(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float glob_small_float)) do m 1, m - 2 array_y_higher 1, m : m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m) rm0 - convfloat(m - 1) rm1, array_y_higher 1, m - 2 if omniabs(hdrc) > glob_small_float glob_small_float glob_h then (rcs : ------, ord_no : hdrc rm1 convfloat((m - 2) (m - 2)) - rm0 convfloat(m - 3) -----------------------------------------------------, hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found_sing : 0, if (1 # found_sing) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found_sing : 1, 1, 2 1, 2 array_type_pole : 2, if glob_display_flag 1 then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if (1 # found_sing) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > - 1.0 glob_smallish_float) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found_sing : 1, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE for equation 1")), if (1 # found_sing) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > - 1.0 1, 1 1, 2 glob_smallish_float)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found_sing : 1, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1"))), if (1 # found_sing) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, 1, 2 1, 2 1 found_sing : 1, if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1"))), if 1 # found_sing then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : 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, 2 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_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, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_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, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_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, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 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 : 1, 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, 2 then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1_g array_x - array_tmp1 array_x 1 2 1 2 array_tmp1 : ----------------------, array_tmp1_g : ----------------------, 2 1 2 1 array_tmp2 : array_tmp1 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_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, 4 then (if 3 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(2, 3), array_y : temporary, 3 4 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h array_y_higher : temporary, 0)), kkk : 4, 2, 3 array_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, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 4.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, 2, 4 array_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, 6 then (if 5 <= glob_max_terms then (temporary : array_tmp2 expt(glob_h, 1) factorial_3(4, 5), array_y : temporary, 5 6 temporary 5.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h array_y_higher : temporary, 0)), kkk : 6, 2, 5 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 : 1, 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(2.0 - cos(x)) (%o56) exact_soln_y(x) := block(2.0 - cos(x)) (%i57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* # Comment 1 */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS, "/* # Comment 2 */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* # Comment 3 */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* # Comment 4 */"), 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, "/* # Comment 5 */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, "/* # Comment 6 */"), omniout_str(ALWAYS, " (2.0 - cos(x)) "), omniout_str(ALWAYS, "/* # Comment 7 */"), 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 : 20, 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 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 20 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 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, "2013-01-28T19:28:20-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "sin diffeq.max"), logitem_str(html_log_file, "sin maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o57) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_max_h, 0.1, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-201, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/sinpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sin(x);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* # Comment 1 */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:20,"), omniout_str(ALWAYS, "/* # Comment 2 */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* # Comment 3 */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:1.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* # Comment 4 */"), 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, "/* # Comment 5 */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, "/* # Comment 6 */"), omniout_str(ALWAYS, " (2.0 - cos(x)) "), omniout_str(ALWAYS, "/* # Comment 7 */"), 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 : 20, 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 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1_g : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 1.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 20 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, if glob_max_h < glob_h then glob_h : glob_max_h, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 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, "2013-01-28T19:28:20-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 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, "sin diffeq.max"), logitem_str(html_log_file, "sin maxima results"), logitem_str(html_log_file, "All Tests - All Languages"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i58) main() "##############ECHO OF PROBLEM#################" "##############temp/sinpostode.ode#################" "diff ( y , x , 1 ) = sin(x);" "!" "/* BEGIN FIRST INPUT BLOCK */" "/* # Comment 1 */" "Digits:32," "max_terms:20," "/* # Comment 2 */" "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "/* # Comment 3 */" "x_start:0.1," "x_end:1.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_look_poles:true," "glob_max_iter:1000000," "/* # Comment 4 */" "/* 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 */" "/* # Comment 5 */" "exact_soln_y (x) := (block(" "/* # Comment 6 */" " (2.0 - cos(x)) " "/* # Comment 7 */" "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 0.9 "" estimated_steps = 900. "" step_error = 1.11111111111111100000000000000E-13 "" est_needed_step_err = 1.11111111111111100000000000000E-13 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 4.755585815822891400000000000000000000000000000000000000000000000000000000000000E-62 "" max_value3 = 4.755585815822891400000000000000000000000000000000000000000000000000000000000000E-62 "" value3 = 4.755585815822891400000000000000000000000000000000000000000000000000000000000000E-62 "" best_h = 1.000E-3 "" "START of Soultion" " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 1.0049958347219743 " " y[1] (numeric) = 1.0049958347219743 " " 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) = 1.0050961656240234 " " y[1] (numeric) = 1.0050961656240234 " " 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) = 1.0051974914298238 " " y[1] (numeric) = 1.0051974914298238 " " 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) = 1.00529981203805 " " y[1] (numeric) = 1.00529981203805 " " 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) = 1.0054031273463815 " " y[1] (numeric) = 1.0054031273463815 " " 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) = 1.0055074372515027 " " y[1] (numeric) = 1.0055074372515025 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.208284063337985500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = 1.0056127416491036 " " y[1] (numeric) = 1.0056127416491034 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20805281922840900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = 1.0057190404338798 " " y[1] (numeric) = 1.0057190404338798 " " 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) = 1.0058263334995332 " " y[1] (numeric) = 1.005826333499533 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.207583929051449300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = 1.00593462073877 " " y[1] (numeric) = 1.0059346207387698 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.207346286202568300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = 1.0060439020433032 " " y[1] (numeric) = 1.006043902043303 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.2071065136824800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = 1.0061541773038516 " " y[1] (numeric) = 1.0061541773038514 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.206864613135481600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = 1.0062654464101397 " " y[1] (numeric) = 1.0062654464101397 " " 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) = 1.0063777092508988 " " y[1] (numeric) = 1.0063777092508988 " " 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) = 1.0064909657138656 " " y[1] (numeric) = 1.0064909657138656 " " 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) = 1.0066052156857843 " " y[1] (numeric) = 1.006605215685784 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20587576405270070000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = 1.0067204590524041 " " y[1] (numeric) = 1.0067204590524041 " " 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) = 1.0068366956984822 " " y[1] (numeric) = 1.0068366956984822 " " 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) = 1.006953925507782 " " y[1] (numeric) = 1.006953925507782 " " 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) = 1.0070721483630733 " " y[1] (numeric) = 1.0070721483630733 " " 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) = 1.0071913641461339 " " y[1] (numeric) = 1.0071913641461336 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.204592025203412600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = 1.007311572737747 " " y[1] (numeric) = 1.007311572737747 " " 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) = 1.0074327740177051 " " y[1] (numeric) = 1.0074327740177051 " " 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) = 1.0075549678648064 " " y[1] (numeric) = 1.0075549678648064 " " 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) = 1.0076781541568571 " " y[1] (numeric) = 1.0076781541568571 " " 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) = 1.0078023327706709 " " y[1] (numeric) = 1.0078023327706709 " " 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) = 1.0079275035820694 " " y[1] (numeric) = 1.0079275035820692 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20298190232837100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = 1.0080536664658815 " " y[1] (numeric) = 1.0080536664658812 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.202706188287512400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = 1.0081808212959444 " " y[1] (numeric) = 1.0081808212959442 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.202428376286793800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = 1.0083089679451036 " " y[1] (numeric) = 1.0083089679451032 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.40429693643506900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = 1.008438106285212 " " y[1] (numeric) = 1.0084381062852117 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20186646598449200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = 1.0085682361871315 " " y[1] (numeric) = 1.0085682361871313 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20158237150582600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = 1.0086993575207321 " " y[1] (numeric) = 1.0086993575207321 " " 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) = 1.0088314701548928 " " y[1] (numeric) = 1.0088314701548928 " " 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) = 1.0089645739575008 " " y[1] (numeric) = 1.0089645739575006 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.20071755397810600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = 1.0090986687954522 " " y[1] (numeric) = 1.009098668795452 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.200425109965540300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = 1.0092337545346521 " " y[1] (numeric) = 1.009233754534652 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.200130583498110500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = 1.009369831040015 " " y[1] (numeric) = 1.0093698310400148 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19983397657373300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = 1.0095068981754642 " " y[1] (numeric) = 1.009506898175464 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.199535291203501300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = 1.0096449558039327 " " y[1] (numeric) = 1.0096449558039327 " " 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) = 1.0097840037873629 " " y[1] (numeric) = 1.0097840037873629 " " 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) = 1.0099240419867068 " " y[1] (numeric) = 1.0099240419867068 " " 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) = 1.010065070261926 " " y[1] (numeric) = 1.0100650702619263 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.1983198059452900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = 1.0102070884719927 " " y[1] (numeric) = 1.010207088471993 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.198010758971103400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = 1.0103500964748884 " " y[1] (numeric) = 1.0103500964748886 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.197699645892497700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = 1.0104940941276053 " " y[1] (numeric) = 1.0104940941276053 " " 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) = 1.0106390812861454 " " y[1] (numeric) = 1.0106390812861454 " " 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) = 1.010785057805522 " " y[1] (numeric) = 1.010785057805522 " " 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) = 1.010932023539758 " " y[1] (numeric) = 1.010932023539758 " " 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) = 1.0110799783418882 " " y[1] (numeric) = 1.0110799783418882 " " 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) = 1.0112289220639576 " " y[1] (numeric) = 1.0112289220639576 " " 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) = 1.0113788545570226 " " y[1] (numeric) = 1.0113788545570226 " " 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) = 1.0115297756711508 " " y[1] (numeric) = 1.0115297756711508 " " 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) = 1.0116816852554207 " " y[1] (numeric) = 1.011681685255421 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.194807004625880800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.0118345831579232 " " y[1] (numeric) = 1.0118345831579234 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19447534825339570000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.0119884692257601 " " y[1] (numeric) = 1.0119884692257604 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.194141649607040700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.0121433433050455 " " y[1] (numeric) = 1.0121433433050457 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19380591092926100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.0122992052409052 " " y[1] (numeric) = 1.0122992052409054 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.193468134475019300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.0124560548774775 " " y[1] (numeric) = 1.0124560548774777 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.193128322511756500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.0126138920579124 " " y[1] (numeric) = 1.0126138920579126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.192786477319356700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.0127727166243732 " " y[1] (numeric) = 1.0127727166243734 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.192442601190108300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.0129325284180348 " " y[1] (numeric) = 1.0129325284180353 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.38419339285733840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = 1.013093327279086 " " y[1] (numeric) = 1.0130933272790863 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.191748765352026200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = 1.0132551130467276 " " y[1] (numeric) = 1.0132551130467278 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19139881028946220000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = 1.0134178855591738 " " y[1] (numeric) = 1.013417885559174 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19104683358251280000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = 1.0135816446536523 " " y[1] (numeric) = 1.0135816446536525 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.190692837584933300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = 1.0137463901664039 " " y[1] (numeric) = 1.013746390166404 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.19033682466265780000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = 1.0139121219326834 " " y[1] (numeric) = 1.0139121219326834 " " 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) = 1.0140788397867584 " " y[1] (numeric) = 1.0140788397867586 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.189618757568426400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = 1.014246543561912 " " y[1] (numeric) = 1.014246543561912 " " 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) = 1.0144152330904395 " " y[1] (numeric) = 1.0144152330904395 " " 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) = 1.0145849082036515 " " y[1] (numeric) = 1.0145849082036518 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.188526589836300200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = 1.0147555687318737 " " y[1] (numeric) = 1.0147555687318737 " " 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) = 1.0149272145044448 " " y[1] (numeric) = 1.0149272145044448 " " 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) = 1.0150998453497193 " " y[1] (numeric) = 1.0150998453497193 " " 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) = 1.0152734610950667 " " y[1] (numeric) = 1.0152734610950664 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.187042343109565600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = 1.0154480615668704 " " y[1] (numeric) = 1.0154480615668704 " " 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) = 1.015623646590531 " " y[1] (numeric) = 1.0156236465905308 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.1862882542213300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = 1.0158002159904627 " " y[1] (numeric) = 1.0158002159904627 " " 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) = 1.0159777695900964 " " y[1] (numeric) = 1.0159777695900964 " " 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) = 1.0161563072118787 " " y[1] (numeric) = 1.0161563072118787 " " 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) = 1.0163358286772715 " " y[1] (numeric) = 1.0163358286772717 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.18475624552186900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = 1.016516333806754 " " y[1] (numeric) = 1.016516333806754 " " 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) = 1.0166978224198204 " " y[1] (numeric) = 1.0166978224198207 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.183978366320759600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = 1.0168802943349826 " " y[1] (numeric) = 1.0168802943349828 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.18358646698177600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = 1.0170637493697685 " " y[1] (numeric) = 1.0170637493697687 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.183192597933246400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = 1.0172481873407233 " " y[1] (numeric) = 1.0172481873407233 " " 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) = 1.0174336080634085 " " y[1] (numeric) = 1.0174336080634088 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.182398961124085700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = 1.017620011352404 " " y[1] (numeric) = 1.0176200113524043 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.181999198600043700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = 1.0178073970213064 " " y[1] (numeric) = 1.0178073970213066 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.18159747683955100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = 1.0179957648827296 " " y[1] (numeric) = 1.01799576488273 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.36238759697807300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = 1.0181851147483063 " " y[1] (numeric) = 1.0181851147483068 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.36157633241221300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = 1.0183754464286865 " " y[1] (numeric) = 1.018375446428687 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.3607611653190100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = 1.0185667597335382 " " y[1] (numeric) = 1.0185667597335388 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.53991315158721300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = 1.0187590544715488 " " y[1] (numeric) = 1.0187590544715492 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.359119145011386400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = 1.0189523304504227 " " y[1] (numeric) = 1.0189523304504233 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.53743845387382300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = 1.0191465874768846 " " y[1] (numeric) = 1.0191465874768852 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.53619236879604100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = 1.0193418253566775 " " y[1] (numeric) = 1.019341825356678 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.356626980303408600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = 1.019538043894563 " " y[1] (numeric) = 1.0195380438945636 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.53368276705506800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = 1.019735242894323 " " y[1] (numeric) = 1.0197352428943236 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.53241926683244500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = 1.0199334221587584 " " y[1] (numeric) = 1.019933422158759 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.5311499780561800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = 1.02013258148969 " " y[1] (numeric) = 1.0201325814896907 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.52987490902746200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = 1.0203327206879584 " " y[1] (numeric) = 1.020332720687959 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.52859406807961400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = 1.0205338395534245 " " y[1] (numeric) = 1.0205338395534251 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.52730746357795900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = 1.0207359378849694 " " y[1] (numeric) = 1.02073593788497 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.52601510391968800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = 1.020939015480495 " " y[1] (numeric) = 1.0209390154804956 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.52471699753373300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = 1.0211430721369235 " " y[1] (numeric) = 1.021143072136924 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.34894210192041900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = 1.021348107650198 " " y[1] (numeric) = 1.0213481076501987 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.52210357845239600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = 1.0215541218152835 " " y[1] (numeric) = 1.0215541218152842 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.5207882827723910000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = 1.0217611144261656 " " y[1] (numeric) = 1.0217611144261662 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.51946727439518400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = 1.0219690852758516 " " y[1] (numeric) = 1.0219690852758525 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.69085408254190600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = 1.0221780341563713 " " y[1] (numeric) = 1.022178034156372 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.51680815392272200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = 1.022387960858775 " " y[1] (numeric) = 1.0223879608587758 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.68729341212197200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = 1.0225988651731364 " " y[1] (numeric) = 1.0225988651731373 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.6855017147877200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = 1.0228107468885512 " " y[1] (numeric) = 1.0228107468885521 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.68370245817239200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = 1.0230236057931377 " " y[1] (numeric) = 1.0230236057931386 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.68189565392805800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = 1.0232374416740369 " " y[1] (numeric) = 1.0232374416740377 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.68008131374715600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = 1.0234522543174132 " " y[1] (numeric) = 1.023452254317414 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.67825944936231300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = 1.0236680435084535 " " y[1] (numeric) = 1.0236680435084546 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.08455375906827190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = 1.0238848090313692 " " y[1] (numeric) = 1.0238848090313704 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.08432414938890080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = 1.0241025506693946 " " y[1] (numeric) = 1.0241025506693957 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0840936036136910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = 1.0243212682047877 " " y[1] (numeric) = 1.024321268204789 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.30063454787490930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = 1.0245409614188317 " " y[1] (numeric) = 1.0245409614188328 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.08362970972645970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = 1.0247616300918327 " " y[1] (numeric) = 1.0247616300918339 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.08339636460204430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = 1.0249832740031222 " " y[1] (numeric) = 1.0249832740031235 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2997945072283490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = 1.0252058929310568 " " y[1] (numeric) = 1.025205892931058 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.08292688549715260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = 1.025429486653017 " " y[1] (numeric) = 1.0254294866530183 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29922890544008550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = 1.0256540549454094 " " y[1] (numeric) = 1.0256540549454107 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29894443757753970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = 1.0258795975836656 " " y[1] (numeric) = 1.025879597583667 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2986588608333590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = 1.0261061143422432 " " y[1] (numeric) = 1.0261061143422445 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29837217703765550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = 1.0263336049946252 " " y[1] (numeric) = 1.0263336049946266 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29808438802621550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = 1.026562069313321 " " y[1] (numeric) = 1.0265620693133224 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29779549564047000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = 1.0267915070698665 " " y[1] (numeric) = 1.0267915070698679 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29750550172746560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = 1.0270219180348237 " " y[1] (numeric) = 1.0270219180348252 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.5134168094964810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = 1.0272533019777819 " " y[1] (numeric) = 1.0272533019777834 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.51307591952509170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = 1.027485658667357 " " y[1] (numeric) = 1.0274856586673586 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.51273375094223030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = 1.0277189878711925 " " y[1] (numeric) = 1.027718987871194 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.51239030592867300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = 1.0279532893559589 " " y[1] (numeric) = 1.0279532893559606 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7280520990532430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = 1.028188562887355 " " y[1] (numeric) = 1.0281885628873568 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7276566804165690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = 1.0284248082301075 " " y[1] (numeric) = 1.028424808230109 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.51135233420725270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = 1.0286620251479706 " " y[1] (numeric) = 1.0286620251479721 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.51100380540599320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = 1.0289002134037273 " " y[1] (numeric) = 1.028900213403729 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.72646172705499370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = 1.02913937275919 " " y[1] (numeric) = 1.0291393727591918 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.72606051854543420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = 1.029379502975199 " " y[1] (numeric) = 1.0293795029752006 