(%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_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4 : exp(array_tmp3 ), array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4 : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp5 : array_tmp4 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp5 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, array_tmp3 : 0.0, 2, 2 3 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 3 2.0 array_tmp4 : att(2, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 4 4 2.0 array_tmp4 : att(3, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 5 5 2.0 array_tmp4 : att(4, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4 : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4 : exp(array_tmp3 ), array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4 : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp5 : array_tmp4 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp5 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, array_tmp3 : 0.0, 2, 2 3 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : -----------------------------------, 3 2.0 array_tmp4 : att(2, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 4 4 2.0 array_tmp4 : att(3, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 5 5 2.0 array_tmp4 : att(4, array_tmp4, array_tmp3, 1), array_tmp5 : array_tmp4 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4 : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole_debug(typ, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%o27) display_pole_debug(typ, radius, order2) := (if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex"), omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "), omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ")) (%i28) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o28) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o29) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o30) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o31) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o32) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i33) log_revs(file, revs) := printf(file, revs) (%o33) log_revs(file, revs) := printf(file, revs) (%i34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o34) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o35) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i36) logstart(file) := printf(file, "") (%o36) logstart(file) := printf(file, "") (%i37) logend(file) := printf(file, "~%") (%o37) logend(file) := printf(file, "~%") (%i38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o38) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o39) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o40) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i41) factorial_2(nnn) := nnn! (%o41) factorial_2(nnn) := nnn! (%i42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o42) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o43) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i44) convfp(mmm) := mmm (%o44) convfp(mmm) := mmm (%i45) convfloat(mmm) := mmm (%o45) convfloat(mmm) := mmm (%i46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o46) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i47) Si(x) := 0.0 (%o47) Si(x) := 0.0 (%i48) Ci(x) := 0.0 (%o48) Ci(x) := 0.0 (%i49) ln(x) := log(x) (%o49) ln(x) := log(x) (%i50) arcsin(x) := asin(x) (%o50) arcsin(x) := asin(x) (%i51) arccos(x) := acos(x) (%o51) arccos(x) := acos(x) (%i52) arctan(x) := atan(x) (%o52) arctan(x) := atan(x) (%i53) omniabs(x) := abs(x) (%o53) omniabs(x) := abs(x) (%i54) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o54) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o55) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i56) exact_soln_y(x) := block(20.0 exp(sqrt(0.2 + 0.1 x)) sqrt(0.2 + 0.1 x) - 20.0 exp(sqrt(0.2 + 0.1 x))) (%o56) exact_soln_y(x) := block(20.0 exp(sqrt(0.2 + 0.1 x)) sqrt(0.2 + 0.1 x) - 20.0 exp(sqrt(0.2 + 0.1 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/exp_sqrtpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (20.\ 0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x \ + 0.2))) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T13:49:08-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "exp_sqrt"), logitem_str(html_log_file, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "exp_sqrt diffeq.max"), logitem_str(html_log_file, "exp_sqrt 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/exp_sqrtpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.0,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (20.\ 0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x \ + 0.2))) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T13:49:08-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "exp_sqrt"), logitem_str(html_log_file, "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "exp_sqrt diffeq.max"), logitem_str(html_log_file, "exp_sqrt 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/exp_sqrtpostode.ode#################" "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.0," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (20.0 * exp(sqrt(0.1 * x + 0.2)) * sqrt( 0.1 * x + 0.2) - 20.0 * exp(sqrt(0.1 * x + 0.2))) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 5. "" estimated_steps = 5000. "" step_error = 2.00000000000000E-14 "" est_needed_step_err = 2.00000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.1718092041239421000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" max_value3 = 1.1718092041239421000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" value3 = 1.1718092041239421000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-90 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.0 " " y[1] (analytic) = -17.290587327796203 " " y[1] (numeric) = -17.290587327796203 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.000E-3 " " y[1] (analytic) = -17.28902329205693 " " y[1] (numeric) = -17.289023292056925 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.054895536194181200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.000E-3 " " y[1] (analytic) = -17.287459081487064 " " y[1] (numeric) = -17.28745908148706 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.055081468048164400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.000E-3 " " y[1] (analytic) = -17.285894696110752 " " y[1] (numeric) = -17.28589469611075 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.05526745433653820000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.000E-3 " " y[1] (analytic) = -17.2843301359521 " " y[1] (numeric) = -17.284330135952096 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.05545349507685830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.000E-3 " " y[1] (analytic) = -17.282765401035206 " " y[1] (numeric) = -17.282765401035203 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.055639590286690900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.000E-3 " " y[1] (analytic) = -17.28120049138414 " " y[1] (numeric) = -17.281200491384137 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.055825739983615000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.000E-3 " " y[1] (analytic) = -17.27963540702296 " " y[1] (numeric) = -17.279635407022955 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.056011944185218200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.000E-3 " " y[1] (analytic) = -17.27807014797569 " " y[1] (numeric) = -17.278070147975686 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.056198202909101700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.000000000000001000E-3 " " y[1] (analytic) = -17.27650471426635 " " y[1] (numeric) = -17.276504714266345 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.056384516172875500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.000000000000000200E-2 " " y[1] (analytic) = -17.274939105918932 " " y[1] (numeric) = -17.274939105918925 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.11314176798832300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.100000000000000300E-2 " " y[1] (analytic) = -17.273373322957404 " " y[1] (numeric) = -17.273373322957397 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.113514612781187000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.200000000000000400E-2 " " y[1] (analytic) = -17.27180736540572 " " y[1] (numeric) = -17.271807365405717 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.056943783379815700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.300000000000000600E-2 " " y[1] (analytic) = -17.27024123328782 " " y[1] (numeric) = -17.270241233287813 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.11426062995896350000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.400000000000000700E-2 " " y[1] (analytic) = -17.268674926627604 " " y[1] (numeric) = -17.2686749266276 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.0573169012072600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.500000000000000800E-2 " " y[1] (analytic) = -17.267108445448976 " " y[1] (numeric) = -17.267108445448972 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.057503542080825800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.600000000000001000E-2 " " y[1] (analytic) = -17.265541789775803 " " y[1] (numeric) = -17.2655417897758 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.057690237617868200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.700000000000001000E-2 " " y[1] (analytic) = -17.263974959631938 " " y[1] (numeric) = -17.263974959631934 