(%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 - 3 + 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 - 3 + 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 - 3 + 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 - 3 + 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 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 4 then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(0, 3), 1 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, glob_h 2, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, glob_h 3, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 4, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 , if not array_y_set_initial 2 2 1, 5 then (if 2 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(1, 4), array_y : temporary, 2 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 4 glob_h temporary 2.0 array_y_higher : temporary, temporary : -------------, 3, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 4, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2 : array_tmp1 , if not array_y_set_initial 3 3 1, 6 then (if 3 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(2, 5), array_y : temporary, 3 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 2, 5 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 3, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 4, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2 : array_tmp1 , if not array_y_set_initial 4 4 1, 7 then (if 4 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(3, 6), array_y : temporary, 4 7 temporary 6.0 array_y_higher : temporary, temporary : -------------, 1, 7 glob_h temporary 5.0 array_y_higher : temporary, temporary : -------------, 2, 6 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 4, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2 : array_tmp1 , if not array_y_set_initial 5 5 1, 8 then (if 5 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(4, 7), array_y : temporary, 5 8 temporary 7.0 array_y_higher : temporary, temporary : -------------, 1, 8 glob_h temporary 6.0 array_y_higher : temporary, temporary : -------------, 2, 7 glob_h temporary 5.0 array_y_higher : temporary, temporary : -------------, 3, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 4, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 , kkk kkk - 1 kkk kkk order_d : 3, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp2 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 : sin(array_x ), array_tmp1_g : cos(array_x ), 1 1 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 4 then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(0, 3), 1 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, glob_h 2, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, glob_h 3, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 4, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 , if not array_y_set_initial 2 2 1, 5 then (if 2 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(1, 4), array_y : temporary, 2 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 4 glob_h temporary 2.0 array_y_higher : temporary, temporary : -------------, 3, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 4, 2 array_tmp1_g array_x - array_tmp1 array_x 2 2 2 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 3 2 3 2 array_tmp2 : array_tmp1 , if not array_y_set_initial 3 3 1, 6 then (if 3 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(2, 5), array_y : temporary, 3 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 2, 5 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 3, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 4, 3 array_tmp1_g array_x - array_tmp1 array_x 3 2 3 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 4 3 4 3 array_tmp2 : array_tmp1 , if not array_y_set_initial 4 4 1, 7 then (if 4 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(3, 6), array_y : temporary, 4 7 temporary 6.0 array_y_higher : temporary, temporary : -------------, 1, 7 glob_h temporary 5.0 array_y_higher : temporary, temporary : -------------, 2, 6 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 4, 4 array_tmp1_g array_x - array_tmp1 array_x 4 2 4 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 5 4 5 4 array_tmp2 : array_tmp1 , if not array_y_set_initial 5 5 1, 8 then (if 5 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 3) factorial_3(4, 7), array_y : temporary, 5 8 temporary 7.0 array_y_higher : temporary, temporary : -------------, 1, 8 glob_h temporary 6.0 array_y_higher : temporary, temporary : -------------, 2, 7 glob_h temporary 5.0 array_y_higher : temporary, temporary : -------------, 3, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 4, 5 array_tmp1_g array_x kkk - 1 2 while kkk <= glob_max_terms do (array_tmp1 : ----------------------------, kkk kkk - 1 - array_tmp1 array_x kkk - 1 2 array_tmp1_g : ----------------------------, array_tmp2 : array_tmp1 , kkk kkk - 1 kkk kkk order_d : 3, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp2 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(cos(x) + 1.0) (%o56) exact_soln_y(x) := block(cos(x) + 1.0) (%i57) exact_soln_yp(x) := block(- sin(x)) (%o57) exact_soln_yp(x) := block(- sin(x)) (%i58) exact_soln_ypp(x) := block(- cos(x)) (%o58) exact_soln_ypp(x) := block(- cos(x)) (%i59) 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/h3sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"), omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:20,"), 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, " (1.0 + cos(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_yp (x) := (block("), omniout_str(ALWAYS, " (-sin(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_ypp (x) := (block("), omniout_str(ALWAYS, " (-cos(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 4, 1 + max_terms), array(array_y_higher_work, 1 + 4, 1 + max_terms), array(array_y_higher_work2, 1 + 4, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 4 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 4 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 <= 4 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term), term array_const_3 : 3, 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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 array_y_init : exact_soln_yp(x_start), 1 + 1 array_y_init : exact_soln_ypp(x_start), glob_look_poles : true, 1 + 2 glob_max_iter : 20, 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 : true, array_y_set_initial : true, 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 : 3, 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 : 3, 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 : 4, ord : 4, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 4, iii array_y_higher 4, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, calc_term : 3, factorial_1(calc_term - 1) 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 : 3, 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 : 2, calc_term : 2, factorial_1(calc_term - 1) 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 : 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 : 2, calc_term : 1, factorial_1(calc_term - 1) 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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 , 3 ) = sin(x);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T15:07:50-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "h3sin"), logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(x);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "h3sin diffeq.max"), logitem_str(html_log_file, "h3sin maxima results" ), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o59) 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/h3sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"), omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:20,"), 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, " (1.0 + cos(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_yp (x) := (block("), omniout_str(ALWAYS, " (-sin(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "exact_soln_ypp (x) := (block("), omniout_str(ALWAYS, " (-cos(x)) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1_g, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 4, 1 + max_terms), array(array_y_higher_work, 1 + 4, 1 + max_terms), array(array_y_higher_work2, 1 + 4, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 4 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 4 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 <= 4 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term), term array_const_3 : 3, 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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 array_y_init : exact_soln_yp(x_start), 1 + 1 array_y_init : exact_soln_ypp(x_start), glob_look_poles : true, 1 + 2 glob_max_iter : 20, 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 : true, array_y_set_initial : true, 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 : 3, 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 : 3, 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 : 4, ord : 4, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 4, iii array_y_higher 4, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, calc_term : 3, factorial_1(calc_term - 1) 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 : 3, 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 : 2, calc_term : 2, factorial_1(calc_term - 1) 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 : 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 : 2, calc_term : 1, factorial_1(calc_term - 1) 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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 , 3 ) = sin(x);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-28T15:07:50-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "h3sin"), logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(x);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 165 "), logitem_str(html_log_file, "h3sin diffeq.max"), logitem_str(html_log_file, "h3sin maxima results" ), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i60) main() "##############ECHO OF