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50995063529321820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = 1.0296206038116242 " " y[1] (numeric) = 1.0296206038116258 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50959705810198660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = 1.0298626750273647 " " y[1] (numeric) = 1.0298626750273663 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50924222439066360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = 1.030105716380349 " " y[1] (numeric) = 1.0301057163803509 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7244412987456530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = 1.0303497276275366 " " y[1] (numeric) = 1.0303497276275382 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50852879638659040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = 1.0305947085249154 " " y[1] (numeric) = 1.0305947085249172 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.72362309325529150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = 1.0308406588275052 " " y[1] (numeric) = 1.0308406588275068 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50781036929909130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 1.0310875782893554 " " y[1] (numeric) = 1.0310875782893567 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2920993886479660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = 1.0313354666635464 " " y[1] (numeric) = 1.0313354666635477 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2917888239218430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = 1.03158432370219 " " y[1] (numeric) = 1.0315843237021913 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29147719574575740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = 1.0318341491564291 " " y[1] (numeric) = 1.0318341491564305 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29116450607820700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = 1.0320849427764385 " " y[1] (numeric) = 1.0320849427764398 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29085075688268460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = 1.0323367043114244 " " y[1] (numeric) = 1.0323367043114258 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29053595012764670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = 1.0325894335096255 " " y[1] (numeric) = 1.0325894335096268 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.29022008778648700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = 1.0328431301183123 " " y[1] (numeric) = 1.0328431301183136 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2899031718375050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = 1.0330977938837886 " " y[1] (numeric) = 1.0330977938837898 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07465433688656530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = 1.0333534245513902 " " y[1] (numeric) = 1.0333534245513916 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28926618705363570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 1.0336100218654867 " " y[1] (numeric) = 1.0336100218654882 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.50377047589956150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = 1.033867585569481 " " y[1] (numeric) = 1.0338675855694823 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28862501169948200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = 1.034126115405809 " " y[1] (numeric) = 1.0341261154058103 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28830285755561130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = 1.0343856111159413 " " y[1] (numeric) = 1.0343856111159426 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2879796617751460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = 1.034646072440382 " " y[1] (numeric) = 1.0346460724403832 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07304618864160360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = 1.0349074991186697 " " y[1] (numeric) = 1.0349074991186709 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07277512779705030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = 1.035169890889378 " " y[1] (numeric) = 1.0351698908893792 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07250320396326040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = 1.035433247490115 " " y[1] (numeric) = 1.035433247490116 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07223041882838090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000001 " " y[1] (analytic) = 1.035697568657524 " " y[1] (numeric) = 1.0356975686575252 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07195677408438130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.26900000000000013 " " y[1] (analytic) = 1.035962854127284 " " y[1] (numeric) = 1.0359628541272852 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07168227142702980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 1.0362291036341094 " " y[1] (numeric) = 1.0362291036341107 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28568829506704260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27100000000000013 " " y[1] (analytic) = 1.0364963169117511 " " y[1] (numeric) = 1.0364963169117523 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07113069917418980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = 1.0367644936929956 " " y[1] (numeric) = 1.0367644936929967 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07085363298901060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = 1.0370336337096662 " " y[1] (numeric) = 1.0370336337096673 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.07057571571104990000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27400000000000013 " " y[1] (analytic) = 1.0373037366926225 " " y[1] (numeric) = 1.0373037366926239 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28435633886564320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27500000000000013 " " y[1] (analytic) = 1.0375748023717621 " " y[1] (numeric) = 1.0375748023717635 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28402080168561920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = 1.037846830476019 " " y[1] (numeric) = 1.0378468304760204 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28368424937919750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = 1.0381198207333653 " " y[1] (numeric) = 1.0381198207333668 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49723779801949730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = 1.038393772870811 " " y[1] (numeric) = 1.0383937728708124 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28300810767278980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.27900000000000014 " " y[1] (analytic) = 1.0386686866144035 " " y[1] (numeric) = 1.0386686866144048 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28266852242632430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 1.0389445616892292 " " y[1] (numeric) = 1.0389445616892306 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2823279303604440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28100000000000014 " " y[1] (analytic) = 1.039221397819413 " " y[1] (numeric) = 1.0392213978194145 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49565072248956380000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = 1.0394991947281191 " " y[1] (numeric) = 1.0394991947281205 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28164373412395230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = 1.0397779521375505 " " y[1] (numeric) = 1.0397779521375519 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28130013414050950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = 1.0400576697689496 " " y[1] (numeric) = 1.040057669768951 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.28095553571193150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28500000000000014 " " y[1] (analytic) = 1.040338347342599 " " y[1] (numeric) = 1.0403383473426004 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49404493109909470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28600000000000014 " " y[1] (analytic) = 1.040619984577821 " " y[1] (numeric) = 1.0406199845778226 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49364057726202800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28700000000000014 " " y[1] (analytic) = 1.0409025811929786 " " y[1] (numeric) = 1.0409025811929802 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49323506594999660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28800000000000014 " " y[1] (analytic) = 1.041186136905475 " " y[1] (numeric) = 1.0411861369054767 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.70608959957898350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = 1.0414706514317547 " " y[1] (numeric) = 1.0414706514317562 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49242058078011050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 1.041756124487303 " " y[1] (numeric) = 1.0417561244873046 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.49201161187333450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = 1.0420425557866468 " " y[1] (numeric) = 1.0420425557866486 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7046874233070680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = 1.0423299450433552 " " y[1] (numeric) = 1.042329945043357 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.70421741008924350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = 1.0426182919700386 " " y[1] (numeric) = 1.0426182919700404 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.70374609104910760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = 1.0429075962783503 " " y[1] (numeric) = 1.042907596278352 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.70327346903909580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = 1.0431978576789862 " " y[1] (numeric) = 1.0431978576789878 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.4899496035521131000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = 1.0434890758816846 " " y[1] (numeric) = 1.0434890758816862 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.48953378660137900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = 1.0437812505952273 " " y[1] (numeric) = 1.0437812505952289 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.48911683706605800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = 1.0440743815274396 " " y[1] (numeric) = 1.0440743815274414 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7013700085251690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = 1.0443684683851908 " " y[1] (numeric) = 1.0443684683851926 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7008909146279230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 1.044663510874394 " " y[1] (numeric) = 1.0446635108743958 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.7004105349802268000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = 1.0449595087000068 " " y[1] (numeric) = 1.0449595087000085 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.6999288724690840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = 1.0452564615660314 " " y[1] (numeric) = 1.045256461566033 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.48701518873799320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30300000000000016 " " y[1] (analytic) = 1.0455543691755145 " " y[1] (numeric) = 1.0455543691755163 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.69896171042833470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30400000000000016 " " y[1] (analytic) = 1.045853231230549 " " y[1] (numeric) = 1.0458532312305509 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.69847621669647870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = 1.046153047432273 " " y[1] (numeric) = 1.0461530474322747 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.48574077023452320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30600000000000016 " " y[1] (analytic) = 1.04645381748087 " " y[1] (numeric) = 1.0464538174808715 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.4853137410468029000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30700000000000016 " " y[1] (analytic) = 1.0467555410755698 " " y[1] (numeric) = 1.0467555410755716 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.69701211953938700000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30800000000000016 " " y[1] (analytic) = 1.0470582179146493 " " y[1] (numeric) = 1.047058217914651 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.69652155821678470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.30900000000000016 " " y[1] (analytic) = 1.0473618476954316 " " y[1] (numeric) = 1.0473618476954332 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.48402602013359450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 1.0476664301142866 " " y[1] (numeric) = 1.0476664301142882 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.4835945772412160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = 1.0479719648666324 " " y[1] (numeric) = 1.0479719648666337 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.27128174628195870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = 1.0482784516469337 " " y[1] (numeric) = 1.048278451646935 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2709100596860340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31300000000000017 " " y[1] (analytic) = 1.0485858901487042 " " y[1] (numeric) = 1.0485858901487055 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.27053743719673120000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = 1.0488942800645051 " " y[1] (numeric) = 1.0488942800645065 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2701638810236010000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = 1.0492036210859468 " " y[1] (numeric) = 1.0492036210859481 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2697893933793940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31600000000000017 " " y[1] (analytic) = 1.0495139129036881 " " y[1] (numeric) = 1.0495139129036894 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26941397648003100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = 1.0498251552074374 " " y[1] (numeric) = 1.0498251552074387 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26903763254457540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = 1.0501373476859523 " " y[1] (numeric) = 1.0501373476859535 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05721696982933420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = 1.0504504900270404 " " y[1] (numeric) = 1.0504504900270415 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05690181038097050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 1.050764581917559 " " y[1] (numeric) = 1.0507645819175604 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2679030607587752000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = 1.051079623043417 " " y[1] (numeric) = 1.0510796230434183 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26752303093136430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = 1.0513956130895727 " " y[1] (numeric) = 1.051395613089574 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26714208520925850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = 1.0517125517400363 " " y[1] (numeric) = 1.0517125517400376 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2667602258297470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = 1.0520304386778692 " " y[1] (numeric) = 1.0520304386778705 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26637745503305450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = 1.0523492735851843 " " y[1] (numeric) = 1.0523492735851856 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26599377506231070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = 1.0526690561431469 " " y[1] (numeric) = 1.0526690561431482 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26560918816352100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = 1.0529897860319744 " " y[1] (numeric) = 1.0529897860319757 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26522369658553650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = 1.053311462930937 " " y[1] (numeric) = 1.0533114629309381 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05403108548335530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = 1.0536340865183578 " " y[1] (numeric) = 1.0536340865183589 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05370834033453880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 1.053957656471613 " " y[1] (numeric) = 1.0539576564716142 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0533848469225090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = 1.0542821724671332 " " y[1] (numeric) = 1.0542821724671343 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.0530606071305519000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = 1.0546076341804018 " " y[1] (numeric) = 1.0546076341804032 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26328274741304340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = 1.0549340412859576 " " y[1] (numeric) = 1.054934041285959 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2628918751414660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = 1.0552613934573936 " " y[1] (numeric) = 1.0552613934573947 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05208342834156950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = 1.055589690367357 " " y[1] (numeric) = 1.0555896903673583 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26210746628886070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = 1.0559189316875517 " " y[1] (numeric) = 1.0559189316875528 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05142827854295310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = 1.0562491170887358 " " y[1] (numeric) = 1.056249117088737 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.05109960014469430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = 1.056580246240724 " " y[1] (numeric) = 1.0565802462407254 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.26092422633335230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = 1.0569123188123877 " " y[1] (numeric) = 1.056912318812389 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2605280550114190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 1.057245334471654 " " y[1] (numeric) = 1.0572453344716553 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2601310084910170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = 1.057579292885507 " " y[1] (numeric) = 1.0575792928855083 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25973308905776630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = 1.0579141937199887 " " y[1] (numeric) = 1.05791419371999 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25933429899969330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = 1.0582500366401981 " " y[1] (numeric) = 1.0582500366401995 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25893464060720360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = 1.0585868213102925 " " y[1] (numeric) = 1.0585868213102938 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25853411617305040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = 1.0589245473934872 " " y[1] (numeric) = 1.0589245473934883 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04844393999358980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = 1.0592632145520557 " " y[1] (numeric) = 1.059263214552057 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25773047836234080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = 1.0596028224473315 " " y[1] (numeric) = 1.0596028224473328 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25732736958277520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = 1.0599433707397066 " " y[1] (numeric) = 1.059943370739708 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.2569234039554710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = 1.0602848590886325 " " y[1] (numeric) = 1.0602848590886338 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25651858378449170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 1.060627287152621 " " y[1] (numeric) = 1.0606272871526223 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25611291137607580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3510000000000002 " " y[1] (analytic) = 1.0609706545892443 " " y[1] (numeric) = 1.0609706545892454 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04642199086550630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3520000000000002 " " y[1] (analytic) = 1.0613149610551345 " " y[1] (numeric) = 1.0613149610551358 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25529901908259050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3530000000000002 " " y[1] (analytic) = 1.0616602062059854 " " y[1] (numeric) = 1.0616602062059868 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.25489080382061390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3540000000000002 " " y[1] (analytic) = 1.0620063896965521 " " y[1] (numeric) = 1.0620063896965533 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04540145463944090000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3550000000000002 " " y[1] (analytic) = 1.0623535111806508 " " y[1] (numeric) = 1.062353511180652 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04505987219951450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3560000000000002 " " y[1] (analytic) = 1.0627015703111602 " " y[1] (numeric) = 1.0627015703111613 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04471759112963580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3570000000000002 " " y[1] (analytic) = 1.0630505667400212 " " y[1] (numeric) = 1.0630505667400223 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04437461336368570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3580000000000002 " " y[1] (analytic) = 1.0634005001182374 " " y[1] (numeric) = 1.0634005001182385 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04403094083716630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3590000000000002 " " y[1] (analytic) = 1.0637513700958754 " " y[1] (numeric) = 1.0637513700958765 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04368657548717670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 1.0641031763220652 " " y[1] (numeric) = 1.0641031763220663 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04334151925238930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3610000000000002 " " y[1] (analytic) = 1.0644559184450006 " " y[1] (numeric) = 1.0644559184450018 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.04299577407302530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3620000000000002 " " y[1] (analytic) = 1.06480959611194 " " y[1] (numeric) = 1.0648095961119408 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.34119473512665400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3630000000000002 " " y[1] (analytic) = 1.065164208969205 " " y[1] (numeric) = 1.065164208969206 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.33841779719246400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3640000000000002 " " y[1] (analytic) = 1.0655197566621832 " " y[1] (numeric) = 1.0655197566621841 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.3356353943394490000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3650000000000002 " " y[1] (analytic) = 1.065876238835327 " " y[1] (numeric) = 1.0658762388353278 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.33284754213706400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3660000000000002 " " y[1] (analytic) = 1.066233655132154 " " y[1] (numeric) = 1.0662336551321547 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.24754069212465600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3670000000000002 " " y[1] (analytic) = 1.0665920051952482 " " y[1] (numeric) = 1.0665920051952489 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.2454416640142810000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3680000000000002 " " y[1] (analytic) = 1.0669512886662593 " " y[1] (numeric) = 1.06695128866626 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.24333858397409500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3690000000000002 " " y[1] (analytic) = 1.067311505185904 " " y[1] (numeric) = 1.0673115051859046 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.24123146371468200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 1.0676726543939656 " " y[1] (numeric) = 1.0676726543939663 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.23912031495464400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3710000000000002 " " y[1] (analytic) = 1.0680347359292952 " " y[1] (numeric) = 1.0680347359292959 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.23700514942046400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3720000000000002 " " y[1] (analytic) = 1.0683977494298116 " " y[1] (numeric) = 1.068397749429812 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.156590652564240400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3730000000000002 " " y[1] (analytic) = 1.0687616945325005 " " y[1] (numeric) = 1.0687616945325011 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.23276281497415900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3740000000000002 " " y[1] (analytic) = 1.0691265708734172 " " y[1] (numeric) = 1.0691265708734181 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.30751422607084500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3750000000000002 " " y[1] (analytic) = 1.069492378087686 " " y[1] (numeric) = 1.0694923780876866 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.22850455433987900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3760000000000002 " " y[1] (analytic) = 1.0698591158094986 " " y[1] (numeric) = 1.0698591158094994 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.30182597479756500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3770000000000002 " " y[1] (analytic) = 1.0702267836721182 " " y[1] (numeric) = 1.0702267836721189 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.2242304615988300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3780000000000002 " " y[1] (analytic) = 1.0705953813078763 " " y[1] (numeric) = 1.0705953813078772 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.29611667682608300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3790000000000002 " " y[1] (analytic) = 1.070964908348176 " " y[1] (numeric) = 1.070964908348177 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.29325417459312300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 1.07133536442349 " " y[1] (numeric) = 1.0713353644234906 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.21778984336576700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.3810000000000002 " " y[1] (analytic) = 1.0717067491633618 " " y[1] (numeric) = 1.0717067491633627 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.28751354223989300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38200000000000023 " " y[1] (analytic) = 1.0720790621964074 " " y[1] (numeric) = 1.0720790621964083 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.2846354435882910000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38300000000000023 " " y[1] (analytic) = 1.0724523031503133 " " y[1] (numeric) = 1.0724523031503141 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.28175217761306400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38400000000000023 " " y[1] (analytic) = 1.0728264716518388 " " y[1] (numeric) = 1.0728264716518396 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.27886376006914200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38500000000000023 " " y[1] (analytic) = 1.0732015673268154 " " y[1] (numeric) = 1.0732015673268163 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.27597020671936600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38600000000000023 " " y[1] (analytic) = 1.0735775898001474 " " y[1] (numeric) = 1.0735775898001483 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.27307153333430400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38700000000000023 " " y[1] (analytic) = 1.0739545386958125 " " y[1] (numeric) = 1.0739545386958134 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.27016775569206300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38800000000000023 " " y[1] (analytic) = 1.0743324136368617 " " y[1] (numeric) = 1.0743324136368626 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.2672588895781100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.38900000000000023 " " y[1] (analytic) = 1.07471121424542 " " y[1] (numeric) = 1.074711214245421 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.26434495078509200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 1.0750909401426871 " " y[1] (numeric) = 1.075090940142688 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.26142595511264600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39100000000000024 " " y[1] (analytic) = 1.0754715909489367 " " y[1] (numeric) = 1.0754715909489379 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.03231273979590400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39200000000000024 " " y[1] (analytic) = 1.0758531662835187 " " y[1] (numeric) = 1.0758531662835196 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.25557285636192700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39300000000000024 " " y[1] (analytic) = 1.076235665764857 " " y[1] (numeric) = 1.0762356657648582 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.03157984811453480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39400000000000024 " " y[1] (analytic) = 1.076619089010453 " " y[1] (numeric) = 1.076619089010454 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.24969971985609000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39500000000000024 " " y[1] (analytic) = 1.077003435636883 " " y[1] (numeric) = 1.0770034356368836 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.18506675775994700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39600000000000024 " " y[1] (analytic) = 1.0773887052598001 " " y[1] (numeric) = 1.0773887052598008 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.18285500416920800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39700000000000024 " " y[1] (analytic) = 1.0777748974939354 " " y[1] (numeric) = 1.0777748974939358 