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.057876987836087200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.80000000000000100E-2 " " y[1] (analytic) = -17.262407955041212 " " y[1] (numeric) = -17.26240795504121 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.05806379275319300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 1.90000000000000100E-2 " " y[1] (analytic) = -17.26084077602744 " " y[1] (numeric) = -17.260840776027436 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.058250652386907400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.00000000000000120E-2 " " y[1] (analytic) = -17.259273422614413 " " y[1] (numeric) = -17.25927342261441 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.058437566754962600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.10000000000000130E-2 " " y[1] (analytic) = -17.25770589482591 " " y[1] (numeric) = -17.257705894825904 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.117249071750204700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.200000000000001400E-2 " " y[1] (analytic) = -17.25613819268568 " " y[1] (numeric) = -17.256138192685672 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.117623119530164400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.300000000000001500E-2 " " y[1] (analytic) = -17.254570316217453 " " y[1] (numeric) = -17.254570316217446 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.117997276885335000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.400000000000001600E-2 " " y[1] (analytic) = -17.253002265444948 " " y[1] (numeric) = -17.25300226544494 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.118371543851272500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.500000000000001700E-2 " " y[1] (analytic) = -17.251434040391857 " " y[1] (numeric) = -17.25143404039185 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.118745920463552400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.600000000000002000E-2 " " y[1] (analytic) = -17.249865641081854 " " y[1] (numeric) = -17.249865641081847 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.11912040675777300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.700000000000002000E-2 " " y[1] (analytic) = -17.248297067538598 " " y[1] (numeric) = -17.248297067538587 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.17924250415433200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.800000000000002000E-2 " " y[1] (analytic) = -17.246728319785717 " " y[1] (numeric) = -17.246728319785706 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.17980456280181300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 2.90000000000000200E-2 " " y[1] (analytic) = -17.245159397846834 " " y[1] (numeric) = -17.24515939784682 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.24048904817679900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.00000000000000200E-2 " " y[1] (analytic) = -17.243590301745535 " " y[1] (numeric) = -17.243590301745524 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.18092917420022500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.10000000000000200E-2 " " y[1] (analytic) = -17.242021031505406 " " y[1] (numeric) = -17.242021031505395 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.1814917270582500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.20000000000000230E-2 " " y[1] (analytic) = -17.240451587149998 " " y[1] (numeric) = -17.240451587149987 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.18205444476027800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.30000000000000240E-2 " " y[1] (analytic) = -17.23888196870285 " " y[1] (numeric) = -17.23888196870284 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.12174488490662500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.40000000000000250E-2 " " y[1] (analytic) = -17.23731217618748 " " y[1] (numeric) = -17.237312176187473 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.122120249940596000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.500000000000002600E-2 " " y[1] (analytic) = -17.23574220962739 " " y[1] (numeric) = -17.23574220962738 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.18374358746684700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.600000000000002600E-2 " " y[1] (analytic) = -17.234172069046046 " " y[1] (numeric) = -17.23417206904604 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.12287131005435300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.700000000000003000E-2 " " y[1] (analytic) = -17.23260175446692 " " y[1] (numeric) = -17.232601754466913 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.123247005205804600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.80000000000000300E-2 " " y[1] (analytic) = -17.231031265913444 " " y[1] (numeric) = -17.23103126591344 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.061811405234059400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 3.90000000000000300E-2 " " y[1] (analytic) = -17.229460603409045 " " y[1] (numeric) = -17.22946060340904 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.061999362938591300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.00000000000000300E-2 " " y[1] (analytic) = -17.22788976697712 " " y[1] (numeric) = -17.227889766977114 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.12437475146890900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.10000000000000300E-2 " " y[1] (analytic) = -17.22631875664105 " " y[1] (numeric) = -17.226318756641046 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.062375443639615200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.20000000000000300E-2 " " y[1] (analytic) = -17.2247475724242 " " y[1] (numeric) = -17.224747572424196 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06256356667205100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.30000000000000300E-2 " " y[1] (analytic) = -17.223176214349905 " " y[1] (numeric) = -17.223176214349905 " " 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] = 4.40000000000000340E-2 " " y[1] (analytic) = -17.221604682441505 " " y[1] (numeric) = -17.2216046824415 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06293997819071600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.50000000000000340E-2 " " y[1] (analytic) = -17.220032976722294 " " y[1] (numeric) = -17.22003297672229 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06312826671295600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.600000000000003500E-2 " " y[1] (analytic) = -17.21846109721556 " " y[1] (numeric) = -17.218461097215553 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.126633220868988000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.700000000000003600E-2 " " y[1] (analytic) = -17.216889043944562 " " y[1] (numeric) = -17.21688904394456 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06350500937336500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.800000000000003700E-2 " " y[1] (analytic) = -17.215316816932557 " " y[1] (numeric) = -17.215316816932553 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.063693463547612600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 4.90000000000000400E-2 " " y[1] (analytic) = -17.213744416202765 " " y[1] (numeric) = -17.213744416202765 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.00000000000000300E-2 " " y[1] (analytic) = -17.2121718417784 " " y[1] (numeric) = -17.2121718417784 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.10000000000000300E-2 " " y[1] (analytic) = -17.210599093682653 " " y[1] (numeric) = -17.21059909368265 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06425915766323600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.20000000000000400E-2 " " y[1] (analytic) = -17.209026171938685 " " y[1] (numeric) = -17.209026171938685 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.30000000000000400E-2 " " y[1] (analytic) = -17.20745307656966 " " y[1] (numeric) = -17.20745307656966 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.40000000000000400E-2 " " y[1] (analytic) = -17.2058798075987 " " y[1] (numeric) = -17.205879807598702 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.064825349547950700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.50000000000000400E-2 " " y[1] (analytic) = -17.20430636504893 " " y[1] (numeric) = -17.20430636504893 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.60000000000000400E-2 " " y[1] (analytic) = -17.202732748943433 " " y[1] (numeric) = -17.202732748943433 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.700000000000004000E-2 " " y[1] (analytic) = -17.20115895930529 " " y[1] (numeric) = -17.20115895930529 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.800000000000004000E-2 " " y[1] (analytic) = -17.199584996157554 " " y[1] (numeric) = -17.199584996157554 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 5.900000000000004000E-2 " " y[1] (analytic) = -17.198010859523265 " " y[1] (numeric) = -17.19801085952327 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.065770110171324700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.000000000000004000E-2 " " y[1] (analytic) = -17.196436549425442 " " y[1] (numeric) = -17.196436549425446 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.065959228581692500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.10000000000000400E-2 " " y[1] (analytic) = -17.194862065887087 " " y[1] (numeric) = -17.19486206588709 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.066148402463044400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.20000000000000400E-2 " " y[1] (analytic) = -17.193287408931177 " " y[1] (numeric) = -17.19328740893118 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06633763183358300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 6.30000000000000400E-2 " " y[1] (analytic) = -17.19171257858068 " " y[1] (numeric) = -17.19171257858068 " " 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] = 6.40000000000000500E-2 " " y[1] (analytic) = -17.190137574858532 " " y[1] (numeric) = -17.190137574858532 " " 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] = 6.50000000000000500E-2 " " y[1] (analytic) = -17.188562397787663 " " y[1] (numeric) = -17.188562397787663 " " 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] = 6.60000000000000500E-2 " " y[1] (analytic) = -17.186987047390975 " " y[1] (numeric) = -17.186987047390975 " " 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] = 6.70000000000000500E-2 " " y[1] (analytic) = -17.185411523691357 " " y[1] (numeric) = -17.185411523691357 " " 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] = 6.80000000000000500E-2 " " y[1] (analytic) = -17.18383582671168 " " y[1] (numeric) = -17.18383582671168 " " 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] = 6.90000000000000500E-2 " " y[1] (analytic) = -17.18225995647479 " " y[1] (numeric) = -17.182259956474788 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06766379265594320000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.00000000000000500E-2 " " y[1] (analytic) = -17.18068391300352 " " y[1] (numeric) = -17.180683913003516 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06785346659661420000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.10000000000000500E-2 " " y[1] (analytic) = -17.17910769632068 " " y[1] (numeric) = -17.179107696320678 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06804319619080100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.20000000000000500E-2 " " y[1] (analytic) = -17.17753130644907 " " y[1] (numeric) = -17.177531306449065 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06823298145681900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.30000000000000500E-2 " " y[1] (analytic) = -17.17595474341146 " " y[1] (numeric) = -17.175954743411452 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.13684564482599100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.40000000000000500E-2 " " y[1] (analytic) = -17.1743780072306 " " y[1] (numeric) = -17.174378007230597 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.06861271907766900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.50000000000000600E-2 " " y[1] (analytic) = -17.172801097929245 " " y[1] (numeric) = -17.172801097929238 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.13760534293837360000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.60000000000000600E-2 " " y[1] (analytic) = -17.171224015530104 " " y[1] (numeric) = -17.171224015530097 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.13798535921182300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.70000000000000600E-2 " " y[1] (analytic) = -17.169646760055876 " " y[1] (numeric) = -17.169646760055873 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.069182743506215000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.80000000000000600E-2 " " y[1] (analytic) = -17.168069331529253 " " y[1] (numeric) = -17.168069331529246 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.13874572637695840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 7.90000000000000600E-2 " " y[1] (analytic) = -17.16649172997289 " " y[1] (numeric) = -17.166491729972883 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.13912607734220060000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.00000000000000600E-2 " " y[1] (analytic) = -17.164913955409432 " " y[1] (numeric) = -17.16491395540943 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.069753269972484700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.10000000000000600E-2 " " y[1] (analytic) = -17.163336007861517 " " y[1] (numeric) = -17.16333600786151 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.13988711422209670000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.20000000000000600E-2 " " y[1] (analytic) = -17.161757887351744 " " y[1] (numeric) = -17.161757887351737 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.140267800210442600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.30000000000000600E-2 " " y[1] (analytic) = -17.16017959390271 " " y[1] (numeric) = -17.1601795939027 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.21097289692032800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.40000000000000600E-2 " " y[1] (analytic) = -17.158601127536983 " " y[1] (numeric) = -17.158601127536972 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.21154426120249600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.50000000000000600E-2 " " y[1] (analytic) = -17.157022488277114 " " y[1] (numeric) = -17.157022488277107 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14141052881170400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.60000000000000700E-2 " " y[1] (analytic) = -17.155443676145648 " " y[1] (numeric) = -17.15544367614564 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.141791662013951700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.70000000000000700E-2 " " y[1] (analytic) = -17.153864691165097 " " y[1] (numeric) = -17.15386469116509 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14217290711204670000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.80000000000000700E-2 " " y[1] (analytic) = -17.15228553335796 " " y[1] (numeric) = -17.15228553335795 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.21383139621447400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 8.90000000000000700E-2 " " y[1] (analytic) = -17.15070620274672 " " y[1] (numeric) = -17.150706202746708 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.21440359971566800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.00000000000000700E-2 " " y[1] (analytic) = -17.149126699353832 " " y[1] (numeric) = -17.149126699353822 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.21497597122720800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.10000000000000700E-2 " " y[1] (analytic) = -17.147547023201746 " " y[1] (numeric) = -17.14754702320174 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14369900720312770000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.20000000000000700E-2 " " y[1] (analytic) = -17.14596717431289 " " y[1] (numeric) = -17.145967174312883 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14408081233582900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.30000000000000700E-2 " " y[1] (analytic) = -17.144387152709673 " " y[1] (numeric) = -17.144387152709665 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14446272958668500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.40000000000000700E-2 " " y[1] (analytic) = -17.14280695841448 " " y[1] (numeric) = -17.14280695841447 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14484475899282700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.50000000000000700E-2 " " y[1] (analytic) = -17.141226591449684 " " y[1] (numeric) = -17.141226591449676 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.145226900591409400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.60000000000000700E-2 " " y[1] (analytic) = -17.139646051837644 " " y[1] (numeric) = -17.139646051837634 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.21841373162941100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.70000000000000800E-2 " " y[1] (analytic) = -17.138065339600686 " " y[1] (numeric) = -17.13806533960068 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.145991520514623600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.80000000000000800E-2 " " y[1] (analytic) = -17.13648445476114 " " y[1] (numeric) = -17.13648445476113 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14637399891367830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 9.90000000000000800E-2 " " y[1] (analytic) = -17.134903397341297 " " y[1] (numeric) = -17.134903397341287 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.22013488448102600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10000000000000007 " " y[1] (analytic) = -17.13332216736344 " " y[1] (numeric) = -17.13332216736343 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14713929277290900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10100000000000008 " " y[1] (analytic) = -17.13174076484983 " " y[1] (numeric) = -17.131740764849823 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14752210830764630000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000008 " " y[1] (analytic) = -17.13015918982272 " " y[1] (numeric) = -17.130159189822713 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14790503629554160000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000008 " " y[1] (analytic) = -17.128577442304334 " " y[1] (numeric) = -17.128577442304326 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.148288076773933300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000008 " " y[1] (analytic) = -17.126995522316882 " " y[1] (numeric) = -17.126995522316875 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.1486712297801803000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000008 " " y[1] (analytic) = -17.12541342988256 " " y[1] (numeric) = -17.12541342988255 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.22358174302749800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000008 " " y[1] (analytic) = -17.12383116502353 " " y[1] (numeric) = -17.123831165023525 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14943787352579750000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000008 " " y[1] (analytic) = -17.122248727761963 " " y[1] (numeric) = -17.122248727761956 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.14982136434000200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000008 " " y[1] (analytic) = -17.120666118119992 " " y[1] (numeric) = -17.120666118119985 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.150204967831732600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000008 " " y[1] (analytic) = -17.119083336119736 " " y[1] (numeric) = -17.11908333611973 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.15058868403846400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000008 " " y[1] (analytic) = -17.1175003817833 " " y[1] (numeric) = -17.11750038178329 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.22645876949654100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000008 " " y[1] (analytic) = -17.115917255132764 " " y[1] (numeric) = -17.115917255132757 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.15135645474694500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000009 " " y[1] (analytic) = -17.1143339561902 " " y[1] (numeric) = -17.114333956190194 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.151740509323759000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000009 " " y[1] (analytic) = -17.112750484977663 " " y[1] (numeric) = -17.112750484977653 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.22818701514855500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000009 " " y[1] (analytic) = -17.111166841517175 " " y[1] (numeric) = -17.111166841517164 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.22876343566555400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000009 " " y[1] (analytic) = -17.109583025830755 " " y[1] (numeric) = -17.109583025830744 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.22934002559305300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000009 " " y[1] (analytic) = -17.107999037940402 " " y[1] (numeric) = -17.107999037940388 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.30655571331667600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000009 " " y[1] (analytic) = -17.10641487786809 " " y[1] (numeric) = -17.106414877868076 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.30732495187387300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000009 " " y[1] (analytic) = -17.104830545635785 " " y[1] (numeric) = -17.10483054563577 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.30809441653769100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000009 " " y[1] (analytic) = -17.10324604126543 " " y[1] (numeric) = -17.103246041265415 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.30886410738354500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000009 " " y[1] (analytic) = -17.10166136477895 " " y[1] (numeric) = -17.101661364778934 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.3096340244868890000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1210000000000001 " " y[1] (analytic) = -17.10007651619825 " " y[1] (numeric) = -17.100076516198236 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31040416792322800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1220000000000001 " " y[1] (analytic) = -17.098491495545233 " " y[1] (numeric) = -17.098491495545215 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.03889681722101320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1230000000000001 " " y[1] (analytic) = -17.09690630284176 " " y[1] (numeric) = -17.09690630284174 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.03899314176214080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1240000000000001 " " y[1] (analytic) = -17.095320938109687 " " y[1] (numeric) = -17.095320938109673 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31271595698592800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000008 " " y[1] (analytic) = -17.093735401370864 " " y[1] (numeric) = -17.09373540137085 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31348700651019600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000008 " " y[1] (analytic) = -17.092149692647112 " " y[1] (numeric) = -17.092149692647094 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.03928228534320820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000009 " " y[1] (analytic) = -17.090563811960223 " " y[1] (numeric) = -17.090563811960205 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.03937872322101530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000009 " " y[1] (analytic) = -17.08897775933199 " " y[1] (numeric) = -17.088977759331975 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.3158015156533900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1290000000000001 " " y[1] (analytic) = -17.08739153478418 " " y[1] (numeric) = -17.087391534784167 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31657347247734300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1300000000000001 " " y[1] (analytic) = -17.085805138338557 " " y[1] (numeric) = -17.08580513833854 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.03966820703948720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1310000000000001 " " y[1] (analytic) = -17.084218570016837 " " y[1] (numeric) = -17.084218570016823 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31811806724502600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1320000000000001 " " y[1] (analytic) = -17.08263182984075 " " y[1] (numeric) = -17.082631829840736 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31889070534073700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1330000000000001 " " y[1] (analytic) = -17.08104491783199 " " y[1] (numeric) = -17.081044917831974 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.31966357067909100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1340000000000001 " " y[1] (analytic) = -17.07945783401224 " " y[1] (numeric) = -17.079457834012224 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.32043666333619600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1350000000000001 " " y[1] (analytic) = -17.077870578403164 " " y[1] (numeric) = -17.077870578403154 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2409074875411510000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1360000000000001 " " y[1] (analytic) = -17.07628315102642 " " y[1] (numeric) = -17.076283151026406 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.32198353091130300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1370000000000001 " " y[1] (analytic) = -17.074695551903623 " " y[1] (numeric) = -17.074695551903613 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.24206797948631500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1380000000000001 " " y[1] (analytic) = -17.073107781056407 " " y[1] (numeric) = -17.07310778105639 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.04044141358447960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1390000000000001 " " y[1] (analytic) = -17.071519838506347 " " y[1] (numeric) = -17.071519838506333 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.32430553906989800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1400000000000001 " " y[1] (analytic) = -17.069931724275037 " " y[1] (numeric) = -17.069931724275023 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.32507999724031800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1410000000000001 " " y[1] (analytic) = -17.06834343838403 " " y[1] (numeric) = -17.06834343838402 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.24439101244764900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1420000000000001 " " y[1] (analytic) = -17.066754980854878 " " y[1] (numeric) = -17.066754980854867 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2449721979120100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1430000000000001 " " y[1] (analytic) = -17.065166351709106 " " y[1] (numeric) = -17.065166351709095 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.24555355438071800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1440000000000001 " " y[1] (analytic) = -17.063577550968226 " " y[1] (numeric) = -17.063577550968215 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.246135081911199000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1450000000000001 " " y[1] (analytic) = -17.061988578653732 " " y[1] (numeric) = -17.06198857865372 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2467167805609200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1460000000000001 " " y[1] (analytic) = -17.060399434787097 " " y[1] (numeric) = -17.06039943478709 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16486576692491900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1470000000000001 " " y[1] (analytic) = -17.058810119389786 " " y[1] (numeric) = -17.05881011938978 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.165253794298738300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1480000000000001 " " y[1] (analytic) = -17.05722063248324 " " y[1] (numeric) = -17.057220632483233 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16564193586711700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1490000000000001 " " y[1] (analytic) = -17.055630974088885 " " y[1] (numeric) = -17.055630974088878 