PROBLEM#################" "##############temp/h3sinpostode.ode#################" "diff ( y , x , 3 ) = sin(x);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "array_y_init[1 + 1] : exact_soln_yp(x_start)," "array_y_init[2 + 1] : exact_soln_ypp(x_start)," "glob_look_poles:true," "glob_max_iter:20," "/* 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(" " (1.0 + cos(x)) " "));" "exact_soln_yp (x) := (block(" " (-sin(x)) " "));" "exact_soln_ypp (x) := (block(" " (-cos(x)) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" max_value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" value3 = 2.467204025104944900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-105 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 1.9950041652780257 " " y[1] (numeric) = 1.9950041652780257 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.101 " " y[1] (analytic) = 1.9949038343759766 " " y[1] (numeric) = 1.9949038343759766 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000001 " " y[1] (analytic) = 1.9948025085701762 " " y[1] (numeric) = 1.9948025085701762 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000001 " " y[1] (analytic) = 1.99470018796195 " " y[1] (numeric) = 1.99470018796195 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000001 " " y[1] (analytic) = 1.9945968726536185 " " y[1] (numeric) = 1.9945968726536185 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000001 " " y[1] (analytic) = 1.9944925627484973 " " y[1] (numeric) = 1.9944925627484975 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113288708477529900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = 1.9943872583508964 " " y[1] (numeric) = 1.9943872583508966 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113347490540196500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = 1.9942809595661202 " " y[1] (numeric) = 1.9942809595661202 " " 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] = 0.10800000000000001 " " y[1] (analytic) = 1.9941736665004668 " " y[1] (numeric) = 1.994173666500467 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113466738905908300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = 1.99406537926123 " " y[1] (numeric) = 1.9940653792612302 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11352720544847600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = 1.9939560979566968 " " y[1] (numeric) = 1.993956097956697 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113588233725763300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = 1.9938458226961484 " " y[1] (numeric) = 1.9938458226961486 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.113649823860376500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = 1.9937345535898603 " " y[1] (numeric) = 1.9937345535898603 " " 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] = 0.11300000000000002 " " y[1] (analytic) = 1.9936222907491012 " " y[1] (numeric) = 1.9936222907491012 " " 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] = 0.11400000000000002 " " y[1] (analytic) = 1.9935090342861344 " " y[1] (numeric) = 1.9935090342861344 " " 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] = 0.11500000000000002 " " y[1] (analytic) = 1.9933947843142157 " " y[1] (numeric) = 1.993394784314216 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11390180546409400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = 1.9932795409475959 " " y[1] (numeric) = 1.9932795409475959 " " 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] = 0.11700000000000002 " " y[1] (analytic) = 1.9931633043015178 " " y[1] (numeric) = 1.9931633043015178 " " 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] = 0.11800000000000002 " " y[1] (analytic) = 1.993046074492218 " " y[1] (numeric) = 1.993046074492218 " " 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] = 0.11900000000000002 " " y[1] (analytic) = 1.9929278516369267 " " y[1] (numeric) = 1.9929278516369267 " " 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] = 0.12000000000000002 " " y[1] (analytic) = 1.9928086358538661 " " y[1] (numeric) = 1.9928086358538664 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114229439445855500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = 1.992688427262253 " " y[1] (numeric) = 1.992688427262253 " " 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] = 0.12200000000000003 " " y[1] (analytic) = 1.9925672259822949 " " y[1] (numeric) = 1.9925672259822949 " " 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] = 0.12300000000000003 " " y[1] (analytic) = 1.9924450321351936 " " y[1] (numeric) = 1.9924450321351936 " " 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] = 0.12400000000000003 " " y[1] (analytic) = 1.9923218458431429 " " y[1] (numeric) = 1.9923218458431429 " " 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] = 0.12500000000000003 " " y[1] (analytic) = 1.9921976672293291 " " y[1] (numeric) = 1.9921976672293291 " " 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] = 0.12600000000000003 " " y[1] (analytic) = 1.9920724964179306 " " y[1] (numeric) = 1.9920724964179308 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11464118562102300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = 1.9919463335341185 " " y[1] (numeric) = 1.9919463335341188 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114711783078407300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = 1.9918191787040556 " " y[1] (numeric) = 1.9918191787040558 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114782944652139400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = 1.9916910320548964 " " y[1] (numeric) = 1.9916910320548968 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.229709340970825500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = 1.991561893714788 " " y[1] (numeric) = 1.9915618937147883 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114926960722569200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = 1.9914317638128685 " " y[1] (numeric) = 1.9914317638128687 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.114999815509101500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = 1.9913006424792679 " " y[1] (numeric) = 1.9913006424792679 " " 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] = 0.13300000000000003 " " y[1] (analytic) = 1.9911685298451072 " " y[1] (numeric) = 1.9911685298451072 " " 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] = 0.13400000000000004 " " y[1] (analytic) = 1.9910354260424992 " " y[1] (numeric) = 1.9910354260424994 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115221768637137800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = 1.9909013312045478 " " y[1] (numeric) = 1.990901331204548 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11529688309911600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = 1.9907662454653479 " " y[1] (numeric) = 1.990766245465348 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115372562855201900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = 1.990630168959985 " " y[1] (numeric) = 1.9906301689599852 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115448808057800400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = 1.9904931018245358 " " y[1] (numeric) = 1.990493101824536 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115525618860470600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = 1.9903550441960673 " " y[1] (numeric) = 1.9903550441960673 " " 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] = 0.14000000000000004 " " y[1] (analytic) = 1.9902159962126371 " " y[1] (numeric) = 1.9902159962126371 " " 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] = 0.14100000000000004 " " y[1] (analytic) = 1.9900759580132932 " " y[1] (numeric) = 1.9900759580132932 " " 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] = 0.14200000000000004 " " y[1] (analytic) = 1.989934929738074 " " y[1] (numeric) = 1.9899349297380737 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115838521183494200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = 1.9897929115280073 " " y[1] (numeric) = 1.989792911528007 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115918162330361300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = 1.9896499035251116 " " y[1] (numeric) = 1.9896499035251114 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.115998370022934400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = 1.9895059058723947 " " y[1] (numeric) = 1.9895059058723947 " " 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] = 0.14600000000000005 " " y[1] (analytic) = 1.9893609187138546 " " y[1] (numeric) = 1.9893609187138546 " " 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] = 0.14700000000000005 " " y[1] (analytic) = 1.989214942194478 " " y[1] (numeric) = 1.989214942194478 " " 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] = 0.14800000000000005 " " y[1] (analytic) = 1.989067976460242 " " y[1] (numeric) = 1.989067976460242 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14900000000000005 " " y[1] (analytic) = 1.9889200216581118 " " y[1] (numeric) = 1.9889200216581118 " " 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] = 0.15000000000000005 " " y[1] (analytic) = 1.9887710779360424 " " y[1] (numeric) = 1.9887710779360424 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15100000000000005 " " y[1] (analytic) = 1.9886211454429774 " " y[1] (numeric) = 1.9886211454429774 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15200000000000005 " " y[1] (analytic) = 1.9884702243288492 " " y[1] (numeric) = 1.9884702243288492 " " 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] = 0.15300000000000005 " " y[1] (analytic) = 1.9883183147445793 " " y[1] (numeric) = 1.988318314744579 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116745760869558200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.9881654168420768 " " y[1] (numeric) = 1.9881654168420766 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116831643102001900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.9880115307742399 " " y[1] (numeric) = 1.9880115307742396 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.116918093722298700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.9878566566949545 " " y[1] (numeric) = 1.9878566566949543 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117005112904904300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.9877007947590948 " " y[1] (numeric) = 1.9877007947590946 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117092700825441200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.9875439451225225 " " y[1] (numeric) = 1.9875439451225223 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11718085766070100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.9873861079420876 " " y[1] (numeric) = 1.9873861079420874 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117269583588644500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.9872272833756268 " " y[1] (numeric) = 1.9872272833756266 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117358878788402300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.9870674715819652 " " y[1] (numeric) = 1.9870674715819647 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.234897486880551600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = 1.986906672720914 " " y[1] (numeric) = 1.9869066727209137 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117539177725738300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = 1.9867448869532724 " " y[1] (numeric) = 1.9867448869532722 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117630181827435200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = 1.9865821144408262 " " y[1] (numeric) = 1.986582114440826 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117721755929184800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = 1.9864183553463477 " " y[1] (numeric) = 1.9864183553463475 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117813900215979800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = 1.9862536098335961 " " y[1] (numeric) = 1.986253609833596 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.117906614873987500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = 1.9860878780673166 " " y[1] (numeric) = 1.9860878780673166 " " 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] = 0.16800000000000007 " " y[1] (analytic) = 1.9859211602132416 " " y[1] (numeric) = 1.9859211602132414 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118093756054187500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = 1.985753456438088 " " y[1] (numeric) = 1.985753456438088 " " 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] = 0.17000000000000007 " " y[1] (analytic) = 1.9855847669095605 " " y[1] (numeric) = 1.9855847669095605 " " 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] = 0.17100000000000007 " " y[1] (analytic) = 1.9854150917963485 " " y[1] (numeric) = 1.9854150917963482 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118378750330398200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = 1.9852444312681263 " " y[1] (numeric) = 1.9852444312681263 " " 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] = 0.17300000000000007 " " y[1] (analytic) = 1.9850727854955552 " " y[1] (numeric) = 1.9850727854955552 " " 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] = 0.17400000000000007 " " y[1] (analytic) = 1.9849001546502807 " " y[1] (numeric) = 1.9849001546502807 " " 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] = 0.17500000000000007 " " y[1] (analytic) = 1.9847265389049333 " " y[1] (numeric) = 1.9847265389049336 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118766744800740700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = 1.9845519384331296 " " y[1] (numeric) = 1.9845519384331296 " " 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] = 0.17700000000000007 " " y[1] (analytic) = 1.984376353409469 " " y[1] (numeric) = 1.9843763534094692 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.118964175034256600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = 1.9841997840095373 " " y[1] (numeric) = 1.9841997840095373 " " 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] = 0.17900000000000008 " " y[1] (analytic) = 1.9840222304099036 " " y[1] (numeric) = 1.9840222304099036 " " 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] = 0.18000000000000008 " " y[1] (analytic) = 1.9838436927881213 " " y[1] (numeric) = 1.9838436927881213 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000008 " " y[1] (analytic) = 1.9836641713227285 " " y[1] (numeric) = 1.9836641713227283 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11936590948743900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = 1.983483666193246 " " y[1] (numeric) = 1.983483666193246 " " 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] = 0.18300000000000008 " " y[1] (analytic) = 1.9833021775801796 " " y[1] (numeric) = 1.9833021775801793 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.11957021695981400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = 1.9831197056650174 " " y[1] (numeric) = 1.9831197056650172 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119673231478334200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = 1.9829362506302315 " " y[1] (numeric) = 1.9829362506302313 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.1197768201295400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = 1.9827518126592767 " " y[1] (numeric) = 1.9827518126592767 " " 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] = 0.18700000000000008 " " y[1] (analytic) = 1.9825663919365915 " " y[1] (numeric) = 1.9825663919365912 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.119985720670548800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = 1.982379988647596 " " y[1] (numeric) = 1.9823799886475957 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.120091032983605200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = 1.9821926029786936 " " y[1] (numeric) = 1.9821926029786934 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.12019692027585500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = 1.9820042351172704 " " y[1] (numeric) = 1.98200423511727 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24060676552382320000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = 1.9818148852516937 " " y[1] (numeric) = 1.9818148852516932 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.240820841315169200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = 1.9816245535713135 " " y[1] (numeric) = 1.981624553571313 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.241036068359762700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = 1.9814332402664618 " " y[1] (numeric) = 1.9814332402664612 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36187867064101900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = 1.9812409455284512 " " y[1] (numeric) = 1.9812409455284508 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24146997795672900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = 1.9810476695495773 " " y[1] (numeric) = 1.9810476695495767 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.362532992083678300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = 1.9808534125231154 " " y[1] (numeric) = 1.9808534125231148 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36286274675219300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = 1.9806581746433225 " " y[1] (numeric) = 1.980658174643322 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.24212948773977300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = 1.980461956105437 " " y[1] (numeric) = 1.9804619561054364 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36352744732870750000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = 1.980264757105677 " " y[1] (numeric) = 1.9802647571056764 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36386239458558200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = 1.9800665778412416 " " y[1] (numeric) = 1.980066577841241 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36419907406014240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = 1.97986741851031 " " y[1] (numeric) = 1.9798674185103093 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36453748643586300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = 1.9796672793120416 " " y[1] (numeric) = 1.979667279312041 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36487763239984200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = 1.9794661604465755 " " y[1] (numeric) = 1.9794661604465749 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.365219512642800300000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = 1.9792640621150306 " " y[1] (numeric) = 1.97926406211503 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.365563127859085000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = 1.979060984519505 " " y[1] (numeric) = 1.9790609845195044 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36590847874667200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = 1.9788569278630765 " " y[1] (numeric) = 1.978856927863076 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.244170377338116400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = 1.978651892349802 " " y[1] (numeric) = 1.9786518923498013 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36660439034583600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = 1.9784458781847165 " " y[1] (numeric) = 1.9784458781847158 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.366954952471541400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = 1.9782388855738344 " " y[1] (numeric) = 1.9782388855738338 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.36730725309681840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = 1.9780309147241484 " " y[1] (numeric) = 1.9780309147241475 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.4902150572504500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = 1.9778219658436287 " " y[1] (numeric) = 1.977821965843628 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.368017072714420400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = 1.977612039141225 " " y[1] (numeric) = 1.9776120391412242 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.491166124200049500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = 1.9774011348268636 " " y[1] (numeric) = 1.9774011348268627 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.49164513996241800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = 1.9771892531114488 " " y[1] (numeric) = 1.9771892531114479 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.492126478547377500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = 1.9769763942068623 " " y[1] (numeric) = 1.9769763942068614 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.492610140934187000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = 1.9767625583259631 " " y[1] (numeric) = 1.9767625583259623 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.4930961281069900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = 1.9765477456825868 " " y[1] (numeric) = 1.976547745682586 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.493584441054820400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = 1.9763319564915465 " " y[1] (numeric) = 1.9763319564915454 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.61759385096450700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = 1.9761151909686308 " " y[1] (numeric) = 1.9761151909686296 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.61821006032021600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = 1.9758974493306054 " " y[1] (numeric) = 1.9758974493306043 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.618829180640310000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = 1.9756787317952123 " " y[1] (numeric) = 1.975678731795211 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74334145582270300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = 1.9754590385811683 " " y[1] (numeric) = 1.9754590385811672 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.62007615922297600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = 1.9752383699081673 " " y[1] (numeric) = 1.9752383699081661 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.620704020025558000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = 1.9750167259968778 " " y[1] (numeric) = 1.9750167259968765 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.7456017562470700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = 1.9747941070689432 " " y[1] (numeric) = 1.974794107068942 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.62196849104936500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = 1.974570513346983 " " y[1] (numeric) = 1.9745705133469817 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74712612461702300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = 1.9743459450545906 " " y[1] (numeric) = 1.9743459450545893 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74789356387768500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = 1.9741204024163344 " " y[1] (numeric) = 1.974120402416333 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74866450860588400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = 1.9738938856577568 " " y[1] (numeric) = 1.9738938856577555 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.74943896037369400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = 1.9736663950053748 " " y[1] (numeric) = 1.9736663950053734 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.75021692076061200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = 1.973437930686679 " " y[1] (numeric) = 1.9734379306866776 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.75099839135356500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = 1.9732084929301335 " " y[1] (numeric) = 1.9732084929301321 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.75178337374691400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = 1.9729780819651763 " " y[1] (numeric) = 1.9729780819651748 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.87800051446619800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = 1.9727466980222181 " " y[1] (numeric) = 1.9727466980222166 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.8789245270743500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = 1.972514341332643 " " y[1] (numeric) = 1.9725143413326414 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.87985264241534600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = 1.9722810121288075 " " y[1] (numeric) = 1.972281012128806 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.88078486238404600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = 1.9720467106440411 " " y[1] (numeric) = 1.9720467106440394 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.00768135872460500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = 1.971811437112645 " " y[1] (numeric) = 1.9718114371126432 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.00875614151725500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = 1.9715751917698925 " " y[1] (numeric) = 1.971575191769891 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.88360616913578400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = 1.9713379748520294 " " y[1] (numeric) = 1.9713379748520279 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.88455482673835900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = 1.9710997865962727 " " y[1] (numeric) = 1.971099786596271 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.01200868408439300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = 1.97086062724081 " " y[1] (numeric) = 1.9708606272408082 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.01310227038802100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = 1.970620497024801 " " y[1] (numeric) = 1.9706204970247994 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.88742549274142600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = 1.9703793961883758 " " y[1] (numeric) = 1.9703793961883742 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.88839061899437900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = 1.9701373249726353 " " y[1] (numeric) = 1.9701373249726337 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.8893598673219800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = 1.969894283619651 " " y[1] (numeric) = 1.9698942836196491 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.01752370252185100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = 1.9696502723724634 " " y[1] (numeric) = 1.9696502723724618 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.8913107381394900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = 1.9694052914750846 " " y[1] (numeric) = 1.9694052914750828 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 9.01976270242352800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = 1.9691593411724948 " " y[1] (numeric) = 1.9691593411724932 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.8932781211587300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 1.9689124217106446 " " y[1] (numeric) = 1.9689124217106433 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.76651543694705000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = 1.9686645333364536 " " y[1] (numeric) = 1.9686645333364523 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.76736745641618800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = 1.96841567629781 " " y[1] (numeric) = 1.9684156762978087 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.76822302114517100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = 1.9681658508435709 " " y[1] (numeric) = 1.9681658508435695 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.76908213288614800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = 1.9679150572235615 " " y[1] (numeric) = 1.9679150572235602 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.76994479339886400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = 1.9676632956885756 " " y[1] (numeric) = 1.9676632956885742 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.7708110044506700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = 1.9674105664903745 " " y[1] (numeric) = 1.9674105664903732 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.77168076781652100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = 1.9671568698816877 " " y[1] (numeric) = 1.9671568698816864 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.77255408527900100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = 1.9669022061162114 " " y[1] (numeric) = 1.9669022061162102 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.644525798856930000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = 1.9666465754486098 " " y[1] (numeric) = 1.9666465754486087 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.645259491385252000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 1.9663899781345133 " " y[1] (numeric) = 1.966389978134512 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.77519538018644500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = 1.966132414430519 " " y[1] (numeric) = 1.966132414430518 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.646735776678232000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = 1.965873884594191 " " y[1] (numeric) = 1.9658738845941899 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.647478372471163000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = 1.9656143888840587 " " y[1] (numeric) = 1.9656143888840576 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.6482239390578800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = 1.965353927559618 " " y[1] (numeric) = 1.965353927559617 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.51917798237479460000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = 1.9650925008813303 " " y[1] (numeric) = 1.9650925008813294 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.51977919259161250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = 1.964830109110622 " " y[1] (numeric) = 1.964830109110621 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.52038278313109800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = 1.964566752509885 " " y[1] (numeric) = 1.9645667525098842 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.520988755232720000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000001 " " y[1] (analytic) = 1.964302431342476 " " y[1] (numeric) = 1.964302431342475 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.52159711014108800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.26900000000000013 " " y[1] (analytic) = 1.964037145872716 " " y[1] (numeric) = 1.964037145872715 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.522207849105955000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 1.9637708963658906 " " y[1] (numeric) = 1.9637708963658895 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.65352621672777600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27100000000000013 " " y[1] (analytic) = 1.9635036830882489 " " y[1] (numeric) = 1.963503683088248 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.52343648422994300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = 1.9632355063070044 " " y[1] (numeric) = 1.9632355063070035 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.524054382914337600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = 1.9629663662903338 " " y[1] (numeric) = 1.962966366290333 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.524674670705787000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27400000000000013 " " y[1] (analytic) = 1.9626962633073775 " " y[1] (numeric) = 1.9626962633073763 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.656621686099805000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27500000000000013 " " y[1] (analytic) = 1.9624251976282379 " " y[1] (numeric) = 1.9624251976282368 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.657403023396550000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = 1.962153169523981 " " y[1] (numeric) = 1.9621531695239798 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.65818735187985900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = 1.9618801792666347 " " y[1] (numeric) = 1.9618801792666334 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.7907696077963300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = 1.961606227129189 " " y[1] (numeric) = 1.9616062271291879 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.65976498886816900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27900000000000014 " " y[1] (analytic) = 1.9613313133855965 " " y[1] (numeric) = 1.9613313133855954 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.66055830062040900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 1.9610554383107708 " " y[1] (numeric) = 1.9610554383107697 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.66135461005370200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28100000000000014 " " y[1] (analytic) = 1.960778602180587 " " y[1] (numeric) = 1.9607786021805858 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.79458470256952800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = 1.9605008052718809 " " y[1] (numeric) = 1.9605008052718798 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.66295622852953400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = 1.9602220478624495 " " y[1] (numeric) = 1.9602220478624484 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.66376154087142500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = 1.9599423302310504 " " y[1] (numeric) = 1.9599423302310492 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.66456985749308500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28500000000000014 " " y[1] (analytic) = 1.959661652657401 " " y[1] (numeric) = 1.9596616526573998 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.79845741607264200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28600000000000014 " " y[1] (analytic) = 1.959380015422179 " " y[1] (numeric) = 1.9593800154221777 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.79943461229561500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28700000000000014 " " y[1] (analytic) = 1.9590974188070214 " " y[1] (numeric) = 1.95909741880702 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.80041541967557200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28800000000000014 " " y[1] (analytic) = 1.958813863094525 " " y[1] (numeric) = 1.9588138630945235 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.93496648027456700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = 1.9585293485682453 " " y[1] (numeric) = 1.958529348568244 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.80238787600565200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 1.958243875512697 " " y[1] (numeric) = 1.9582438755126956 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.8033795290251100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = 1.9579574442133532 " " y[1] (numeric) = 1.9579574442133516 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.93843726823028000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = 1.9576700549566448 " " y[1] (numeric) = 1.9576700549566433 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.93960264417305700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = 1.9573817080299614 " " y[1] (numeric) = 1.9573817080299598 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.9407722474303800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = 1.9570924037216497 " " y[1] (numeric) = 1.9570924037216482 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.94194608041758800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = 1.9568021423210138 " " y[1] (numeric) = 1.9568021423210125 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.80839212476510600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = 1.9565109241183154 " " y[1] (numeric) = 1.956510924118314 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.80940552453374500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = 1.9562187494047727 " " y[1] (numeric) = 1.9562187494047714 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.81042255604370800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = 1.9559256184725604 " " y[1] (numeric) = 1.9559256184725589 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.94668375829663200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = 1.9556315316148092 " " y[1] (numeric) = 1.9556315316148076 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.94787877648806700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 1.955336489125606 " " y[1] (numeric) = 1.9553364891256044 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.9490780390963900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = 1.9550404912999932 " " y[1] (numeric) = 1.9550404912999917 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.95028154860203400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = 1.9547435384339686 " " y[1] (numeric) = 1.9547435384339673 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.81556226356694400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30300000000000016 " " y[1] (analytic) = 1.9544456308244855 " " y[1] (numeric) = 1.954445630824484 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.95270131827371700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30400000000000016 " " y[1] (analytic) = 1.954146768769451 " " y[1] (numeric) = 1.9541467687694494 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.95391758344736700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = 1.953846952567727 " " y[1] (numeric) = 1.9538469525677256 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.81868980474307100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30600000000000016 " " y[1] (analytic) = 1.95354618251913 " " y[1] (numeric) = 1.9535461825191287 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.81973961747966900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30700000000000016 " " y[1] (analytic) = 1.9532444589244302 " " y[1] (numeric) = 1.9532444589244287 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.95759193056210600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30800000000000016 " " y[1] (analytic) = 1.9529417820853507 " " y[1] (numeric) = 1.9529417820853492 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 7.95882523858711700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30900000000000016 " " y[1] (analytic) = 1.9526381523045684 " " y[1] (numeric) = 1.952638152304567 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.82291098316296500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 1.9523335698857134 " " y[1] (numeric) = 1.952333569885712 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 6.82397542151660400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = 1.9520280351333676 " " y[1] (numeric) = 1.9520280351333665 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.68753626814229300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = 1.9517215483530663 " " y[1] (numeric) = 1.9517215483530652 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.68842940511674500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31300000000000017 " " y[1] (analytic) = 1.9514141098512958 " " y[1] (numeric) = 1.9514141098512947 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.68932559737286700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = 1.9511057199354949 " " y[1] (numeric) = 1.9511057199354938 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69022484676976600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = 1.9507963789140532 " " y[1] (numeric) = 1.950796378914052 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69112715517332800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31600000000000017 " " y[1] (analytic) = 1.9504860870963119 " " y[1] (numeric) = 1.9504860870963108 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69203252445622500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = 1.9501748447925626 " " y[1] (numeric) = 1.9501748447925615 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69294095649792500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = 1.9498626523140477 " " y[1] (numeric) = 1.9498626523140468 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.5550819625477595000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = 1.9495495099729596 " " y[1] (numeric) = 1.9495495099729587 