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.12042636066833670000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39800000000000024 " " y[1] (analytic) = 1.0781620119530961 " " y[1] (numeric) = 1.0781620119530966 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.11894692009777500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.39900000000000024 " " y[1] (analytic) = 1.0785500482501682 " " y[1] (numeric) = 1.0785500482501686 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.11746502232835400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 1.078939005997115 " " y[1] (numeric) = 1.0789390059971156 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.17397101293486100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40100000000000025 " " y[1] (analytic) = 1.0793288848049793 " " y[1] (numeric) = 1.0793288848049798 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.114493886914772400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40200000000000025 " " y[1] (analytic) = 1.0797196842838819 " " y[1] (numeric) = 1.0797196842838825 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.16950699770657200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40300000000000025 " " y[1] (analytic) = 1.0801114040430235 " " y[1] (numeric) = 1.0801114040430242 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.16726952684373400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40400000000000025 " " y[1] (analytic) = 1.0805040436906848 " " y[1] (numeric) = 1.0805040436906852 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.11001895312843200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40500000000000025 " " y[1] (analytic) = 1.0808976028342254 " " y[1] (numeric) = 1.0808976028342259 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.108522478777034700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40600000000000025 " " y[1] (analytic) = 1.0812920810800866 " " y[1] (numeric) = 1.0812920810800872 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.16053540417777500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40700000000000025 " " y[1] (analytic) = 1.0816874780337904 " " y[1] (numeric) = 1.0816874780337908 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.105522333098413600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40800000000000025 " " y[1] (analytic) = 1.0820837932999394 " " y[1] (numeric) = 1.0820837932999399 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.10401867766415130000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.40900000000000025 " " y[1] (analytic) = 1.0824810264822187 " " y[1] (numeric) = 1.082481026482219 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.102512644431624600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 1.082879177183395 " " y[1] (numeric) = 1.0828791771833954 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.10100424135177830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41100000000000025 " " y[1] (analytic) = 1.0832782450053178 " " y[1] (numeric) = 1.0832782450053182 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.09949347637718500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41200000000000025 " " y[1] (analytic) = 1.083678229548919 " " y[1] (numeric) = 1.0836782295489196 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.14697053619294500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41300000000000026 " " y[1] (analytic) = 1.0840791304142146 " " y[1] (numeric) = 1.084079130414215 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.09646489256168100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41400000000000026 " " y[1] (analytic) = 1.0844809472003032 " " y[1] (numeric) = 1.0844809472003036 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.094947089633281000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41500000000000026 " " y[1] (analytic) = 1.0848836795053685 " " y[1] (numeric) = 1.084883679505369 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.09342695663498600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41600000000000026 " " y[1] (analytic) = 1.0852873269266778 " " y[1] (numeric) = 1.0852873269266783 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.091904501526215700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41700000000000026 " " y[1] (analytic) = 1.085691889060584 " " y[1] (numeric) = 1.0856918890605847 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.13556959840124700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41800000000000026 " " y[1] (analytic) = 1.0860973655025252 " " y[1] (numeric) = 1.0860973655025257 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.0888526568203900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.41900000000000026 " " y[1] (analytic) = 1.0865037558470245 " " y[1] (numeric) = 1.086503755847025 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.08732328314738600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 1.0869110596876919 " " y[1] (numeric) = 1.0869110596876923 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.08579161921183500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42100000000000026 " " y[1] (analytic) = 1.0873192766172235 " " y[1] (numeric) = 1.087319276617224 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.08425767297785500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42200000000000026 " " y[1] (analytic) = 1.0877284062274024 " " y[1] (numeric) = 1.0877284062274029 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.08272145241024900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42300000000000026 " " y[1] (analytic) = 1.088138448109099 " " y[1] (numeric) = 1.0881384481090994 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.081182965474420000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42400000000000027 " " y[1] (analytic) = 1.0885494018522717 " " y[1] (numeric) = 1.0885494018522721 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.079642220136284000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42500000000000027 " " y[1] (analytic) = 1.0889612670459665 " " y[1] (numeric) = 1.088961267045967 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.07809922436219200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42600000000000027 " " y[1] (analytic) = 1.089374043278318 " " y[1] (numeric) = 1.0893740432783188 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.11483097917826100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42700000000000027 " " y[1] (analytic) = 1.089787730136551 " " y[1] (numeric) = 1.0897877301365515 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.075006513373186000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42800000000000027 " " y[1] (analytic) = 1.0902023272069776 " " y[1] (numeric) = 1.090202327206978 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.07345681409237300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.42900000000000027 " " y[1] (analytic) = 1.0906178340750012 " " y[1] (numeric) = 1.0906178340750017 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.07190489624363550000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 1.091034250325115 " " y[1] (numeric) = 1.0910342503251154 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.070350767794223600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.43100000000000027 " " y[1] (analytic) = 1.0914515755409027 " " y[1] (numeric) = 1.091451575540903 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.068794436711316600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4320000000000003 " " y[1] (analytic) = 1.0918698093050392 " " y[1] (numeric) = 1.0918698093050396 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06723591096194500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4330000000000003 " " y[1] (analytic) = 1.0922889511992906 " " y[1] (numeric) = 1.092288951199291 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06567519851290300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4340000000000003 " " y[1] (analytic) = 1.0927090008045153 " " y[1] (numeric) = 1.0927090008045157 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06411230733066730000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4350000000000003 " " y[1] (analytic) = 1.0931299577006635 " " y[1] (numeric) = 1.093129957700664 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06254724538131700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4360000000000003 " " y[1] (analytic) = 1.0935518214667783 " " y[1] (numeric) = 1.0935518214667788 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.06098002063045200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4370000000000003 " " y[1] (analytic) = 1.0939745916809964 " " y[1] (numeric) = 1.0939745916809966 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.02970532052155400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4380000000000003 " " y[1] (analytic) = 1.094398267920547 " " y[1] (numeric) = 1.0943982679205475 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.057839114583680600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4390000000000003 " " y[1] (analytic) = 1.0948228497617545 " " y[1] (numeric) = 1.094822849761755 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.056265449215837300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 1.0952483367800367 " " y[1] (numeric) = 1.0952483367800372 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.05468965290244400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4410000000000003 " " y[1] (analytic) = 1.0956747285499067 " " y[1] (numeric) = 1.095674728549907 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.0531117336054800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4420000000000003 " " y[1] (analytic) = 1.0961020246449729 " " y[1] (numeric) = 1.0961020246449733 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.05153169928595850000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4430000000000003 " " y[1] (analytic) = 1.096530224637939 " " y[1] (numeric) = 1.0965302246379394 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.049949557903846400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4440000000000003 " " y[1] (analytic) = 1.0969593281006051 " " y[1] (numeric) = 1.0969593281006056 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.04836531741798500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4450000000000003 " " y[1] (analytic) = 1.097389334603868 " " y[1] (numeric) = 1.0973893346038683 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.04677898578601100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4460000000000003 " " y[1] (analytic) = 1.0978202437177211 " " y[1] (numeric) = 1.0978202437177214 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.022595285482136600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4470000000000003 " " y[1] (analytic) = 1.0982520550112551 " " y[1] (numeric) = 1.0982520550112556 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.043600080907761600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4480000000000003 " " y[1] (analytic) = 1.0986847680526592 " " y[1] (numeric) = 1.0986847680526595 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 2.02100376178500800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4490000000000003 " " y[1] (analytic) = 1.0991183824092199 " " y[1] (numeric) = 1.0991183824092203 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.04041290690306100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 1.0995528976473232 " " y[1] (numeric) = 1.0995528976473237 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03881623885731700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4510000000000003 " " y[1] (analytic) = 1.099988313332454 " " y[1] (numeric) = 1.0999883133324544 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.03721752738152700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4520000000000003 " " y[1] (analytic) = 1.1004246290291961 " " y[1] (numeric) = 1.1004246290291968 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.05342517063401900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4530000000000003 " " y[1] (analytic) = 1.1008618443012343 " " y[1] (numeric) = 1.100861844301235 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.0510210088888890000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4540000000000003 " " y[1] (analytic) = 1.1012999587113534 " " y[1] (numeric) = 1.101299958711354 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.04861381775176300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4550000000000003 " " y[1] (analytic) = 1.101738971821439 " " y[1] (numeric) = 1.1017389718214396 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.0462036091345200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4560000000000003 " " y[1] (analytic) = 1.1021788831924777 " " y[1] (numeric) = 1.1021788831924784 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.04379039494593900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4570000000000003 " " y[1] (analytic) = 1.1026196923845586 " " y[1] (numeric) = 1.1026196923845593 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.04137418709158700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4580000000000003 " " y[1] (analytic) = 1.1030613989568723 " " y[1] (numeric) = 1.103061398956873 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.03895499747370400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4590000000000003 " " y[1] (analytic) = 1.1035040024677123 " " y[1] (numeric) = 1.103504002467713 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 6.03653283799108400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 1.103947502474475 " " y[1] (numeric) = 1.1039475024744758 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.04547696071862200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4610000000000003 " " y[1] (analytic) = 1.1043918985336605 " " y[1] (numeric) = 1.1043918985336614 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.0422395426785610000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4620000000000003 " " y[1] (analytic) = 1.104837190200873 " " y[1] (numeric) = 1.1048371902008738 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.03899821238497100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4630000000000003 " " y[1] (analytic) = 1.1052833770308206 " " y[1] (numeric) = 1.1052833770308215 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.03575298568304300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4640000000000003 " " y[1] (analytic) = 1.1057304585773164 " " y[1] (numeric) = 1.1057304585773176 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.00406298480157670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4650000000000003 " " y[1] (analytic) = 1.1061784343932795 " " y[1] (numeric) = 1.1061784343932806 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.00365636330100340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4660000000000003 " " y[1] (analytic) = 1.1066273040307335 " " y[1] (numeric) = 1.1066273040307346 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 1.00324926068724850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4670000000000003 " " y[1] (analytic) = 1.1070770670408092 " " y[1] (numeric) = 1.10707706704081 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.02273343150540600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4680000000000003 " " y[1] (analytic) = 1.1075277229737432 " " y[1] (numeric) = 1.1075277229737441 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.01946896024725200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4690000000000003 " " y[1] (analytic) = 1.10797927137888 " " y[1] (numeric) = 1.107979271378881 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.01620068753440900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 1.1084317118046711 " " y[1] (numeric) = 1.108431711804672 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.01292862917152700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4710000000000003 " " y[1] (analytic) = 1.1088850437986761 " " y[1] (numeric) = 1.108885043798677 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.00965280095687500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4720000000000003 " " y[1] (analytic) = 1.109339266907563 " " y[1] (numeric) = 1.109339266907564 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.00637321868219600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4730000000000003 " " y[1] (analytic) = 1.109794380677109 " " y[1] (numeric) = 1.1097943806771098 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.00308989813256200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4740000000000003 " " y[1] (analytic) = 1.1102503846521998 " " y[1] (numeric) = 1.1102503846522007 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.99980285508622900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4750000000000003 " " y[1] (analytic) = 1.110707278376832 " " y[1] (numeric) = 1.1107072783768328 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.99651210531449400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4760000000000003 " " y[1] (analytic) = 1.1111650613941115 " " y[1] (numeric) = 1.1111650613941124 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.99321766458154800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4770000000000003 " " y[1] (analytic) = 1.1116237332462557 " " y[1] (numeric) = 1.1116237332462566 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98991954864433300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4780000000000003 " " y[1] (analytic) = 1.1120832934745928 " " y[1] (numeric) = 1.1120832934745934 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.98996332993930300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4790000000000003 " " y[1] (analytic) = 1.112543741619562 " " y[1] (numeric) = 1.112543741619563 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98331235414778600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 1.1130050772207158 " " y[1] (numeric) = 1.1130050772207167 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.98000330706482400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4810000000000003 " " y[1] (analytic) = 1.1134672998167185 " " y[1] (numeric) = 1.1134672998167194 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.97669064773005100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4820000000000003 " " y[1] (analytic) = 1.1139304089453477 " " y[1] (numeric) = 1.1139304089453486 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.97337439186204700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4830000000000003 " " y[1] (analytic) = 1.114394404143494 " " y[1] (numeric) = 1.1143944041434948 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.97754091637846900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4840000000000003 " " y[1] (analytic) = 1.1148592849471624 " " y[1] (numeric) = 1.114859284947163 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.97504836502002800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4850000000000003 " " y[1] (analytic) = 1.1153250508914718 " " y[1] (numeric) = 1.1153250508914727 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.96340420212215500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4860000000000003 " " y[1] (analytic) = 1.1157917015106569 " " y[1] (numeric) = 1.1157917015106578 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.96007371714300500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4870000000000003 " " y[1] (analytic) = 1.1162592363380666 " " y[1] (numeric) = 1.1162592363380675 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.95673971409930100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4880000000000003 " " y[1] (analytic) = 1.1167276549061664 " " y[1] (numeric) = 1.1167276549061673 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.95340220865896600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4890000000000003 " " y[1] (analytic) = 1.1171969567465376 " " y[1] (numeric) = 1.1171969567465385 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.95006121648100300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 1.1176671413898787 " " y[1] (numeric) = 1.1176671413898795 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.94671675321534500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4910000000000003 " " y[1] (analytic) = 1.1181382083660047 " " y[1] (numeric) = 1.1181382083660056 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.94336883450273900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4920000000000003 " " y[1] (analytic) = 1.118610157203849 " " y[1] (numeric) = 1.1186101572038498 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.94001747597459700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4930000000000003 " " y[1] (analytic) = 1.1190829874314625 " " y[1] (numeric) = 1.1190829874314634 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.93666269325286400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.4940000000000003 " " y[1] (analytic) = 1.119556698576015 " " y[1] (numeric) = 1.1195566985760161 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.91663062743736000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.49500000000000033 " " y[1] (analytic) = 1.1200312901637959 " " y[1] (numeric) = 1.120031290163797 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.91242864708534300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.49600000000000033 " " y[1] (analytic) = 1.1205067617202134 " " y[1] (numeric) = 1.1205067617202142 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.92657795600077200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.49700000000000033 " " y[1] (analytic) = 1.1209831127697956 " " y[1] (numeric) = 1.1209831127697965 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.92320963253012900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.49800000000000033 " " y[1] (analytic) = 1.1214603428361918 " " y[1] (numeric) = 1.1214603428361927 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.91983796282896100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.49900000000000033 " " y[1] (analytic) = 1.1219384514421717 " " y[1] (numeric) = 1.1219384514421729 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.89557870307452300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5000000000000003 " " y[1] (analytic) = 1.1224174381096275 " " y[1] (numeric) = 1.1224174381096284 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.91308464697406100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5010000000000003 " " y[1] (analytic) = 1.1228973023595716 " " y[1] (numeric) = 1.1228973023595727 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.88712878989216300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5020000000000003 " " y[1] (analytic) = 1.1233780437121408 " " y[1] (numeric) = 1.1233780437121417 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.90631813280940200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5030000000000003 " " y[1] (analytic) = 1.1238596616865928 " " y[1] (numeric) = 1.1238596616865937 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.90292996518108600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5040000000000003 " " y[1] (analytic) = 1.12434215580131 " " y[1] (numeric) = 1.1243421558013111 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.87442318067233800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5050000000000003 " " y[1] (analytic) = 1.1248255255737987 " " y[1] (numeric) = 1.1248255255737998 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.87017985797225800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5060000000000003 " " y[1] (analytic) = 1.125309770520689 " " y[1] (numeric) = 1.1253097705206898 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.89274600618777900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5070000000000003 " " y[1] (analytic) = 1.1257948901577357 " " y[1] (numeric) = 1.1257948901577366 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.88934491944338200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5080000000000003 " " y[1] (analytic) = 1.1262808839998195 " " y[1] (numeric) = 1.1262808839998204 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.8859406416087900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5090000000000003 " " y[1] (analytic) = 1.1267677515609464 " " y[1] (numeric) = 1.1267677515609473 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.88253318813663200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5100000000000003 " " y[1] (analytic) = 1.1272554923542488 " " y[1] (numeric) = 1.12725549235425 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.84890321808483500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5110000000000003 " " y[1] (analytic) = 1.1277441058919864 " " y[1] (numeric) = 1.1277441058919875 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.84463602003956800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5120000000000003 " " y[1] (analytic) = 1.1282335916855453 " " y[1] (numeric) = 1.1282335916855464 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.84036491030654800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5130000000000003 " " y[1] (analytic) = 1.12872394924544 " " y[1] (numeric) = 1.128723949245441 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.83608990814227600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5140000000000003 " " y[1] (analytic) = 1.1292151780813127 " " y[1] (numeric) = 1.1292151780813138 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.83181103278804400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5150000000000003 " " y[1] (analytic) = 1.1297072777019346 " " y[1] (numeric) = 1.129707277701936 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.17930339641637450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5160000000000003 " " y[1] (analytic) = 1.1302002476152064 " " y[1] (numeric) = 1.1302002476152078 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.1787890087277510000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5170000000000003 " " y[1] (analytic) = 1.1306940873281583 " " y[1] (numeric) = 1.1306940873281595 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.8189513597672100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5180000000000003 " " y[1] (analytic) = 1.1311887963469505 " " y[1] (numeric) = 1.1311887963469514 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.8517257470052700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5190000000000003 " " y[1] (analytic) = 1.1316843741768736 " " y[1] (numeric) = 1.1316843741768745 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.84828738442322700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5200000000000004 " " y[1] (analytic) = 1.1321808203223502 " " y[1] (numeric) = 1.1321808203223511 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.84484601538512600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5210000000000004 " " y[1] (analytic) = 1.1326781342869343 " " y[1] (numeric) = 1.1326781342869352 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.84140165519544200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5220000000000004 " " y[1] (analytic) = 1.1331763155733119 " " y[1] (numeric) = 1.1331763155733128 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.83795431914552500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5230000000000004 " " y[1] (analytic) = 1.1336753636833015 " " y[1] (numeric) = 1.1336753636833026 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.79313002814184400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5240000000000004 " " y[1] (analytic) = 1.1341752781178553 " " y[1] (numeric) = 1.1341752781178565 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.78881347570503300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5250000000000004 " " y[1] (analytic) = 1.134676058377059 " " y[1] (numeric) = 1.13467605837706 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.7844932606855400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5260000000000004 " " y[1] (analytic) = 1.135177703960132 " " y[1] (numeric) = 1.1351777039601332 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.78016940213043500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5270000000000004 " " y[1] (analytic) = 1.135680214365429 " " y[1] (numeric) = 1.13568021436543 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.77584191906964900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5280000000000004 " " y[1] (analytic) = 1.1361835890904395 " " y[1] (numeric) = 1.1361835890904408 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.17258129966189840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5290000000000004 " " y[1] (analytic) = 1.136687827631789 " " y[1] (numeric) = 1.1366878276317904 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.17206113865569920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5300000000000004 " " y[1] (analytic) = 1.1371929294852392 " " y[1] (numeric) = 1.1371929294852405 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.17154054954707740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5310000000000004 " " y[1] (analytic) = 1.1376988941456878 " " y[1] (numeric) = 1.1376988941456891 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.17101953461122410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5320000000000004 " " y[1] (analytic) = 1.1382057211071703 " " y[1] (numeric) = 1.1382057211071717 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.1704980961211890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5330000000000004 " " y[1] (analytic) = 1.1387134098628602 " " y[1] (numeric) = 1.1387134098628613 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.74980196956550500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5340000000000004 " " y[1] (analytic) = 1.1392219599050681 " " y[1] (numeric) = 1.1392219599050692 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.7454496463329400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5350000000000004 " " y[1] (analytic) = 1.1397313707252446 " " y[1] (numeric) = 1.1397313707252457 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.74109385019988400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5360000000000004 " " y[1] (analytic) = 1.1402416418139785 " " y[1] (numeric) = 1.1402416418139796 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.73673460003560100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5370000000000004 " " y[1] (analytic) = 1.140752772660999 " " y[1] (numeric) = 1.140752772661 