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.166030191668459000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1500000000000001 " " y[1] (analytic) = -17.05404114422813 " " y[1] (numeric) = -17.054041144228123 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16641856174118900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1510000000000001 " " y[1] (analytic) = -17.052451142922365 " " y[1] (numeric) = -17.052451142922358 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16680704612375700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1520000000000001 " " y[1] (analytic) = -17.05086097019297 " " y[1] (numeric) = -17.05086097019296 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25079346728195100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1530000000000001 " " y[1] (analytic) = -17.049270626061297 " " y[1] (numeric) = -17.04927062606129 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16758435797232100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1540000000000001 " " y[1] (analytic) = -17.04768011054869 " " y[1] (numeric) = -17.047680110548683 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16797318551533400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1550000000000001 " " y[1] (analytic) = -17.046089423676477 " " y[1] (numeric) = -17.046089423676467 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25254319128332300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1560000000000001 " " y[1] (analytic) = -17.04449856546596 " " y[1] (numeric) = -17.04449856546595 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25312677604730200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1570000000000001 " " y[1] (analytic) = -17.042907535938433 " " y[1] (numeric) = -17.042907535938422 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25371053262282200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1580000000000001 " " y[1] (analytic) = -17.04131633511517 " " y[1] (numeric) = -17.04131633511516 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25429446106780100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1590000000000001 " " y[1] (analytic) = -17.039724963017424 " " y[1] (numeric) = -17.039724963017417 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.16991904096013100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000011 " " y[1] (analytic) = -17.038133419666444 " " y[1] (numeric) = -17.038133419666433 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25546283379799800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000012 " " y[1] (analytic) = -17.036541705083444 " " y[1] (numeric) = -17.036541705083437 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17069818546615700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000012 " " y[1] (analytic) = -17.03494981928964 " " y[1] (numeric) = -17.034949819289633 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.171087929801309000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000012 " " y[1] (analytic) = -17.033357762306217 " " y[1] (numeric) = -17.03335776230621 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17147778890952450000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000012 " " y[1] (analytic) = -17.03176553415435 " " y[1] (numeric) = -17.031765534154342 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17186776282955500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000012 " " y[1] (analytic) = -17.030173134855193 " " y[1] (numeric) = -17.030173134855186 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.172257851600179600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000012 " " y[1] (analytic) = -17.028580564429895 " " y[1] (numeric) = -17.028580564429884 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.25897208289029800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000012 " " y[1] (analytic) = -17.02698782289957 " " y[1] (numeric) = -17.02698782289956 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2595575607726610000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000012 " " y[1] (analytic) = -17.02539491028533 " " y[1] (numeric) = -17.02539491028532 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.173428807403752300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000012 " " y[1] (analytic) = -17.023801826608263 " " y[1] (numeric) = -17.023801826608256 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17381935596500700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000012 " " y[1] (analytic) = -17.02220857188945 " " y[1] (numeric) = -17.02220857188944 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.26131502935665100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000012 " " y[1] (analytic) = -17.02061514614994 " " y[1] (numeric) = -17.02061514614993 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.2619011973914310000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000013 " " y[1] (analytic) = -17.019021549410773 " " y[1] (numeric) = -17.019021549410766 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.1749916920735100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000013 " " y[1] (analytic) = -17.017427781692987 " " y[1] (numeric) = -17.017427781692977 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.26307405157160100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000013 " " y[1] (analytic) = -17.015833843017575 " " y[1] (numeric) = -17.015833843017568 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.1757738252226200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000013 " " y[1] (analytic) = -17.014239733405535 " " y[1] (numeric) = -17.014239733405528 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17616506463718060000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000013 " " y[1] (analytic) = -17.012645452877845 " " y[1] (numeric) = -17.012645452877837 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17655641933045400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000013 " " y[1] (analytic) = -17.011051001455456 " " y[1] (numeric) = -17.01105100145545 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17694788934150240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000013 " " y[1] (analytic) = -17.009456379159317 " " y[1] (numeric) = -17.00945637915931 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.177339474709410600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000013 " " y[1] (analytic) = -17.00786158601035 " " y[1] (numeric) = -17.007861586010343 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.177731175473289300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000013 " " y[1] (analytic) = -17.006266622029468 " " y[1] (numeric) = -17.006266622029457 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.26718448750840400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000013 " " y[1] (analytic) = -17.004671487237562 " " y[1] (numeric) = -17.004671487237548 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.35702984669101800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000013 " " y[1] (analytic) = -17.003076181655505 " " y[1] (numeric) = -17.003076181655494 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.26836045579828200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000013 " " y[1] (analytic) = -17.001480705304164 " " y[1] (numeric) = -17.001480705304154 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.26894869990726700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000014 " " y[1] (analytic) = -16.999885058204377 " " y[1] (numeric) = -16.99988505820437 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.17969141160270730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000014 " " y[1] (analytic) = -16.99828924037698 " " y[1] (numeric) = -16.998289240376973 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.180083805565024700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000014 " " y[1] (analytic) = -16.99669325184278 " " y[1] (numeric) = -16.99669325184277 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.180476315197741400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000014 " " y[1] (analytic) = -16.995097092622572 " " y[1] (numeric) = -16.99509709262256 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.27130341081023400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000014 " " y[1] (analytic) = -16.993500762737135 " " y[1] (numeric) = -16.993500762737124 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.27189252244738900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000014 " " y[1] (analytic) = -16.991904262207235 " " y[1] (numeric) = -16.99190426220722 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.36330907702279100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000014 " " y[1] (analytic) = -16.990307591053615 " " y[1] (numeric) = -16.9903075910536 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.36409502243787700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19100000000000014 " " y[1] (analytic) = -16.988710749297006 " " y[1] (numeric) = -16.98871074929699 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.36488119958723200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19200000000000014 " " y[1] (analytic) = -16.987113736958126 " " y[1] (numeric) = -16.98711373695811 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.36566760854968800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19300000000000014 " " y[1] (analytic) = -16.98551655405767 " " y[1] (numeric) = -16.985516554057657 