value3 = 1.058672991960640700000000000000000000000000000000000000000000000000000000000000000000000000E-74 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 1.5209567545525315 " " y[1] (numeric) = 1.5209567545525315 " " 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] = 0.101 " " y[1] (analytic) = 1.5276363683101828 " " y[1] (numeric) = 1.5276363683101828 " " 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) = 1.5343508520732434 " " y[1] (numeric) = 1.5343508520732434 " " 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) = 1.541100401960597 " " y[1] (numeric) = 1.541100401960597 " " 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] = 0.10400000000000001 " " y[1] (analytic) = 1.5478852152658196 " " y[1] (numeric) = 1.5478852152658196 " " 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) = 1.5547054904645634 " " y[1] (numeric) = 1.5547054904645634 " " 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] = 0.10600000000000001 " " y[1] (analytic) = 1.5615614272219898 " " y[1] (numeric) = 1.5615614272219895 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.421939611559486200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = 1.5684532264002486 " " y[1] (numeric) = 1.5684532264002484 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.415691594671554800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000001 " " y[1] (analytic) = 1.5753810900660097 " " y[1] (numeric) = 1.5753810900660095 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.40946597826515400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = 1.5823452214980398 " " y[1] (numeric) = 1.5823452214980396 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.40326271352351900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = 1.5893458251948314 " " y[1] (numeric) = 1.589345825194831 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.79416350306028300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = 1.5963831068822798 " " y[1] (numeric) = 1.5963831068822794 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.78184608654099600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = 1.603457273521412 " " y[1] (numeric) = 1.6034572735214117 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.769573079267536600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000002 " " y[1] (analytic) = 1.6105685333161648 " " y[1] (numeric) = 1.6105685333161643 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.757344382829098300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000002 " " y[1] (analytic) = 1.6177170957212128 " " y[1] (numeric) = 1.6177170957212124 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.74515989862911200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000002 " " y[1] (analytic) = 1.6249031714498503 " " y[1] (numeric) = 1.6249031714498499 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.733019527888641600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = 1.6321269724819214 " " y[1] (numeric) = 1.6321269724819212 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.360461585824878600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000002 " " y[1] (analytic) = 1.6393887120718058 " " y[1] (numeric) = 1.6393887120718054 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.708870730778896000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000002 " " y[1] (analytic) = 1.6466886047564515 " " y[1] (numeric) = 1.646688604756451 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.696862105970207500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000002 " " y[1] (analytic) = 1.6540268663634659 " " y[1] (numeric) = 1.6540268663634652 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.02734579662331600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (analytic) = 1.6614037140192548 " " y[1] (numeric) = 1.6614037140192541 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.009463859711666000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = 1.6688193661572188 " " y[1] (numeric) = 1.6688193661572182 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.99164719851613800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12200000000000003 " " y[1] (analytic) = 1.676274042526 " " y[1] (numeric) = 1.6762740425259992 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.29852755079185700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12300000000000003 " " y[1] (analytic) = 1.683767964197784 " " y[1] (numeric) = 1.6837679641977834 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.95620910326837900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12400000000000003 " " y[1] (analytic) = 1.6913013535766572 " " y[1] (numeric) = 1.6913013535766566 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.93858736863419500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000003 " " y[1] (analytic) = 1.698874434407017 " " y[1] (numeric) = 1.6988744344070164 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.92103030856194100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000003 " " y[1] (analytic) = 1.7064874317820384 " " y[1] (numeric) = 1.7064874317820378 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.903537772203037000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = 1.7141405721521958 " " y[1] (numeric) = 1.714140572152195 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.18147947799269100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = 1.7218340833338395 " " y[1] (numeric) = 1.7218340833338386 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.158327554885088000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = 1.7295681945178305 " " y[1] (numeric) = 1.7295681945178296 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.13526105831133100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = 1.7373431362782308 " " y[1] (numeric) = 1.73734313627823 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.11227978603465600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = 1.74515914058105 " " y[1] (numeric) = 1.7451591405810492 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.089383535557718000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = 1.7530164407930502 " " y[1] (numeric) = 1.7530164407930493 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.06657210412881600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13300000000000003 " " y[1] (analytic) = 1.7609152716906087 " " y[1] (numeric) = 1.7609152716906078 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 5.043845288748098000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13400000000000004 " " y[1] (analytic) = 1.7688558694686385 " " y[1] (numeric) = 1.7688558694686374 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.2765036077171500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = 1.7768384717495669 " " y[1] (numeric) = 1.7768384717495658 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.24830586615998800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = 1.784863317592375 " " y[1] (numeric) = 1.7848633175923736 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 7.46425575795518500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = 1.7929306475016928 " " y[1] (numeric) = 1.7929306475016917 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.19222514921123500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = 1.80104070343696 " " y[1] (numeric) = 1.8010407034369589 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.16434166371974300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = 1.8091937288216398 " " y[1] (numeric) = 1.8091937288216386 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.13656241970429900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (analytic) = 1.8173899685524986 " " y[1] (numeric) = 1.8173899685524977 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.887109729165805500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14100000000000004 " " y[1] (analytic) = 1.8256296690089457 " " y[1] (numeric) = 1.8256296690089446 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.08131563302127900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14200000000000004 " " y[1] (analytic) = 1.8339130780624315 " " y[1] (numeric) = 1.8339130780624306 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.843078062557385500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = 1.8422404450859124 " " y[1] (numeric) = 1.8422404450859113 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 6.02648274054900400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = 1.8506120209633727 " " y[1] (numeric) = 1.8506120209633716 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.99922086341581300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = 1.8590280580994132 " " y[1] (numeric) = 1.8590280580994125 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.58323701394867200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14600000000000005 " " y[1] (analytic) = 1.8674888104289022 " " y[1] (numeric) = 1.8674888104289016 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.56700297776940570000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14700000000000005 " " y[1] (analytic) = 1.8759945334266876 " " y[1] (numeric) = 1.8759945334266868 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.73444034017402200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14800000000000005 " " y[1] (analytic) = 1.8845454841173745 " " y[1] (numeric) = 1.8845454841173739 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.53471869153148700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14900000000000005 " " y[1] (analytic) = 1.8931419210851703 " " y[1] (numeric) = 1.8931419210851692 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.86444688726117300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (analytic) = 1.9017841044837869 " " y[1] (numeric) = 1.901784104483786 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.67023789717292360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15100000000000005 " " y[1] (analytic) = 1.9104722960464176 " " y[1] (numeric) = 1.9104722960464167 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.64899921102308270000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15200000000000005 " " y[1] (analytic) = 1.9192067590957729 " " y[1] (numeric) = 1.9192067590957718 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.78480155597322900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15300000000000005 " " y[1] (analytic) = 1.927987758554184 " " y[1] (numeric) = 1.9279877585541831 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.60676379172748730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.9368155609537758 " " y[1] (numeric) = 1.936815560953775 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.5857666450322500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.9456904344467032 " " y[1] (numeric) = 1.9456904344467023 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.56484959773519600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.9546126488154565 " " y[1] (numeric) = 1.9546126488154556 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.544012442763957000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.9635824754832358 " " y[1] (numeric) = 1.963582475483235 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.523254972936879000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.9726001875243924 " " y[1] (numeric) = 1.9726001875243915 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.50257698096838700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.9816660596749396 " " y[1] (numeric) = 1.9816660596749387 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.481978259474336000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.9907803683431335 " " y[1] (numeric) = 1.9907803683431324 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.576823251221639000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.999943391620122 " " y[1] (numeric) = 1.999943391620121 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.441017797911901000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = 2.009155409290667 " " y[1] (numeric) = 2.009155409290666 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.420655642629939000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = 2.018416702843935 " " y[1] (numeric) = 2.018416702843934 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.400371927405714600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = 2.0277275554843586 " " y[1] (numeric) = 2.0277275554843577 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.38016644444114260000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = 2.0370882521425737 " " y[1] (numeric) = 2.037088252142573 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.3600389858709104000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = 2.046499079486424 " " y[1] (numeric) = 2.046499079486423 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.339989343767585700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = 2.055960325932041 " " y[1] (numeric) = 2.0559603259320403 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.32001731014669200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000007 " " y[1] (analytic) = 2.065472281654999 " " y[1] (numeric) = 2.065472281654998 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.30012267697175500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = 2.0750352386015387 " " y[1] (numeric) = 2.075035238601538 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.28030523615931140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (analytic) = 2.0846494904998707 " " y[1] (numeric) = 2.08464949049987 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.26056477958389130000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000007 " " y[1] (analytic) = 2.0943153328715507 " " y[1] (numeric) = 2.09431533287155 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.24090109908295900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = 2.10403306304293 " " y[1] (numeric) = 2.104033063042929 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.221313986461834000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000007 " " y[1] (analytic) = 2.113802980156683 " " y[1] (numeric) = 2.113802980156682 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.20180323349856400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000007 " " y[1] (analytic) = 2.123625385183412 " " y[1] (numeric) = 2.123625385183411 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.182368631948782400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000007 " " y[1] (analytic) = 2.133500580933325 " " y[1] (numeric) = 2.1335005809333243 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.16300997355051600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = 2.1434288720679957 " " y[1] (numeric) = 2.143428872067995 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.143727050028976300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000007 " " y[1] (analytic) = 2.153410565112197 " " y[1] (numeric) = 2.1534105651121966 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.062259826550654200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = 2.163445968465819 " " y[1] (numeric) = 2.163445968465818 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.10538757448130800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000008 " " y[1] (analytic) = 2.1735353924158556 " " y[1] (numeric) = 2.173535392415855 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.043165302942057700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (analytic) = 2.1836791491484853 " " y[1] (numeric) = 2.1836791491484853 " " 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] = 0.18100000000000008 " " y[1] (analytic) = 2.1938775527612187 " " y[1] (numeric) = 2.193877552761218 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.024220582826653500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = 2.204130919275132 " " y[1] (numeric) = 2.2041309192751317 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.01480413874920500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000008 " " y[1] (analytic) = 2.2144395666471857 " " y[1] (numeric) = 2.2144395666471848 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.01084966633290700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = 2.2248038147826157 " " y[1] (numeric) = 2.224803814782615 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.99216512394783300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = 2.2352239855474174 " " y[1] (numeric) = 2.2352239855474165 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.97355444216301200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = 2.245700402780905 " " y[1] (numeric) = 2.2457004027809035 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.93252611924729100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000008 " " y[1] (analytic) = 2.2562333923083546 " " y[1] (numeric) = 2.2562333923083537 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.93655382784415300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = 2.2668232819537386 " " y[1] (numeric) = 2.2668232819537377 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.91816347913375330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = 2.277470401552535 " " y[1] (numeric) = 2.277470401552534 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.8998461586796496000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = 2.288175082964628 " " y[1] (numeric) = 2.288175082964627 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.88160165851196500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = 2.2989376600872937 " " y[1] (numeric) = 2.2989376600872924 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.79514465607388400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = 2.30975846886827 " " y[1] (numeric) = 2.3097584688682686 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.7679954311541900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = 2.320637847318916 " " y[1] (numeric) = 2.3206378473189146 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.74095450132120400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = 2.331576135527457 " " y[1] (numeric) = 2.3315761355274556 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.71402155498901500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = 2.3425736756723183 " " y[1] (numeric) = 2.342573675672317 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.68719628067974000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = 2.3536308120355485 " " y[1] (numeric) = 2.3536308120355476 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.77365224468649800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = 2.364747891016332 " " y[1] (numeric) = 2.364747891016331 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.633867502795825000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = 2.3759252611445887 " " y[1] (numeric) = 2.375925261144588 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.738242251240892500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = 2.3871632730946706 " " y[1] (numeric) = 2.3871632730946692 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.58096567824228800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = 2.3984622796991406 " " y[1] (numeric) = 2.3984622796991397 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.7031160640622500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = 2.4098226359626547 " " y[1] (numeric) = 2.409822635962654 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.68565887980931650000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = 2.421244699075925 " " y[1] (numeric) = 2.4212446990759244 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.834136012851367600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = 2.432728828429784 " " y[1] (numeric) = 2.432728828429783 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.65095529481353700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = 2.4442753856293375 " " y[1] (numeric) = 2.4442753856293367 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.633708480321018500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = 2.455884734508218 " " y[1] (numeric) = 2.455884734508217 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.61653137551661100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = 2.4675572411429254 " " y[1] (numeric) = 2.4675572411429245 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.59942377380772700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = 2.47929327386727 " " y[1] (numeric) = 2.479293273867269 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.582385468721576700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = 2.491093203286909 " " y[1] (numeric) = 2.4910932032869075 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.34812438086342300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = 2.502957402293979 " " y[1] (numeric) = 2.5029574022939776 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.322773884721949000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = 2.51488624608183 " " y[1] (numeric) = 2.5148862460818293 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.531684270347811000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = 2.5268801121598554 " " y[1] (numeric) = 2.526880112159854 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.272381634328626000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = 2.5389393803684173 " " y[1] (numeric) = 2.538939380368416 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.247339262416210000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = 2.5510644328938805 " " y[1] (numeric) = 2.551064432893879 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.22239898127107700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = 2.5632556542837386 " " y[1] (numeric) = 2.5632556542837373 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.197560482598327000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = 2.575513431461846 " " y[1] (numeric) = 2.575513431461845 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.17282345832691200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = 2.58783815374375 " " y[1] (numeric) = 2.5878381537437485 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.14818760061495900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = 2.600230212852124 " " y[1] (numeric) = 2.600230212852123 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.12365260185504300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = 2.61269000293231 " " y[1] (numeric) = 2.612690002932309 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.09921815467942600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = 2.6252179205679558 " " y[1] (numeric) = 2.6252179205679544 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 5.07488395196524100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = 2.637814364796764 " " y[1] (numeric) = 2.637814364796763 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.36709979122642600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = 2.650479737126346 " " y[1] (numeric) = 2.650479737126345 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.351010035123262500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = 2.663214441550177 " " y[1] (numeric) = 2.663214441550176 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.334986495428972000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = 2.676018884563663 " " y[1] (numeric) = 2.6760188845636623 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.3190289680819896000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = 2.688893475180315 " " y[1] (numeric) = 2.688893475180314 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.303137249200862600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = 2.701838624948026 " " y[1] (numeric) = 2.7018386249480257 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.643655567543769700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = 2.714854747965468 " " y[1] (numeric) = 2.714854747965467 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.27155042223062800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = 2.727942260898585 " " y[1] (numeric) = 2.7279422608985837 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.88378236096294200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = 2.741101582997207 " " y[1] (numeric) = 2.7411015829972065 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.620112193596566800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = 2.7543331361117755 " " y[1] (numeric) = 2.754333136111775 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.612329329475999700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = 2.767637344710172 " " y[1] (numeric) = 2.767637344710171 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.209157519852499000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = 2.781014635894668 " " y[1] (numeric) = 2.781014635894667 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.19372076736443800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = 2.7944654394189863 " " y[1] (numeric) = 2.7944654394189854 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.178348199163242000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = 2.807990187705476 " " y[1] (numeric) = 2.807990187705475 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.16303961313302300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = 2.821589315862403 " " y[1] (numeric) = 2.8215893158624024 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.573897403684807000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = 2.835263261701359 " " y[1] (numeric) = 2.835263261701358 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 4.69892037027536070000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = 2.8490124657547797 " " y[1] (numeric) = 2.8490124657547793 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.55874786505158900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = 2.8628373712935944 " " y[1] (numeric) = 