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.55581361312770300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 1.949235418082441 " " y[1] (numeric) = 1.9492354180824398 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69568464807261600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = 1.948920376956583 " " y[1] (numeric) = 1.948920376956582 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69660535008039300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = 1.9486043869104273 " " y[1] (numeric) = 1.9486043869104261 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69752912434652500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = 1.9482874482599637 " " y[1] (numeric) = 1.9482874482599626 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.6984559727914300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = 1.9479695613221308 " " y[1] (numeric) = 1.9479695613221297 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.69938589734237500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = 1.9476507264148157 " " y[1] (numeric) = 1.9476507264148146 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.7003188999334910000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = 1.9473309438568531 " " y[1] (numeric) = 1.947330943856852 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.70125498250577900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = 1.9470102139680256 " " y[1] (numeric) = 1.9470102139680245 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.70219414700712500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = 1.946688537069063 " " y[1] (numeric) = 1.946688537069062 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.5625091163138404000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = 1.9463659134816422 " " y[1] (numeric) = 1.9463659134816413 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.56326538369837940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 1.946042343528387 " " y[1] (numeric) = 1.946042343528386 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.564024121334178700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = 1.9457178275328668 " " y[1] (numeric) = 1.945717827532866 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.564785330801633400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = 1.9453923658195982 " " y[1] (numeric) = 1.945392365819597 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.70693626710834300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = 1.9450659587140424 " " y[1] (numeric) = 1.9450659587140413 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.70789396447597900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = 1.9447386065426064 " " y[1] (numeric) = 1.9447386065426056 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.56708380608099200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = 1.944410309632643 " " y[1] (numeric) = 1.944410309632642 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.7098186484873700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = 1.9440810683124483 " " y[1] (numeric) = 1.9440810683124474 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.56862851131565660000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = 1.9437508829112642 " " y[1] (numeric) = 1.9437508829112633 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.56940458527201200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = 1.943419753759276 " " y[1] (numeric) = 1.9434197537592748 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.71272892784785200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = 1.9430876811876123 " " y[1] (numeric) = 1.9430876811876112 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.71370522994922200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 1.942754665528346 " " y[1] (numeric) = 1.942754665528345 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.71468463993225500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = 1.942420707114493 " " y[1] (numeric) = 1.9424207071144919 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.71566715984209400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = 1.9420858062800113 " " y[1] (numeric) = 1.9420858062800102 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.71665279173089200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = 1.9417499633598019 " " y[1] (numeric) = 1.9417499633598008 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.71764153765782600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = 1.9414131786897075 " " y[1] (numeric) = 1.9414131786897064 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.7186333996891100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = 1.9410754526065128 " " y[1] (numeric) = 1.941075452606512 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.575702703918400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = 1.9407367854479443 " " y[1] (numeric) = 1.9407367854479431 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72062648036479800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = 1.9403971775526685 " " y[1] (numeric) = 1.9403971775526674 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72162770317687500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = 1.9400566292602934 " " y[1] (numeric) = 1.9400566292602923 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72263205042866900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = 1.9397151409113675 " " y[1] (numeric) = 1.9397151409113664 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72363952422170000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 1.939372712847379 " " y[1] (numeric) = 1.9393727128473779 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72465012666457300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3510000000000002 " " y[1] (analytic) = 1.9390293454107557 " " y[1] (numeric) = 1.9390293454107548 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.580531087898400700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3520000000000002 " " y[1] (analytic) = 1.9386850389448655 " " y[1] (numeric) = 1.9386850389448644 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72668072596979600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3530000000000002 " " y[1] (analytic) = 1.9383397937940146 " " y[1] (numeric) = 1.9383397937940134 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 5.72770072708489700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3540000000000002 " " y[1] (analytic) = 1.9379936103034479 " " y[1] (numeric) = 1.937993610303447 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.582979092284291700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3550000000000002 " " y[1] (analytic) = 1.9376464888193492 " " y[1] (numeric) = 1.9376464888193483 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.583800114340319500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3560000000000002 " " y[1] (analytic) = 1.9372984296888398 " " y[1] (numeric) = 1.937298429688839 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.58462364955708200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3570000000000002 " " y[1] (analytic) = 1.9369494332599788 " " y[1] (numeric) = 1.936949433259978 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.58544969966138140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3580000000000002 " " y[1] (analytic) = 1.9365994998817626 " " y[1] (numeric) = 1.9365994998817617 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.58627826638575600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3590000000000002 " " y[1] (analytic) = 1.9362486299041246 " " y[1] (numeric) = 1.9362486299041237 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.587109351468485000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 1.9358968236779348 " " y[1] (numeric) = 1.935896823677934 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.587942956653597300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3610000000000002 " " y[1] (analytic) = 1.9355440815549994 " " y[1] (numeric) = 1.9355440815549985 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.58877908369087800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3620000000000002 " " y[1] (analytic) = 1.93519040388806 " " y[1] (numeric) = 1.9351904038880594 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.44221330075190900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3630000000000002 " " y[1] (analytic) = 1.934835791030795 " " y[1] (numeric) = 1.9348357910307943 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.442844182762441000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3640000000000002 " " y[1] (analytic) = 1.9344802433378168 " " y[1] (numeric) = 1.934480243337816 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.44347696012508500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3650000000000002 " " y[1] (analytic) = 1.934123761164673 " " y[1] (numeric) = 1.9341237611646724 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.44411163416950940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3660000000000002 " " y[1] (analytic) = 1.933766344867846 " " y[1] (numeric) = 1.9337663448678455 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.296498804153155300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3670000000000002 " " y[1] (analytic) = 1.9334079948047518 " " y[1] (numeric) = 1.9334079948047513 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.29692445176275180000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3680000000000002 " " y[1] (analytic) = 1.9330487113337407 " " y[1] (numeric) = 1.9330487113337402 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.297351366503617700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3690000000000002 " " y[1] (analytic) = 1.932688494814096 " " y[1] (numeric) = 1.9326884948140957 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.297779549273817300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 1.9323273456060344 " " y[1] (numeric) = 1.932327345606034 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.298209000974331400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3710000000000002 " " y[1] (analytic) = 1.9319652640707048 " " y[1] (numeric) = 1.9319652640707043 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.298639722509059300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3720000000000002 " " y[1] (analytic) = 1.9316022505701884 " " y[1] (numeric) = 1.9316022505701882 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.149535857392411400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3730000000000002 " " y[1] (analytic) = 1.9312383054674995 " " y[1] (numeric) = 1.931238305467499 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.299504978711370600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3740000000000002 " " y[1] (analytic) = 1.9308734291265828 " " y[1] (numeric) = 1.930873429126582 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.449909272802076000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3750000000000002 " " y[1] (analytic) = 1.930507621912314 " " y[1] (numeric) = 1.9305076219123136 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.300375325170478400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3760000000000002 " " y[1] (analytic) = 1.9301408841905014 " " y[1] (numeric) = 1.9301408841905008 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.451218614305813000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3770000000000002 " " y[1] (analytic) = 1.9297732163278818 " " y[1] (numeric) = 1.9297732163278813 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.301250769223075200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3780000000000002 " " y[1] (analytic) = 1.9294046186921237 " " y[1] (numeric) = 1.929404618692123 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.452535607728786600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3790000000000002 " " y[1] (analytic) = 1.929035091651824 " " y[1] (numeric) = 1.9290350916518233 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.45319697737943470000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 1.92866463557651 " " y[1] (numeric) = 1.9286646355765096 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.302573509454726700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3810000000000002 " " y[1] (analytic) = 1.9282932508366382 " " y[1] (numeric) = 1.9282932508366375 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.454525469536727000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38200000000000023 " " y[1] (analytic) = 1.9279209378035926 " " y[1] (numeric) = 1.927920937803592 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.45519259484776900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38300000000000023 " " y[1] (analytic) = 1.9275476968496867 " " y[1] (numeric) = 1.927547696849686 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.45586164152409100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38400000000000023 " " y[1] (analytic) = 1.9271735283481612 " " y[1] (numeric) = 1.9271735283481606 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.4565326109790295000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38500000000000023 " " y[1] (analytic) = 1.9267984326731846 " " y[1] (numeric) = 1.926798432673184 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.45720550463038900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38600000000000023 " " y[1] (analytic) = 1.9264224101998526 " " y[1] (numeric) = 1.926422410199852 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.457880323900443500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38700000000000023 " " y[1] (analytic) = 1.9260454613041875 " " y[1] (numeric) = 1.9260454613041869 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.458557070215950000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38800000000000023 " " y[1] (analytic) = 1.9256675863631383 " " y[1] (numeric) = 1.9256675863631376 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.459235745008152000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38900000000000023 " " y[1] (analytic) = 1.92528878575458 " " y[1] (numeric) = 1.9252887857545793 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.459916349712781600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 1.9249090598573129 " " y[1] (numeric) = 1.9249090598573122 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.46059888577007540000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39100000000000024 " " y[1] (analytic) = 1.9245284090510633 " " y[1] (numeric) = 1.9245284090510624 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.61504447283302870000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39200000000000024 " " y[1] (analytic) = 1.9241468337164813 " " y[1] (numeric) = 1.9241468337164807 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.46196975772612600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39300000000000024 " " y[1] (analytic) = 1.923764334235143 " " y[1] (numeric) = 1.923764334235142 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 4.61687746203721100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39400000000000024 " " y[1] (analytic) = 1.923380910989547 " " y[1] (numeric) = 1.9233809109895463 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.46334837248841840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39500000000000024 " " y[1] (analytic) = 1.922996564363117 " " y[1] (numeric) = 1.9229965643631166 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.30936039138032400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39600000000000024 " " y[1] (analytic) = 1.9226112947401999 " " y[1] (numeric) = 1.9226112947401994 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.309823161160986800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39700000000000024 " " y[1] (analytic) = 1.9222251025060646 " " y[1] (numeric) = 1.9222251025060644 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.155143612657772900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39800000000000024 " " y[1] (analytic) = 1.9218379880469039 " " y[1] (numeric) = 1.9218379880469036 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.15537629241415600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39900000000000024 " " y[1] (analytic) = 1.9214499517498318 " " y[1] (numeric) = 1.9214499517498316 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.155609620343319700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 1.921060994002885 " " y[1] (numeric) = 1.9210609940028847 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.31168719388092280000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40100000000000025 " " y[1] (analytic) = 1.9206711151950207 " " y[1] (numeric) = 1.9206711151950204 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.156078222702304600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40200000000000025 " " y[1] (analytic) = 1.9202803157161181 " " y[1] (numeric) = 1.9202803157161177 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.312626996254196200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40300000000000025 " " y[1] (analytic) = 1.9198885959569765 " " y[1] (numeric) = 1.919888595956976 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.313098847429241000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40400000000000025 " " y[1] (analytic) = 1.9194959563093152 " " y[1] (numeric) = 1.919495956309315 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.156785999966181600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40500000000000025 " " y[1] (analytic) = 1.9191023971657746 " " y[1] (numeric) = 1.9191023971657744 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.15702322738462400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40600000000000025 " " y[1] (analytic) = 1.9187079189199134 " " y[1] (numeric) = 1.918707918919913 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.314522212948654800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40700000000000025 " " y[1] (analytic) = 1.9183125219662096 " " y[1] (numeric) = 1.9183125219662094 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.157499637741209300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40800000000000025 " " y[1] (analytic) = 1.9179162067000606 " " y[1] (numeric) = 1.9179162067000604 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.157738821692727200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40900000000000025 " " y[1] (analytic) = 1.9175189735177813 " " y[1] (numeric) = 1.9175189735177811 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.157978658837882400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 1.917120822816605 " " y[1] (numeric) = 1.9171208228166048 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.158219149687220700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41100000000000025 " " y[1] (analytic) = 1.9167217549946822 " " y[1] (numeric) = 1.916721754994682 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.158460294752836200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41200000000000025 " " y[1] (analytic) = 1.916321770451081 " " y[1] (numeric) = 1.9163217704510807 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.31740418909674500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41300000000000026 " " y[1] (analytic) = 1.9159208695857854 " " y[1] (numeric) = 1.9159208695857852 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.15894454958902600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41400000000000026 " " y[1] (analytic) = 1.9155190527996968 " " y[1] (numeric) = 1.9155190527996966 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.159187660391547300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41500000000000026 " " y[1] (analytic) = 1.9151163204946315 " " y[1] (numeric) = 1.9151163204946313 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.159431427474244300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41600000000000026 " " y[1] (analytic) = 1.9147126730733222 " " y[1] (numeric) = 1.914712673073322 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.159675851356984900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41700000000000026 " " y[1] (analytic) = 1.914308110939416 " " y[1] (numeric) = 