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.36645424940413200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19400000000000014 " " y[1] (analytic) = -16.983919200616327 " " y[1] (numeric) = -16.98391920061631 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.0459051402786870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19500000000000015 " " y[1] (analytic) = -16.982321676654756 " " y[1] (numeric) = -16.98232167665474 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.0460035283880950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19600000000000015 " " y[1] (analytic) = -16.980723982193606 " " y[1] (numeric) = -16.98072398219359 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.36881556410895500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19700000000000015 " " y[1] (analytic) = -16.979126117253514 " " y[1] (numeric) = -16.979126117253504 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.27720234999086500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19800000000000015 " " y[1] (analytic) = -16.977528081855105 " " y[1] (numeric) = -16.97752808185509 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37039093482047600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19900000000000015 " " y[1] (analytic) = -16.97592987601897 " " y[1] (numeric) = -16.975929876018956 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.371178968686100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20000000000000015 " " y[1] (analytic) = -16.9743314997657 " " y[1] (numeric) = -16.974331499765686 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37196723499724200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20100000000000015 " " y[1] (analytic) = -16.972732953115866 " " y[1] (numeric) = -16.97273295311585 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37275573383316900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20200000000000015 " " y[1] (analytic) = -16.971134236090023 " " y[1] (numeric) = -16.971134236090005 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.04669305815914940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20300000000000015 " " y[1] (analytic) = -16.969535348708707 " " y[1] (numeric) = -16.96953534870869 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.04679167867458540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20400000000000015 " " y[1] (analytic) = -16.967936290992437 " " y[1] (numeric) = -16.967936290992423 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.3751226262830490000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20500000000000015 " " y[1] (analytic) = -16.966337062961728 " " y[1] (numeric) = -16.966337062961713 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37591205601174500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20600000000000016 " " y[1] (analytic) = -16.964737664637063 " " y[1] (numeric) = -16.96473766463705 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37670171866228300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20700000000000016 " " y[1] (analytic) = -16.963138096038918 " " y[1] (numeric) = -16.963138096038907 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.28311871073566100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20800000000000016 " " y[1] (analytic) = -16.961538357187756 " " y[1] (numeric) = -16.961538357187745 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.28371130728535900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.20900000000000016 " " y[1] (analytic) = -16.95993844810402 " " y[1] (numeric) = -16.959938448104005 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37907210494072200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21000000000000016 " " y[1] (analytic) = -16.95833836880813 " " y[1] (numeric) = -16.958338368808114 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.37986270007465100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21100000000000016 " " y[1] (analytic) = -16.956738119320498 " " y[1] (numeric) = -16.956738119320487 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.28549014639650700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21200000000000016 " " y[1] (analytic) = -16.955137699661535 " " y[1] (numeric) = -16.955137699661517 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.04768057379782340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21300000000000016 " " y[1] (analytic) = -16.9535371098516 " " y[1] (numeric) = -16.953537109851585 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38223588571623800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21400000000000016 " " y[1] (analytic) = -16.95193634991107 " " y[1] (numeric) = -16.951936349911055 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38302741460951400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21500000000000016 " " y[1] (analytic) = -16.950335419860288 " " y[1] (numeric) = -16.950335419860274 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38381917714235800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21600000000000016 " " y[1] (analytic) = -16.94873431971959 " " y[1] (numeric) = -16.948734319719577 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38461117339475600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21700000000000016 " " y[1] (analytic) = -16.947133049509294 " " y[1] (numeric) = -16.94713304950928 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38540340344674500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21800000000000017 " " y[1] (analytic) = -16.9455316092497 " " y[1] (numeric) = -16.94553160924968 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 1.04827448342230120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.21900000000000017 " " y[1] (analytic) = -16.943929998961085 " " y[1] (numeric) = -16.94392999896107 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38698856526988700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22000000000000017 " " y[1] (analytic) = -16.942328218663732 " " y[1] (numeric) = -16.942328218663718 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 8.38778149720135500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22100000000000017 " " y[1] (analytic) = -16.940726268377887 " " y[1] (numeric) = -16.940726268377876 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29143099743978300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000017 " " y[1] (analytic) = -16.939124148123796 " " y[1] (numeric) = -16.939124148123785 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29202604762892400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000017 " " y[1] (analytic) = -16.937521857921674 " " y[1] (numeric) = -16.937521857921666 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.19508084901912400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000017 " " y[1] (analytic) = -16.93591939779174 " " y[1] (numeric) = -16.93591939779173 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29321667519934500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000017 " " y[1] (analytic) = -16.934316767754176 " " y[1] (numeric) = -16.934316767754165 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29381225270122400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000017 " " y[1] (analytic) = -16.932713967829162 " " y[1] (numeric) = -16.93271396782915 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29440800609467500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000017 " " y[1] (analytic) = -16.931110998036857 " " y[1] (numeric) = -16.93111099803685 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.19666929029339400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000017 " " y[1] (analytic) = -16.929507858397415 " " y[1] (numeric) = -16.929507858397404 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29560004079789400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000018 " " y[1] (analytic) = -16.927904548930954 " " y[1] (numeric) = -16.927904548930947 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.197464214819034000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000018 " " y[1] (analytic) = -16.926301069657594 " " y[1] (numeric) = -16.92630106965759 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.0989309265975200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000018 " " y[1] (analytic) = -16.924697420597447 " " y[1] (numeric) = -16.924697420597436 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.29738941355045400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000018 " " y[1] (analytic) = -16.923093601770567 " " y[1] (numeric) = -16.923093601770567 " " 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] = 0.23300000000000018 " " y[1] (analytic) = -16.921489613197053 " " y[1] (numeric) = -16.92148961319705 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.099527736630079600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000018 " " y[1] (analytic) = -16.919885454896946 " " y[1] (numeric) = -16.91988545489694 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.19945358172891900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000018 " " y[1] (analytic) = -16.918281126890278 " " y[1] (numeric) = -16.918281126890275 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.099925903910972200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000018 " " y[1] (analytic) = -16.91667662919708 " " y[1] (numeric) = -16.916676629197077 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.100125075789856200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000018 " " y[1] (analytic) = -16.915071961837356 " " y[1] (numeric) = -16.915071961837352 