2.862837371293594 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.55122052793867800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = 2.8767384243449787 " " y[1] (numeric) = 2.876738424344978 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.0874493564786300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = 2.890716073710237 " " y[1] (numeric) = 2.8907160737102364 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.536260215553005300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = 2.904770770982803 " " y[1] (numeric) = 2.904770770982802 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.05765407918786700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = 2.918902970566357 " " y[1] (numeric) = 2.9189029705663567 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.521425050192386500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = 2.9331131296930733 " " y[1] (numeric) = 2.9331131296930724 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 3.02810829459232600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = 2.947401708441978 " " y[1] (numeric) = 2.9474017084419777 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.506714230971970300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = 2.961769169757446 " " y[1] (numeric) = 2.9617691697574458 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.49940520140680400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = 2.9762159794678067 " " y[1] (numeric) = 2.9762159794678062 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.492126958909321400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = 2.9907426063040865 " " y[1] (numeric) = 2.9907426063040856 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.9697588078223900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = 3.0053495219188706 " " y[1] (numeric) = 3.0053495219188697 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.95532487393691400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = 3.020037200905297 " " y[1] (numeric) = 3.0200372009052963 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.94095191752565700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = 3.0348061208161736 " " y[1] (numeric) = 3.034806120816173 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.463319870103037300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 3.0496567621832282 " " y[1] (numeric) = 3.0496567621832273 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.91238814385224250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = 3.0645896085364828 " " y[1] (numeric) = 3.0645896085364823 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.449098465298721300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = 3.079605146423766 " " y[1] (numeric) = 3.0796051464237655 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.442032951418357500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = 3.09470386543035 " " y[1] (numeric) = 3.0947038654303496 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.434997431614696800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = 3.1098862581987237 " " y[1] (numeric) = 3.109886258198723 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.427991807350804700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = 3.1251528204484975 " " y[1] (numeric) = 3.125152820448497 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.42101598022438600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = 3.140504050996444 " " y[1] (numeric) = 3.1405040509964435 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.414069851969012600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = 3.1559404517766723 " " y[1] (numeric) = 3.1559404517766714 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.814306648910676000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = 3.1714625278609376 " " y[1] (numeric) = 3.1714625278609367 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.80053259938460200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = 3.187070787479092 " " y[1] (numeric) = 3.1870707874790916 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.393408679828313800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 3.20276574203967 " " y[1] (numeric) = 3.202765742039669 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.77316073430488200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = 3.2185479061506097 " " y[1] (numeric) = 3.218547906150609 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.759562528191132300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = 3.234417797640122 " " y[1] (numeric) = 3.2344177976401216 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.373011273231542800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = 3.2503759375776964 " " y[1] (numeric) = 3.2503759375776955 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.7325405945566700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = 3.2664228502952453 " " y[1] (numeric) = 3.2664228502952444 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.719116478198297400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = 3.282559063408397 " " y[1] (numeric) = 3.2825590634083968 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.352875001703546200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = 3.2987851078379324 " " y[1] (numeric) = 3.298785107837932 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.346220488248549800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = 3.3151015178313585 " " y[1] (numeric) = 3.3151015178313585 " " 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] = 0.2680000000000001 " " y[1] (analytic) = 3.3315088309846397 " " y[1] (numeric) = 3.3315088309846397 " " 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] = 0.26900000000000013 " " y[1] (analytic) = 3.3480075882640654 " " y[1] (numeric) = 3.348007588264066 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.326428325332207300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 3.3645983340282744 " " y[1] (numeric) = 3.3645983340282744 " " 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] = 0.27100000000000013 " " y[1] (analytic) = 3.381281616050418 " " y[1] (numeric) = 3.3812816160504187 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.31337540103740600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = 3.3980579855404875 " " y[1] (numeric) = 3.398057985540488 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.306891205917508000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = 3.4149279971677764 " " y[1] (numeric) = 3.4149279971677764 " " 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] = 0.27400000000000013 " " y[1] (analytic) = 3.431892209083506 " " y[1] (numeric) = 3.431892209083506 " " 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] = 0.27500000000000013 " " y[1] (analytic) = 3.4489511829436004 " " y[1] (numeric) = 3.4489511829436013 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.575213079537082600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = 3.4661054839316194 " " y[1] (numeric) = 3.466105483931619 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.281233972563149400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = 3.483355680781835 " " y[1] (numeric) = 3.4833556807818344 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.274889074062018600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = 3.5007023458024813 " " y[1] (numeric) = 3.5007023458024813 " " 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] = 0.27900000000000014 " " y[1] (analytic) = 3.5181460548991508 " " y[1] (numeric) = 3.5181460548991503 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.262281903366836200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 3.535687387598348 " " y[1] (numeric) = 3.535687387598348 " " 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] = 0.28100000000000014 " " y[1] (analytic) = 3.553326927071211 " " y[1] (numeric) = 3.5533269270712116 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.249784269684686800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = 3.57106526015739 " " y[1] (numeric) = 3.5710652601573893 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.243576293059651400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = 3.5889029773890777 " " y[1] (numeric) = 3.5889029773890786 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.474790835238109300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = 3.6068406730152294 " " y[1] (numeric) = 3.6068406730152294 " " 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] = 0.28500000000000014 " " y[1] (analytic) = 3.624878945025911 " " y[1] (numeric) = 3.624878945025911 " " 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] = 