1.9143081109394156 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.319841865122396500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41800000000000026 " " y[1] (analytic) = 1.9139026344974748 " " y[1] (numeric) = 1.9139026344974746 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.160166671609878500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41900000000000026 " " y[1] (analytic) = 1.9134962441529755 " " y[1] (numeric) = 1.9134962441529753 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.160413069027585900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 1.9130889403123081 " " y[1] (numeric) = 1.913088940312308 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.160660125340450400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42100000000000026 " " y[1] (analytic) = 1.9126807233827765 " " y[1] (numeric) = 1.9126807233827763 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.160907841076173600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42200000000000026 " " y[1] (analytic) = 1.9122715937725976 " " y[1] (numeric) = 1.9122715937725974 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.161156216764030900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42300000000000026 " " y[1] (analytic) = 1.911861551890901 " " y[1] (numeric) = 1.9118615518909008 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.161405252934874400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42400000000000027 " " y[1] (analytic) = 1.9114505981477283 " " y[1] (numeric) = 1.911450598147728 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.161654950121135100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42500000000000027 " " y[1] (analytic) = 1.9110387329540335 " " y[1] (numeric) = 1.9110387329540333 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.161905308856825700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42600000000000027 " " y[1] (analytic) = 1.910625956721682 " " y[1] (numeric) = 1.9106259567216815 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.32431265935508500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42700000000000027 " " y[1] (analytic) = 1.910212269863449 " " y[1] (numeric) = 1.9102122698634487 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.162408013120469000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42800000000000027 " " y[1] (analytic) = 1.9097976727930224 " " y[1] (numeric) = 1.9097976727930221 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.162660359724376900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42900000000000027 " " y[1] (analytic) = 1.9093821659249988 " " y[1] (numeric) = 1.9093821659249985 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.162913370029629300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 1.908965749674885 " " y[1] (numeric) = 1.9089657496748849 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.163167044578183900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43100000000000027 " " y[1] (analytic) = 1.9085484244590973 " " y[1] (numeric) = 1.9085484244590971 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.163421383913594300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4320000000000003 " " y[1] (analytic) = 1.9081301906949608 " " y[1] (numeric) = 1.9081301906949606 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.163676388581013800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4330000000000003 " " y[1] (analytic) = 1.9077110488007094 " " y[1] (numeric) = 1.9077110488007092 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.163932059127196400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4340000000000003 " " y[1] (analytic) = 1.9072909991954847 " " y[1] (numeric) = 1.9072909991954845 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.164188396100500900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4350000000000003 " " y[1] (analytic) = 1.9068700422993365 " " y[1] (numeric) = 1.9068700422993363 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.164445400050892300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4360000000000003 " " y[1] (analytic) = 1.9064481785332217 " " y[1] (numeric) = 1.9064481785332215 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.164703071529945400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4370000000000003 " " y[1] (analytic) = 1.9060254083190036 " " y[1] (numeric) = 1.9060254083190036 " " 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] = 0.4380000000000003 " " y[1] (analytic) = 1.905601732079453 " " y[1] (numeric) = 1.9056017320794527 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.165220419288395500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4390000000000003 " " y[1] (analytic) = 1.9051771502382455 " " y[1] (numeric) = 1.9051771502382453 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.16548009667901100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 1.9047516632199633 " " y[1] (numeric) = 1.904751663219963 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.165740443820729700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4410000000000003 " " y[1] (analytic) = 1.9043252714500933 " " y[1] (numeric) = 1.9043252714500931 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.16600146127321110000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4420000000000003 " " y[1] (analytic) = 1.9038979753550271 " " y[1] (numeric) = 1.903897975355027 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.166263149597739400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4430000000000003 " " y[1] (analytic) = 1.903469775362061 " " y[1] (numeric) = 1.9034697753620609 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.166525509357226200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4440000000000003 " " y[1] (analytic) = 1.9030406718993949 " " y[1] (numeric) = 1.9030406718993946 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.166788541116213200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4450000000000003 " " y[1] (analytic) = 1.902610665396132 " " y[1] (numeric) = 1.9026106653961319 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.16705224544087500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4460000000000003 " " y[1] (analytic) = 1.9021797562822789 " " y[1] (numeric) = 1.9021797562822789 " " 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] = 0.4470000000000003 " " y[1] (analytic) = 1.9017479449887449 " " y[1] (numeric) = 1.9017479449887447 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.167581674060099600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4480000000000003 " " y[1] (analytic) = 1.9013152319473408 " " y[1] (numeric) = 1.9013152319473408 " " 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] = 0.4490000000000003 " " y[1] (analytic) = 1.9008816175907801 " " y[1] (numeric) = 1.90088161759078 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.16811379977705090000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 1.9004471023526768 " " y[1] (numeric) = 1.9004471023526766 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.168380875480033300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4510000000000003 " " y[1] (analytic) = 1.900011686667546 " " y[1] (numeric) = 1.9000116866675458 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.168648627180173100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4520000000000003 " " y[1] (analytic) = 1.8995753709708039 " " y[1] (numeric) = 1.8995753709708034 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.337834110910296500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4530000000000003 " " y[1] (analytic) = 1.8991381556987657 " " y[1] (numeric) = 1.8991381556987652 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.338372321768582600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4540000000000003 " " y[1] (analytic) = 1.8987000412886466 " " y[1] (numeric) = 1.8987000412886461 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.338911888097182400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4550000000000003 " " y[1] (analytic) = 1.898261028178561 " " y[1] (numeric) = 1.8982610281785606 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.339452811061393800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4560000000000003 " " y[1] (analytic) = 1.8978211168075223 " " y[1] (numeric) = 1.8978211168075219 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.339995091829839300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4570000000000003 " " y[1] (analytic) = 1.8973803076154414 " " y[1] (numeric) = 1.897380307615441 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.340538731574471600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4580000000000003 " " y[1] (analytic) = 1.8969386010431277 " " y[1] (numeric) = 1.8969386010431273 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.341083731470579300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4590000000000003 " " y[1] (analytic) = 1.8964959975322877 " " y[1] (numeric) = 1.8964959975322873 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.341630092696792300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 1.896052497525525 " " y[1] (numeric) = 1.8960524975255244 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.513266724652629500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4610000000000003 " " y[1] (analytic) = 1.8956081014663395 " " y[1] (numeric) = 1.8956081014663388 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.51409035580618640000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4620000000000003 " " y[1] (analytic) = 1.895162809799127 " " y[1] (numeric) = 1.8951628097991264 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 3.514916034288891000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 3 ) = sin(x);" Iterations = 363 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 2 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 37 Minutes 55 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 37 Minutes 47 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 40 Minutes 49 Seconds "Time to Timeout " Unknown Percent Done = 7.428571428571435 "%" (%o60) true (%o60) diffeq.max