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.100324306521363600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000018 " " y[1] (analytic) = -16.9134671248311 " " y[1] (numeric) = -16.913467124831094 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.20104719225151600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000018 " " y[1] (analytic) = -16.911862118198282 " " y[1] (numeric) = -16.91186211819828 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.100722944623316400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000019 " " y[1] (analytic) = -16.91025694195887 " " y[1] (numeric) = -16.910256941958867 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.100922352034325400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2410000000000002 " " y[1] (analytic) = -16.908651596132806 " " y[1] (numeric) = -16.908651596132803 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.101121818379086700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2420000000000002 " " y[1] (analytic) = -16.907046080740024 " " y[1] (numeric) = -16.90704608074002 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.101321343677912400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2430000000000002 " " y[1] (analytic) = -16.905440395800433 " " y[1] (numeric) = -16.905440395800433 " " 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] = 0.2440000000000002 " " y[1] (analytic) = -16.903834541333943 " " y[1] (numeric) = -16.903834541333943 " " 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] = 0.2450000000000002 " " y[1] (analytic) = -16.902228517360435 " " y[1] (numeric) = -16.90222851736043 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.101920273502086400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2460000000000002 " " y[1] (analytic) = -16.900622323899775 " " y[1] (numeric) = -16.90062232389977 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.102120034820541300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2470000000000002 " " y[1] (analytic) = -16.899015960971816 " " y[1] (numeric) = -16.899015960971816 " " 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] = 0.2480000000000002 " " y[1] (analytic) = -16.89740942859641 " " y[1] (numeric) = -16.897409428596408 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.1025197346452698000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2490000000000002 " " y[1] (analytic) = -16.89580272679337 " " y[1] (numeric) = -16.895802726793367 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.102719673192328400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25000000000000017 " " y[1] (analytic) = -16.89419585558251 " " y[1] (numeric) = -16.894195855582506 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.10291967085639300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25100000000000017 " " y[1] (analytic) = -16.89258881498362 " " y[1] (numeric) = -16.89258881498362 " " 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] = 0.25200000000000017 " " y[1] (analytic) = -16.890981605016485 " " y[1] (numeric) = -16.89098160501648 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.103319843617243400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25300000000000017 " " y[1] (analytic) = -16.889374225700863 " " y[1] (numeric) = -16.889374225700863 " " 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] = 0.25400000000000017 " " y[1] (analytic) = -16.88776667705651 " " y[1] (numeric) = -16.887766677056508 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.103720253091351200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25500000000000017 " " y[1] (analytic) = -16.886158959103156 " " y[1] (numeric) = -16.886158959103152 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.10392054664703320000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.25600000000000017 " " y[1] (analytic) = -16.88455107186052 " " y[1] (numeric) = -16.884551071860518 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.10412089944244200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000002 " " y[1] (analytic) = -16.882943015348307 " " y[1] (numeric) = -16.882943015348303 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.104321311498074700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000002 " " y[1] (analytic) = -16.881334789586205 " " y[1] (numeric) = -16.8813347895862 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.104521782834439500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000002 " " y[1] (analytic) = -16.879726394593888 " " y[1] (numeric) = -16.879726394593884 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.10472231347205800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000002 " " y[1] (analytic) = -16.87811783039102 " " y[1] (numeric) = -16.878117830391016 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.104922903431463000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000002 " " y[1] (analytic) = -16.87650909699724 " " y[1] (numeric) = -16.876509096997236 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.10512355273320070000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000002 " " y[1] (analytic) = -16.874900194432175 " " y[1] (numeric) = -16.874900194432172 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.105324261397829600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000002 " " y[1] (analytic) = -16.873291122715447 " " y[1] (numeric) = -16.873291122715443 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.105525029445919300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000002 " " y[1] (analytic) = -16.871681881866653 " " y[1] (numeric) = -16.871681881866646 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.211451713796105500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000002 " " y[1] (analytic) = -16.870072471905374 " " y[1] (numeric) = -16.870072471905367 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21185348754965100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000002 " " y[1] (analytic) = -16.868462892851184 " " y[1] (numeric) = -16.868462892851177 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.2122553801936900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000002 " " y[1] (analytic) = -16.866853144723635 " " y[1] (numeric) = -16.86685314472363 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.106328695884731300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000002 " " y[1] (analytic) = -16.865243227542273 " " y[1] (numeric) = -16.865243227542265 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.213059522318230400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2690000000000002 " " y[1] (analytic) = -16.863633141326613 " " y[1] (numeric) = -16.86363314132661 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.106730885940643300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2700000000000002 " " y[1] (analytic) = -16.86202288609618 " " y[1] (numeric) = -16.862022886096174 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21386414049994100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2710000000000002 " " y[1] (analytic) = -16.860412461870457 " " y[1] (numeric) = -16.860412461870453 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.10713331410776800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2720000000000002 " " y[1] (analytic) = -16.858801868668934 " " y[1] (numeric) = -16.858801868668927 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21466923506943300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2730000000000002 " " y[1] (analytic) = -16.857191106511074 " " y[1] (numeric) = -16.857191106511063 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.3226079416545300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2740000000000002 " " y[1] (analytic) = -16.85558017541633 " " y[1] (numeric) = -16.855580175416318 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.32321220953656700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2750000000000002 " " y[1] (analytic) = -16.85396907540413 " " y[1] (numeric) = -16.853969075404123 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21587777087494500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2760000000000002 " " y[1] (analytic) = -16.85235780649391 " " y[1] (numeric) = -16.852357806493902 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21628085469618200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2770000000000002 " " y[1] (analytic) = -16.850746368705074 " " y[1] (numeric) = -16.850746368705064 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.32502608679436500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2780000000000002 " " y[1] (analytic) = -16.849134762057012 " " y[1] (numeric) = -16.849134762057002 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.32563107062496500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2790000000000002 " " y[1] (analytic) = -16.847522986569103 " " y[1] (numeric) = -16.847522986569093 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 6.32623623359837900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2800000000000002 " " y[1] (analytic) = -16.84591104226071 " " y[1] (numeric) = -16.845911042260703 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21789438385129830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2810000000000002 " " y[1] (analytic) = -16.844298929151186 " " y[1] (numeric) = -16.84429892915118 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.218298064815367300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2820000000000002 " " y[1] (analytic) = -16.84268664725986 " " y[1] (numeric) = -16.842686647259857 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.109350932666370400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2830000000000002 " " y[1] (analytic) = -16.841074196606066 " " y[1] (numeric) = -16.84107419660606 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.21910578544505140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2840000000000002 " " y[1] (analytic) = -16.83946157720909 " " y[1] (numeric) = -16.839461577209086 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.109754912596982800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2850000000000002 " " y[1] (analytic) = -16.837848789088234 " " y[1] (numeric) = -16.837848789088234 " " 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] = 0.2860000000000002 " " y[1] (analytic) = -16.83623583226278 " " y[1] (numeric) = -16.836235832262776 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.110159131884183400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2870000000000002 " " y[1] (analytic) = -16.83462270675198 " " y[1] (numeric) = -16.834622706751976 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11036133133865200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2880000000000002 " " y[1] (analytic) = -16.833009412575084 " " y[1] (numeric) = -16.83300941257508 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.110563590694869700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2890000000000002 " " y[1] (analytic) = -16.831395949751332 " " y[1] (numeric) = -16.831395949751325 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.22153181994745800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2900000000000002 " " y[1] (analytic) = -16.829782318299934 " " y[1] (numeric) = -16.829782318299927 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.22193657839227400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2910000000000002 " " y[1] (analytic) = -16.82816851824009 " " y[1] (numeric) = -16.82816851824009 " " 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] = 0.2920000000000002 " " y[1] (analytic) = -16.82655454959101 " " y[1] (numeric) = -16.826554549591005 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.111373227555283500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2930000000000002 " " y[1] (analytic) = -16.824940412371852 " " y[1] (numeric) = -16.824940412371845 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.22315157346779160000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2940000000000002 " " y[1] (analytic) = -16.823326106601776 " " y[1] (numeric) = -16.823326106601773 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.111778405939805400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2950000000000002 " " y[1] (analytic) = -16.82171163229994 " " y[1] (numeric) = -16.821711632299937 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11198108519397900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2960000000000002 " " y[1] (analytic) = -16.82009698948547 " " y[1] (numeric) = -16.820096989485467 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11218382451739900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2970000000000002 " " y[1] (analytic) = -16.818482178177483 " " y[1] (numeric) = -16.818482178177483 " " 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] = 0.2980000000000002 " " y[1] (analytic) = -16.816867198395094 " " y[1] (numeric) = -16.816867198395087 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.225178966911924400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2990000000000002 " " y[1] (analytic) = -16.815252050157373 " " y[1] (numeric) = -16.81525205015737 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.112792403113131500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3000000000000002 " " y[1] (analytic) = -16.81363673348341 " " y[1] (numeric) = -16.813636733483406 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.112995382923595300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3010000000000002 " " y[1] (analytic) = -16.812021248392263 " " y[1] (numeric) = -16.812021248392256 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.226396845816796600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3020000000000002 " " y[1] (analytic) = -16.810405594902967 " " y[1] (numeric) = -16.810405594902967 " " 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] = 0.3030000000000002 " " y[1] (analytic) = -16.808789773034576 " " y[1] (numeric) = -16.808789773034572 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.113604683485259500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3040000000000002 " " y[1] (analytic) = -16.80717378280609 " " y[1] (numeric) = -16.80717378280609 " " 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] = 0.3050000000000002 " " y[1] (analytic) = -16.80555762423652 " " y[1] (numeric) = -16.80555762423652 " " 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] = 0.3060000000000002 " " y[1] (analytic) = -16.803941297344856 " " y[1] (numeric) = -16.803941297344856 " " 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] = 0.3070000000000002 " " y[1] (analytic) = -16.802324802150075 " " y[1] (numeric) = -16.80232480215007 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11441792765837080000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3080000000000002 " " y[1] (analytic) = -16.800708138671133 " " y[1] (numeric) = -16.80070813867113 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.114621389453829300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3090000000000002 " " y[1] (analytic) = -16.79909130692698 " " y[1] (numeric) = -16.79909130692698 " " 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] = 0.3100000000000002 " " y[1] (analytic) = -16.79747430693655 " " y[1] (numeric) = -16.79747430693655 " " 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] = 0.3110000000000002 " " y[1] (analytic) = -16.79585713871876 " " y[1] (numeric) = -16.795857138718763 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.115232136983699600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3120000000000002 " " y[1] (analytic) = -16.79423980229252 " " y[1] (numeric) = -16.79423980229252 " " 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] = 0.3130000000000002 " " y[1] (analytic) = -16.79262229767671 " " y[1] (numeric) = -16.792622297676715 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.115639604001588700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3140000000000002 " " y[1] (analytic) = -16.79100462489022 " " y[1] (numeric) = -16.791004624890224 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.115843428173511400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3150000000000002 " " y[1] (analytic) = -16.789386783951905 " " y[1] (numeric) = -16.789386783951908 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11604731281570920000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3160000000000002 " " y[1] (analytic) = -16.78776877488061 " " y[1] (numeric) = -16.787768774880618 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.23250251589883100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3170000000000002 " " y[1] (analytic) = -16.786150597695183 " " y[1] (numeric) = -16.786150597695187 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.116455263595874700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3180000000000002 " " y[1] (analytic) = -16.78453225241443 " " y[1] (numeric) = -16.784532252414436 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.233318659552694500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31900000000000023 " " y[1] (analytic) = -16.782913739057165 " " y[1] (numeric) = -16.78291373905717 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 4.23372691302420560000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.32000000000000023 " " y[1] (analytic) = -16.781295057642183 " " y[1] (numeric) = -16.781295057642186 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.117067643824425000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.32100000000000023 " " y[1] (analytic) = -16.779676208188256 " " y[1] (numeric) = -16.77967620818826 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11727189173461200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.32200000000000023 " " y[1] (analytic) = -16.778057190714154 " " y[1] (numeric) = -16.778057190714158 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.117476200263971300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.32300000000000023 " " y[1] (analytic) = -16.776438005238624 " " y[1] (numeric) = -16.776438005238628 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.11768056943382580000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.32400000000000023 " " y[1] (analytic) = -16.774818651780404 " " y[1] (numeric) = -16.774818651780407 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.117884999265510200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.32500000000000023 " " y[1] (analytic) = -16.77319913035822 " " y[1] (numeric) = -16.773199130358222 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 2.118089489780371500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = exp(sqrt(0.1 * x + 0.2));" Iterations = 326 "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 43 Minutes 2 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 42 Minutes 50 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 45 Minutes 50 Seconds "Time to Timeout " Unknown Percent Done = 6.5400000000000045 "%" (%o58) true (%o58) diffeq.max