0.28600000000000014 " " y[1] (analytic) = 3.643018395176845 " " y[1] (numeric) = 3.643018395176845 " " 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] = 0.28700000000000014 " " y[1] (analytic) = 3.6612596290141033 " " y[1] (numeric) = 3.6612596290141033 " " 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] = 0.28800000000000014 " " y[1] (analytic) = 3.679603255898975 " " y[1] (numeric) = 3.6796032558989755 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.206894273555494500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = 3.6980498890330034 " " y[1] (numeric) = 3.698049889033004 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.200874036791825800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 3.716600145483188 " " y[1] (numeric) = 3.7166001454831883 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.194880246640918800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = 3.735254646207364 " " y[1] (numeric) = 3.735254646207365 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.377825620542224300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = 3.754014016079751 " " y[1] (numeric) = 3.754014016079752 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.36594327004573600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = 3.7728788839166745 " " y[1] (numeric) = 3.7728788839166754 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.35411325681914200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = 3.7918498825024636 " " y[1] (numeric) = 3.7918498825024645 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.342335396236636700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = 3.8109276486155252 " " y[1] (numeric) = 3.810927648615526 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.330609504021395600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = 3.8301128230545953 " " y[1] (numeric) = 3.830112823054596 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.31893539624711180000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = 3.8494060506651664 " " y[1] (numeric) = 3.8494060506651673 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.30731288933951400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = 3.8688079803660993 " " y[1] (numeric) = 3.8688079803660997 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.147870900038929100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = 3.8883192651764094 " " y[1] (numeric) = 3.88831926517641 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.14211097279820390000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 3.907940562242244 " " y[1] (numeric) = 3.9079405622422443 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.136376571692941100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = 3.927672532864034 " " y[1] (numeric) = 3.927672532864035 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.261335211294896500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = 3.94751584252384 " " y[1] (numeric) = 3.94751584252384 " " 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] = 0.30300000000000016 " " y[1] (analytic) = 3.9674711609128717 " " y[1] (numeric) = 3.9674711609128717 " " 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] = 0.30400000000000016 " " y[1] (analytic) = 3.9875391619592095 " " y[1] (numeric) = 3.98753916195921 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.113692409811636600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = 4.007720523855706 " " y[1] (numeric) = 4.007720523855706 " " 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] = 0.30600000000000016 " " y[1] (analytic) = 4.0280159290880775 " " y[1] (numeric) = 4.0280159290880775 " " 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] = 0.30700000000000016 " " y[1] (analytic) = 4.04842606446319 " " y[1] (numeric) = 4.04842606446319 " " 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] = 0.30800000000000016 " " y[1] (analytic) = 4.068951621137539 " " y[1] (numeric) = 4.068951621137539 " " 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] = 0.30900000000000016 " " y[1] (analytic) = 4.089593294645918 " " y[1] (numeric) = 4.089593294645917 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.171801339910561500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 4.1103517849302875 " " y[1] (numeric) = 4.110351784930287 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.160833101819748500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = 4.13122779636884 " " y[1] (numeric) = 4.131227796368838 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.29982786464011200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = 4.152222037805259 " " y[1] (numeric) = 4.152222037805259 " " 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] = 0.31300000000000017 " " y[1] (analytic) = 4.1733352225781895 " " y[1] (numeric) = 4.173335222578189 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.128222086965324600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = 4.194568068550890 " " y[1] (numeric) = 4.19456806855089 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.117449055981029400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = 4.215921298141107 " " y[1] (numeric) = 4.215921298141107 " " 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] = 0.31600000000000017 " " y[1] (analytic) = 4.237395638351142 " " y[1] (numeric) = 4.237395638351141 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.09604789239301200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = 4.258991820798123 " " y[1] (numeric) = 4.258991820798121 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.17083881383779300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = 4.28071058174449 " " y[1] (numeric) = 4.280710581744488 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.14967750208504700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = 4.302552662128686 " " y[1] (numeric) = 4.302552662128684 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.12861149855490400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 4.324518807596050 " " y[1] (numeric) = 4.32451880759605 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.053820226518689200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = 4.346609768529942 " " y[1] (numeric) = 4.34660976852994 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.08676401608748200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = 4.368826300083045 " " y[1] (numeric) = 4.368826300083043 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 4.065981839027302000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = 4.3911691622089215 " " y[1] (numeric) = 4.391169162208920 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.02264678697401470000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = 4.413639119693759 " " y[1] (numeric) = 4.413639119693758 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.012349436855978600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = 4.436236942188342 " " y[1] (numeric) = 4.436236942188339 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 6.00629608793166300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = 4.458963404240234 " " y[1] (numeric) = 4.458963404240231 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.97568317462876300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = 4.4818192853262 " " y[1] (numeric) = 4.481819285326198 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.963472702293399700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = 4.504805369884829 " " y[1] (numeric) = 4.504805369884827 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.943248805543102500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = 4.52792244734939 " " y[1] (numeric) = 4.527922447349387 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.88467512437226800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 4.551171312180909 " " y[1] (numeric) = 4.551171312180906 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.85461428790633100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = 4.57455276390148 " " y[1] (numeric) = 4.574552763901478 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.883126790924270600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = 4.598067607127797 " " y[1] (numeric) = 4.5980676071277955 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.863268205640541500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = 4.6217166516049195 " " y[1] (numeric) = 4.621716651604917 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.7652501439591700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = 4.64550071224026 " " y[1] (numeric) = 4.645500712240256 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 7.64764424519317300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = 4.66942060913782 " " y[1] (numeric) = 4.669420609137816 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 7.60846789395673600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = 4.693477167632652 " " y[1] (numeric) = 4.693477167632649 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 7.5694704627538600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = 4.717671218325554 " " y[1] (numeric) = 4.7176712183255525 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.765325638845035000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = 4.742003597118016 " " y[1] (numeric) = 4.742003597118012 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 7.49200966646184400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = 4.7664751452473775 " " y[1] (numeric) = 4.766475145247375 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.59015871876971200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 4.791086709322268 " " y[1] (numeric) = 4.791086709322267 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.707628242135338500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = 4.815839141358256 " " y[1] (numeric) = 4.8158391413582535 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.5328576825115290000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = 4.840733298813750 " " y[1] (numeric) = 4.840733298813748 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.50440417726243100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = 4.8657700446261645 " " y[1] (numeric) = 4.86577004462616 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 9.1268022487113210000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = 4.890950247248301 " " y[1] (numeric) = 4.890950247248298 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.4478887013816400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = 4.916274780685021 " " y[1] (numeric) = 4.916274780685020 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.61321715860791900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = 4.941744524530132 " " y[1] (numeric) = 4.9417445245301295 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.3918919642122200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = 4.967360364003544 " " y[1] (numeric) = 4.967360364003541 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.36408688688903600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = 4.993123189988686 " " y[1] (numeric) = 4.993123189988683 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.336410013762174000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = 5.019033899070170 " " y[1] (numeric) = 5.019033899070168 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.308860853866736000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 5.04509339357172 " " y[1] (numeric) = 5.045093393571717 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.28143891745479400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3510000000000002 " " y[1] (analytic) = 5.071302581594355 " " y[1] (numeric) = 5.071302581594352 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.254143715997082000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3520000000000002 " " y[1] (analytic) = 5.097662377054844 " " y[1] (numeric) = 5.097662377054842 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.484649841456417500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3530000000000002 " " y[1] (analytic) = 5.12417369972442 " " y[1] (numeric) = 5.124173699724417 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 5.1999315699303400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3540000000000002 " " y[1] (analytic) = 5.150837475267752 " " y[1] (numeric) = 5.150837475267750 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.44867576958038550000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3550000000000002 " " y[1] (analytic) = 5.1776546352822095 " " y[1] (numeric) = 5.177654635282209 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.71540684395554500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3560000000000002 " " y[1] (analytic) = 5.204626117337368 " " y[1] (numeric) = 5.204626117337368 " " 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] = 0.3570000000000002 " " y[1] (analytic) = 5.2317528650148075 " " y[1] (numeric) = 5.231752865014806 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.39533782506988300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3580000000000002 " " y[1] (analytic) = 5.259035827948169 " " y[1] (numeric) = 5.259035827948168 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.68886170156907100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3590000000000002 " " y[1] (analytic) = 5.286475961863508 " " y[1] (numeric) = 5.286475961863507 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.680095447529545000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 5.314074228619905 " " y[1] (numeric) = 5.314074228619903 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.34273998250412150000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3610000000000002 " " y[1] (analytic) = 5.34183159625036 " " y[1] (numeric) = 5.341831596250360 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.662685173983343700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3620000000000002 " " y[1] (analytic) = 5.369749039002985 " " y[1] (numeric) = 5.3697490390029845 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.654040837381546300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3630000000000002 " " y[1] (analytic) = 5.397827537382455 " " y[1] (numeric) = 5.397827537382456 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.645436823516643300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3640000000000002 " " y[1] (analytic) = 5.426068078191772 " " y[1] (numeric) = 5.426068078191771 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.636872974870800500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3650000000000002 " " y[1] (analytic) = 5.454471654574283 " " y[1] (numeric) = 5.454471654574283 " " 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] = 0.3660000000000002 " " y[1] (analytic) = 5.483039266056028 " " y[1] (numeric) = 5.483039266056027 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.619865145228105400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3670000000000002 " " y[1] (analytic) = 5.5117719185883445 " " y[1] (numeric) = 5.511771918588343 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.22284170251951330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3680000000000002 " " y[1] (analytic) = 5.540670624590788 " " y[1] (numeric) = 5.5406706245907875 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.603016096568134200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3690000000000002 " " y[1] (analytic) = 5.569736402994343 " " y[1] (numeric) = 5.569736402994343 " " 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] = 0.3700000000000002 " " y[1] (analytic) = 5.598970279284926 " " y[1] (numeric) = 5.598970279284924 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.75897375086741400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3710000000000002 " " y[1] (analytic) = 5.6283732855471875 " " y[1] (numeric) = 5.6283732855471875 " " 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] = 0.3720000000000002 " " y[1] (analytic) = 5.657946460508643 " " y[1] (numeric) = 5.657946460508643 " " 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] = 0.3730000000000002 " " y[1] (analytic) = 5.687690849584065 " " y[1] (numeric) = 5.6876908495840635 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.12315997190697140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3740000000000002 " " y[1] (analytic) = 5.717607504920213 " " y[1] (numeric) = 5.717607504920213 " " 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] = 0.3750000000000002 " " y[1] (analytic) = 5.747697485440875 " " y[1] (numeric) = 5.747697485440872 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.63583072325873100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3760000000000002 " " y[1] (analytic) = 5.777961856892184 " " y[1] (numeric) = 5.777961856892182 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.61154871751534900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3770000000000002 " " y[1] (analytic) = 5.8084016918883 " " y[1] (numeric) = 5.808401691888298 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.587381177203225000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3780000000000002 " " y[1] (analytic) = 5.839018069957364 " " y[1] (numeric) = 5.839018069957362 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 3.042218431451474400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3790000000000002 " " y[1] (analytic) = 5.869812077587790 " " y[1] (numeric) = 5.869812077587788 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.513129224513647400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 5.9007848082748735 " " y[1] (numeric) = 5.900784808274873 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.505186934549116500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3810000000000002 " " y[1] (analytic) = 5.931937362567726 " " y[1] (numeric) = 5.931937362567724 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.99456439073275800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38200000000000023 " " y[1] (analytic) = 5.963270848116519 " " y[1] (numeric) = 5.963270848116518 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 1.48941485691640800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38300000000000023 " " y[1] (analytic) = 5.994786379720080 " " y[1] (numeric) = 5.994786379720079 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.96316953913409560000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38400000000000023 " " y[1] (analytic) = 6.026485079373796 " " y[1] (numeric) = 6.026485079373793 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.421375352309417000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38500000000000023 " " y[1] (analytic) = 6.0583680763178505 " " y[1] (numeric) = 6.058368076317849 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.93207150345325800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38600000000000023 " " y[1] (analytic) = 6.090436507085818 " " y[1] (numeric) = 6.0904365070858155 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.37494957217001770000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38700000000000023 " " y[1] (analytic) = 6.1226915155535595 " " y[1] (numeric) = 6.122691515553557 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.35190185938915800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38800000000000023 " " y[1] (analytic) = 6.155134252988482 " " y[1] (numeric) = 6.155134252988480 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.328963674198776000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38900000000000023 " " y[1] (analytic) = 6.187765878099134 " " y[1] (numeric) = 6.187765878099130 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 7.17689095868775400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 6.22058755708513 " " y[1] (numeric) = 6.2205875570851275 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.283414122297050700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39100000000000024 " " y[1] (analytic) = 6.253600463687455 " " y[1] (numeric) = 6.253600463687452 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.68106916876111400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39200000000000024 " " y[1] (analytic) = 6.286805779239072 " " y[1] (numeric) = 6.286805779239067 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 7.06382900067597300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39300000000000024 " " y[1] (analytic) = 6.320204692715914 " " y[1] (numeric) = 6.32020469271591 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 7.02650042904273200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39400000000000024 " " y[1] (analytic) = 6.353798400788223 " " y[1] (numeric) = 6.353798400788220 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.193610012508149000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39500000000000024 " " y[1] (analytic) = 6.387588107872241 " " y[1] (numeric) = 6.387588107872238 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.17142623178305500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39600000000000024 " " y[1] (analytic) = 6.421575026182249 " " y[1] (numeric) = 6.4215750261822455 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.53246464351076500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39700000000000024 " " y[1] (analytic) = 6.455760375782990 " " y[1] (numeric) = 6.455760375782985 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.87896055615603700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39800000000000024 " " y[1] (analytic) = 6.490145384642433 " " y[1] (numeric) = 6.49014538464243 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 4.10550935485272700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39900000000000024 " " y[1] (analytic) = 6.524731288684930 " " y[1] (numeric) = 6.524731288684926 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.444996156334518000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 6.559519331844706 " " y[1] (numeric) = 6.559519331844702 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.77014865546822400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40100000000000025 " " y[1] (analytic) = 6.594510766119752 " " y[1] (numeric) = 6.594510766119749 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.38738020878376400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40200000000000025 " " y[1] (analytic) = 6.6297068516260795 " " y[1] (numeric) = 6.629706851626076 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.358779442757896000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40300000000000025 " " y[1] (analytic) = 6.665108856652347 " " y[1] (numeric) = 6.665108856652345 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.99773704587126470000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40400000000000025 " " y[1] (analytic) = 6.700718057714878 " " y[1] (numeric) = 6.700718057714876 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.97649212539626300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40500000000000025 " " y[1] (analytic) = 6.73653573961305 " " y[1] (numeric) = 6.736535739613047 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.95534939929440400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40600000000000025 " " y[1] (analytic) = 6.772563195485073 " " y[1] (numeric) = 6.772563195485070 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.934308447467403400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40700000000000025 " " y[1] (analytic) = 6.808801726864162 " " y[1] (numeric) = 6.808801726864158 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.217825134756460000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40800000000000025 " " y[1] (analytic) = 6.845252643735082 " " y[1] (numeric) = 6.845252643735077 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.48755032082712700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40900000000000025 " " y[1] (analytic) = 6.881917264591107 " " y[1] (numeric) = 6.881917264591104 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.871792055405784400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 6.91879691649137 " " y[1] (numeric) = 6.918796916491367 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 5.13487203292872100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41100000000000025 " " y[1] (analytic) = 6.955892935118594 " " y[1] (numeric) = 6.955892935118591 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.83061568651781870000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41200000000000025 " " y[1] (analytic) = 6.993206664837249 " " y[1] (numeric) = 6.993206664837246 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.81017662826697900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41300000000000026 " " y[1] (analytic) = 7.030739458752100 " " y[1] (numeric) = 7.030739458752099 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.526557625725956400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41400000000000026 " " y[1] (analytic) = 7.06849267876717 " " y[1] (numeric) = 7.068492678767167 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.7695947073755800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41500000000000026 " " y[1] (analytic) = 7.1064676956450965 " " y[1] (numeric) = 7.106467695645092 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.24908504294199900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41600000000000026 " " y[1] (analytic) = 7.144665889066925 " " y[1] (numeric) = 7.144665889066921 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.97253998152246200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41700000000000026 " " y[1] (analytic) = 7.183088647692311 " " y[1] (numeric) = 7.183088647692306 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 7.41891236426938100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41800000000000026 " " y[1] (analytic) = 7.221737369220123 " " y[1] (numeric) = 7.221737369220118 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 7.37920841723470100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41900000000000026 " " y[1] (analytic) = 7.260613460449496 " " y[1] (numeric) = 7.260613460449492 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.89313154894291400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 7.299718337341295 " " y[1] (numeric) = 7.299718337341291 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.86691885168609300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42100000000000026 " " y[1] (analytic) = 7.339053425080002 " " y[1] (numeric) = 7.339053425079998 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.05104206398690400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42200000000000026 " " y[1] (analytic) = 7.378620158136045 " " y[1] (numeric) = 7.378620158136040 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 6.01859426739004800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42300000000000026 " " y[1] (analytic) = 7.418419980328562 " " y[1] (numeric) = 7.418419980328557 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 7.18356541195006100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42400000000000027 " " y[1] (analytic) = 7.458454344888593 " " y[1] (numeric) = 7.458454344888586 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 9.52667540623946200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42500000000000027 " " y[1] (analytic) = 7.498724714522711 " " y[1] (numeric) = 7.498724714522709 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.55331787809198400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42600000000000027 " " y[1] (analytic) = 7.539232561477135 " " y[1] (numeric) = 7.539232561477130 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 5.89037685505557200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42700000000000027 " " y[1] (analytic) = 7.5799793676022125 " " y[1] (numeric) = 7.579979367602209 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.68697011760381200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42800000000000027 " " y[1] (analytic) = 7.620966624417436 " " y[1] (numeric) = 7.620966624417433 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.49632191087578600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42900000000000027 " " y[1] (analytic) = 7.662195833176864 " " y[1] (numeric) = 7.662195833176859 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.95501737912542700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 7.703668504935000 " " y[1] (numeric) = 7.703668504934995 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 8.07050424602003800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43100000000000027 " " y[1] (analytic) = 7.745386160613159 " " y[1] (numeric) = 7.7453861606131555 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.58687740692228060000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4320000000000003 " " y[1] (analytic) = 7.787350331066277 " " y[1] (numeric) = 7.787350331066272 " " absolute error = 4.440892098500626000000000000000E-15 " " relative error = 5.70269977553785100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4330000000000003 " " y[1] (analytic) = 7.8295625571501795 " " y[1] (numeric) = 7.829562557150174 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.80634515568700800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4340000000000003 " " y[1] (analytic) = 7.872024389789340 " " y[1] (numeric) = 7.8720243897893365 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 3.384815807426227500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4350000000000003 " " y[1] (analytic) = 7.914737390045109 " " y[1] (numeric) = 7.914737390045105 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.48873222662950900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4360000000000003 " " y[1] (analytic) = 7.957703129184402 " " y[1] (numeric) = 7.957703129184397 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.69674456522096600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4370000000000003 " " y[1] (analytic) = 8.000923188748882 " " y[1] (numeric) = 8.000923188748876 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.66056952739483500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4380000000000003 " " y[1] (analytic) = 8.044399160624632 " " y[1] (numeric) = 8.044399160624625 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.83276328750608600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4390000000000003 " " y[1] (analytic) = 8.08813264711229 " " y[1] (numeric) = 8.088132647112289 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.196250873845972000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 8.132125260997725 " " y[1] (numeric) = 8.132125260997718 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.73747898557239100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4410000000000003 " " y[1] (analytic) = 8.176378625623112 " " y[1] (numeric) = 8.176378625623109 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.34509437670488600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4420000000000003 " " y[1] (analytic) = 8.220894374958633 " " y[1] (numeric) = 8.220894374958629 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.32156589874490200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4430000000000003 " " y[1] (analytic) = 8.265674153674565 " " y[1] (numeric) = 8.265674153674562 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.29815355982925640000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4440000000000003 " " y[1] (analytic) = 8.31071961721394 " " y[1] (numeric) = 8.310719617213937 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.13742843125268500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4450000000000003 " " y[1] (analytic) = 8.35603243186569 " " y[1] (numeric) = 8.356032431865685 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.37751296641497700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4460000000000003 " " y[1] (analytic) = 8.401614274838296 " " y[1] (numeric) = 8.401614274838295 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.114304205467037500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4470000000000003 " " y[1] (analytic) = 8.447466834333992 " " y[1] (numeric) = 8.447466834333987 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.30848350483154200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4480000000000003 " " y[1] (analytic) = 8.493591809623425 " " y[1] (numeric) = 8.49359180962342 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.27422489524725900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4490000000000003 " " y[1] (analytic) = 8.539990911120896 " " y[1] (numeric) = 8.539990911120894 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.080045351204125600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 8.586665860460114 " " y[1] (numeric) = 8.58666586046011 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.13747749887420200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4510000000000003 " " y[1] (analytic) = 8.633618390570447 " " y[1] (numeric) = 8.633618390570444 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.11497650009727100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4520000000000003 " " y[1] (analytic) = 8.680850245753755 " " y[1] (numeric) = 8.680850245753753 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 2.04629361077753500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4530000000000003 " " y[1] (analytic) = 8.728363181761736 " " y[1] (numeric) = 8.72836318176173 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.10546377049944200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4540000000000003 " " y[1] (analytic) = 8.776158965873801 " " y[1] (numeric) = 8.776158965873798 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 4.04814189512208100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4550000000000003 " " y[1] (analytic) = 8.82423937697555 " " y[1] (numeric) = 8.824239376975543 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 8.05216977243464200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4560000000000003 " " y[1] (analytic) = 8.872606205637716 " " y[1] (numeric) = 8.87260620563771 " " absolute error = 5.329070518200751000000000000000E-15 " " relative error = 6.00620651327298100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = expt( 2.0 * x + 1.0 , 3.0 * x + 2.0 ) * ( 3.0 * ln( 2.0 * x + 1.0 )+ ( 2.0 * ( 3.0 * x + 2.0 ) ) / ( 2.0 * x + 1.0) ) ;" Iterations = 357 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 33 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 4 Minutes 32 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 7 Minutes 33 Seconds "Time to Timeout " Unknown Percent Done = 39.777777777777814 "%" (%o58) true (%o58) diffeq.max