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.732371914690800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5380000000000004 " " y[1] (analytic) = 1.1412647627551753 " " y[1] (numeric) = 1.1412647627551764 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.72800581299750700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5390000000000004 " " y[1] (analytic) = 1.141777611584517 " " y[1] (numeric) = 1.1417776115845184 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.16683635765227140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5400000000000004 " " y[1] (analytic) = 1.142291318636176 " " y[1] (numeric) = 1.1422913186361772 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.7192634357993100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5410000000000004 " " y[1] (analytic) = 1.1428058833964447 " " y[1] (numeric) = 1.1428058833964458 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.71488719786381200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5420000000000004 " " y[1] (analytic) = 1.1433213053507587 " " y[1] (numeric) = 1.1433213053507598 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.71050761871836300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5430000000000004 " " y[1] (analytic) = 1.1438375839836958 " " y[1] (numeric) = 1.143837583983697 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.70612471709953500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5440000000000004 " " y[1] (analytic) = 1.1443547187789775 " " y[1] (numeric) = 1.1443547187789789 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.16420862140692930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5450000000000004 " " y[1] (analytic) = 1.1448727092194693 " " y[1] (numeric) = 1.1448727092194706 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.1636818825548541000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5460000000000004 " " y[1] (analytic) = 1.1453915547871807 " " y[1] (numeric) = 1.1453915547871818 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.69295626447535100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5470000000000004 " " y[1] (analytic) = 1.145911254963266 " " y[1] (numeric) = 1.145911254963267 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.6885602599369400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5480000000000004 " " y[1] (analytic) = 1.1464318092280252 " " y[1] (numeric) = 1.1464318092280261 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.74732882105041700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5490000000000004 " " y[1] (analytic) = 1.1469532170609038 " " y[1] (numeric) = 1.146953217060905 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.67975858222125800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5500000000000004 " " y[1] (analytic) = 1.1474754779404943 " " y[1] (numeric) = 1.1474754779404954 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.67535294625904300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5510000000000004 " " y[1] (analytic) = 1.147998591344536 " " y[1] (numeric) = 1.147998591344537 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.73675530960269300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5520000000000004 " " y[1] (analytic) = 1.1485225567499153 " " y[1] (numeric) = 1.1485225567499162 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.73322573840856100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5530000000000004 " " y[1] (analytic) = 1.149047373632667 " " y[1] (numeric) = 1.1490473736326678 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.72969365825348800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5540000000000004 " " y[1] (analytic) = 1.1495730414679741 " " y[1] (numeric) = 1.1495730414679748 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.79461931296213200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5550000000000004 " " y[1] (analytic) = 1.1500995597301689 " " y[1] (numeric) = 1.1500995597301695 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.79196652271894800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5560000000000004 " " y[1] (analytic) = 1.1506269278927328 " " y[1] (numeric) = 1.1506269278927337 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.71908251205924900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5570000000000004 " " y[1] (analytic) = 1.1511551454282984 " " y[1] (numeric) = 1.151155145428299 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.78665540800977300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5580000000000004 " " y[1] (analytic) = 1.1516842118086477 " " y[1] (numeric) = 1.1516842118086483 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.78399710567337400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5590000000000004 " " y[1] (analytic) = 1.1522141265047146 " " y[1] (numeric) = 1.1522141265047152 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.7813369880808200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5600000000000004 " " y[1] (analytic) = 1.1527448889865841 " " y[1] (numeric) = 1.1527448889865848 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.77867506626478300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5610000000000004 " " y[1] (analytic) = 1.153276498723494 " " y[1] (numeric) = 1.153276498723495 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.70134846832660600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5620000000000004 " " y[1] (analytic) = 1.1538089551838349 " " y[1] (numeric) = 1.1538089551838357 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.69779447203729600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5630000000000004 " " y[1] (analytic) = 1.1543422578351499 " " y[1] (numeric) = 1.1543422578351508 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.69423811414313600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5640000000000004 " " y[1] (analytic) = 1.1548764061441368 " " y[1] (numeric) = 1.1548764061441374 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.76800955696341200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5650000000000004 " " y[1] (analytic) = 1.1554113995766468 " " y[1] (numeric) = 1.1554113995766477 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.68711837208428000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5660000000000004 " " y[1] (analytic) = 1.1559472375976871 " " y[1] (numeric) = 1.155947237597688 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.68355501714728300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5670000000000004 " " y[1] (analytic) = 1.1564839196714196 " " y[1] (numeric) = 1.1564839196714203 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.75999201929548700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5680000000000004 " " y[1] (analytic) = 1.1570214452611618 " " y[1] (numeric) = 1.1570214452611627 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.67642141239349600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5690000000000004 " " y[1] (analytic) = 1.1575598138293888 " " y[1] (numeric) = 1.1575598138293894 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.75463839377266500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5700000000000004 " " y[1] (analytic) = 1.1580990248377314 " " y[1] (numeric) = 1.1580990248377323 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.66927871150373900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5710000000000004 " " y[1] (analytic) = 1.1586390777469793 " " y[1] (numeric) = 1.1586390777469802 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.66570398632872100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5720000000000004 " " y[1] (analytic) = 1.1591799720170792 " " y[1] (numeric) = 1.1591799720170801 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.66212703066818400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5730000000000004 " " y[1] (analytic) = 1.159721707107137 " " y[1] (numeric) = 1.159721707107138 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.65854785900005400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5740000000000004 " " y[1] (analytic) = 1.160264282475418 " " y[1] (numeric) = 1.1602642824754186 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.74122486433781000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5750000000000004 " " y[1] (analytic) = 1.160807697579346 " " y[1] (numeric) = 1.1608076975793469 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.65138292546009400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5760000000000004 " " y[1] (analytic) = 1.1613519518755069 " " y[1] (numeric) = 1.1613519518755075 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.7358478943384200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5770000000000004 " " y[1] (analytic) = 1.161897044819646 " " y[1] (numeric) = 1.1618970448196466 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.73315697587038600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5780000000000004 " " y[1] (analytic) = 1.1624429758666701 " " y[1] (numeric) = 1.162442975866671 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.64061926597247100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5790000000000004 " " y[1] (analytic) = 1.1629897444706487 " " y[1] (numeric) = 1.1629897444706496 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.63702710125266200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5800000000000004 " " y[1] (analytic) = 1.1635373500848134 " " y[1] (numeric) = 1.163537350084814 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.72507461601071600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5810000000000004 " " y[1] (analytic) = 1.164085792161558 " " y[1] (numeric) = 1.1640857921615588 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.62983644058477700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5820000000000004 " " y[1] (analytic) = 1.1646350701524408 " " y[1] (numeric) = 1.1646350701524417 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.62623797327235100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5830000000000004 " " y[1] (analytic) = 1.165185183508184 " " y[1] (numeric) = 1.1651851835081848 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.62263743369928400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5840000000000004 " " y[1] (analytic) = 1.1657361316786738 " " y[1] (numeric) = 1.1657361316786747 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.61903483613515300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5850000000000004 " " y[1] (analytic) = 1.1662879141129627 " " y[1] (numeric) = 1.1662879141129636 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.61543019483008400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5860000000000004 " " y[1] (analytic) = 1.1668405302592677 " " y[1] (numeric) = 1.1668405302592688 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.51477940501834500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5870000000000004 " " y[1] (analytic) = 1.1673939795649733 " " y[1] (numeric) = 1.1673939795649744 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.51026854737488600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5880000000000004 " " y[1] (analytic) = 1.1679482614766301 " " y[1] (numeric) = 1.167948261476631 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.60460415067707200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5890000000000004 " " y[1] (analytic) = 1.1685033754399559 " " y[1] (numeric) = 1.1685033754399567 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.60099147651768800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5900000000000004 " " y[1] (analytic) = 1.1690593208998368 " " y[1] (numeric) = 1.1690593208998377 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.59737682957341600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5910000000000004 " " y[1] (analytic) = 1.1696160973003276 " " y[1] (numeric) = 1.1696160973003285 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.59376022397598500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5920000000000004 " " y[1] (analytic) = 1.170173704084652 " " y[1] (numeric) = 1.170173704084653 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.5901416738371100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5930000000000004 " " y[1] (analytic) = 1.1707321406952031 " " y[1] (numeric) = 1.170732140695204 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.58652119324842200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5940000000000004 " " y[1] (analytic) = 1.1712914065735445 " " y[1] (numeric) = 1.1712914065735454 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.58289879628137800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5950000000000004 " " y[1] (analytic) = 1.1718515011604103 " " y[1] (numeric) = 1.1718515011604111 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.5792744969871910000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5960000000000004 " " y[1] (analytic) = 1.1724124238957057 " " y[1] (numeric) = 1.1724124238957068 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.46956038674594100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5970000000000004 " " y[1] (analytic) = 1.1729741742185085 " " y[1] (numeric) = 1.1729741742185094 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.57202024752055800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5980000000000004 " " y[1] (analytic) = 1.173536751567068 " " y[1] (numeric) = 1.173536751567069 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.56839032534862600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.5990000000000004 " " y[1] (analytic) = 1.174100155378807 " " y[1] (numeric) = 1.174100155378808 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.56475855685043300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6000000000000004 " " y[1] (analytic) = 1.1746643850903218 " " y[1] (numeric) = 1.174664385090323 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.4514061949685300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6010000000000004 " " y[1] (analytic) = 1.1752294401373828 " " y[1] (numeric) = 1.175229440137384 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.4468619208124400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6020000000000004 " " y[1] (analytic) = 1.1757953199549351 " " y[1] (numeric) = 1.175795319954936 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.55385231278320200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6030000000000004 " " y[1] (analytic) = 1.1763620239770987 " " y[1] (numeric) = 1.1763620239770995 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.55021329826111700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6040000000000004 " " y[1] (analytic) = 1.1769295516371696 " " y[1] (numeric) = 1.1769295516371705 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.54657250694931800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6050000000000004 " " y[1] (analytic) = 1.1774979023676202 " " y[1] (numeric) = 1.177497902367621 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.5429299526924500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6060000000000004 " " y[1] (analytic) = 1.1780670756001 " " y[1] (numeric) = 1.1780670756001008 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.53928564931409100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6070000000000004 " " y[1] (analytic) = 1.1786370707654357 " " y[1] (numeric) = 1.1786370707654366 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.53563961061669700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6080000000000004 " " y[1] (analytic) = 1.1792078872936322 " " y[1] (numeric) = 1.1792078872936331 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.53199185038152300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6090000000000004 " " y[1] (analytic) = 1.179779524613873 " " y[1] (numeric) = 1.1797795246138738 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.52834238236856100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6100000000000004 " " y[1] (analytic) = 1.1803519821545208 " " y[1] (numeric) = 1.1803519821545216 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.5246912203164600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6110000000000004 " " y[1] (analytic) = 1.180925259343118 " " y[1] (numeric) = 1.180925259343119 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.52103837794246700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6120000000000004 " " y[1] (analytic) = 1.181499355606388 " " y[1] (numeric) = 1.1814993556063886 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.63803790170676900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6130000000000004 " " y[1] (analytic) = 1.1820742703702338 " " y[1] (numeric) = 1.1820742703702345 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.63529578024277800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6140000000000004 " " y[1] (analytic) = 1.182650003059741 " " y[1] (numeric) = 1.182650003059742 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.51006990573913100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6150000000000004 " " y[1] (analytic) = 1.1832265530991775 " " y[1] (numeric) = 1.1832265530991781 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.629807859114695000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6160000000000004 " " y[1] (analytic) = 1.1838039199119925 " " y[1] (numeric) = 1.1838039199119932 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.62706207988073100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6170000000000004 " " y[1] (analytic) = 1.1843821029208197 " " y[1] (numeric) = 1.1843821029208204 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.624315101793018000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6180000000000004 " " y[1] (analytic) = 1.1849611015474757 " " y[1] (numeric) = 1.1849611015474766 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.49542258003428900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6190000000000004 " " y[1] (analytic) = 1.1855409152129628 " " y[1] (numeric) = 1.1855409152129635 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.6188175897365300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6200000000000004 " " y[1] (analytic) = 1.1861215433374663 " " y[1] (numeric) = 1.1861215433374672 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.4880894347555700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6210000000000004 " " y[1] (analytic) = 1.186702985340359 " " y[1] (numeric) = 1.1867029853403597 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.61331540414082400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6220000000000004 " " y[1] (analytic) = 1.1872852406401981 " " y[1] (numeric) = 1.187285240640199 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.480750112089399000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6230000000000004 " " y[1] (analytic) = 1.1878683086547293 " " y[1] (numeric) = 1.1878683086547301 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.47707816791572400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6240000000000004 " " y[1] (analytic) = 1.188452188800884 " " y[1] (numeric) = 1.1884521888008848 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.6050535398248100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6250000000000004 " " y[1] (analytic) = 1.1890368804947824 " " y[1] (numeric) = 1.189036880494783 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.602297335789131000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6260000000000004 " " y[1] (analytic) = 1.1896223831517325 " " y[1] (numeric) = 1.1896223831517332 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.599540023871009000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6270000000000004 " " y[1] (analytic) = 1.1902086961862322 " " y[1] (numeric) = 1.1902086961862328 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.596781614094877000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6280000000000004 " " y[1] (analytic) = 1.190795819011968 " " y[1] (numeric) = 1.1907958190119687 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.59402211646830600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6290000000000004 " " y[1] (analytic) = 1.1913837510418173 " " y[1] (numeric) = 1.1913837510418182 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.45501538797594600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6300000000000004 " " y[1] (analytic) = 1.1919724916878485 " " y[1] (numeric) = 1.1919724916878491 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.58849989760954800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6310000000000004 " " y[1] (analytic) = 1.1925620403613204 " " y[1] (numeric) = 1.192562040361321 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.585737196307790000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6320000000000005 " " y[1] (analytic) = 1.1931523964726847 " " y[1] (numeric) = 1.1931523964726853 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.582973447016364000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6330000000000005 " " y[1] (analytic) = 1.1937435594315853 " " y[1] (numeric) = 1.193743559431586 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.58020865965786800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6340000000000005 " " y[1] (analytic) = 1.1943355286468593 " " y[1] (numeric) = 1.19433552864686 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.57744284413778100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6350000000000005 " " y[1] (analytic) = 1.1949283035265374 " " y[1] (numeric) = 1.1949283035265381 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.57467601034441600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6360000000000005 " " y[1] (analytic) = 1.195521883477845 " " y[1] (numeric) = 1.1955218834778456 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.57190816814888100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6370000000000005 " " y[1] (analytic) = 1.1961162679072022 " " y[1] (numeric) = 1.1961162679072026 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.71275955160335800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6380000000000005 " " y[1] (analytic) = 1.1967114562202243 " " y[1] (numeric) = 1.1967114562202248 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.710912998632975000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6390000000000005 " " y[1] (analytic) = 1.1973074478217234 " " y[1] (numeric) = 1.1973074478217238 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.70906579306760130000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6400000000000005 " " y[1] (analytic) = 1.1979042421157078 " " y[1] (numeric) = 1.1979042421157082 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.70721794144182660000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6410000000000005 " " y[1] (analytic) = 1.1985018385053832 " " y[1] (numeric) = 1.1985018385053836 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.70536945027863600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6420000000000005 " " y[1] (analytic) = 1.199100236393153 " " y[1] (numeric) = 1.1991002363931536 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.703520326089382300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6430000000000005 " " y[1] (analytic) = 1.1996994351806198 " " y[1] (numeric) = 1.1996994351806205 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.552505863060647000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6440000000000005 " " y[1] (analytic) = 1.2002994342685849 " " y[1] (numeric) = 1.2002994342685855 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.549730306929700000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6450000000000005 " " y[1] (analytic) = 1.200900233057049 " " y[1] (numeric) = 1.2009002330570497 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.546953830455699000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6460000000000005 " " y[1] (analytic) = 1.2015018309452137 " " y[1] (numeric) = 1.2015018309452141 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.69611762889034100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6470000000000005 " " y[1] (analytic) = 1.2021042273314806 " " y[1] (numeric) = 1.202104227331481 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.694265436832250000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6480000000000005 " " y[1] (analytic) = 1.2027074216134537 " " y[1] (numeric) = 1.2027074216134541 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.69241265057056800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6490000000000005 " " y[1] (analytic) = 1.2033114131879388 " " y[1] (numeric) = 1.2033114131879392 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.69055927653453300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6500000000000005 " " y[1] (analytic) = 1.2039162014509444 " " y[1] (numeric) = 1.2039162014509448 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.688705321141554400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6510000000000005 " " y[1] (analytic) = 1.2045217857976822 " " y[1] (numeric) = 1.2045217857976827 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.686850790797188700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6520000000000005 " " y[1] (analytic) = 1.2051281656225679 " " y[1] (numeric) = 1.2051281656225683 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.68499569189511600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6530000000000005 " " y[1] (analytic) = 1.2057353403192217 " " y[1] (numeric) = 1.2057353403192221 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.683140030817117500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6540000000000005 " " y[1] (analytic) = 1.206343309280469 " " y[1] (numeric) = 1.2063433092804694 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.681283813933053400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6550000000000005 " " y[1] (analytic) = 1.2069520718983409 " " y[1] (numeric) = 1.2069520718983413 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.67942704760083800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6560000000000005 " " y[1] (analytic) = 1.2075616275640746 " " y[1] (numeric) = 1.2075616275640753 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.516354607249625000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6570000000000005 " " y[1] (analytic) = 1.2081719756681149 " " y[1] (numeric) = 1.2081719756681155 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.513567837945622000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6580000000000005 " " y[1] (analytic) = 1.2087831156001136 " " y[1] (numeric) = 1.208783115600114 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.67385351531477700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6590000000000005 " " y[1] (analytic) = 1.2093950467489307 " " y[1] (numeric) = 1.2093950467489312 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.67199461452941740000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6600000000000005 " " y[1] (analytic) = 1.2100077685026354 " " y[1] (numeric) = 1.2100077685026356 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.835067597952762500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6610000000000005 " " y[1] (analytic) = 1.2106212802485055 " " y[1] (numeric) = 1.2106212802485057 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.834137632864441300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6620000000000005 " " y[1] (analytic) = 1.2112355813730296 " " y[1] (numeric) = 1.2112355813730298 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.833207415136587400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6630000000000005 " " y[1] (analytic) = 1.2118506712619064 " " y[1] (numeric) = 1.2118506712619068 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.664553895799968500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6640000000000005 " " y[1] (analytic) = 1.2124665493000464 " " y[1] (numeric) = 1.2124665493000468 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.662692468558692600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6650000000000005 " " y[1] (analytic) = 1.2130832148715716 " " y[1] (numeric) = 1.213083214871572 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.660830554786615500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6660000000000005 " " y[1] (analytic) = 1.2137006673598163 " " y[1] (numeric) = 1.2137006673598167 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.6589681607088300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6670000000000005 " " y[1] (analytic) = 1.214318906147328 " " y[1] (numeric) = 1.2143189061473285 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.657105292538228600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6680000000000005 " " y[1] (analytic) = 1.2149379306158683 " " y[1] (numeric) = 1.2149379306158687 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.655241956475487300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6690000000000005 " " y[1] (analytic) = 1.2155577401464124 " " y[1] (numeric) = 1.2155577401464128 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.653378158709043600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6700000000000005 " " y[1] (analytic) = 1.216178334119151 " " y[1] (numeric) = 1.2161783341191514 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.65151390541507900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6710000000000005 " " y[1] (analytic) = 1.2167997119134903 " " y[1] (numeric) = 1.2167997119134906 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.8248246013787500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6720000000000005 " " y[1] (analytic) = 1.2174218729080521 " " y[1] (numeric) = 1.2174218729080526 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.647784056887921600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6730000000000005 " " y[1] (analytic) = 1.218044816480676 " " y[1] (numeric) = 1.2180448164806765 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.64591847394564200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6740000000000005 " " y[1] (analytic) = 1.2186685420084182 " " y[1] (numeric) = 1.2186685420084187 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.644052460057633500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6750000000000005 " " y[1] (analytic) = 1.2192930488675535 " " y[1] (numeric) = 1.2192930488675537 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.82109301066925900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6760000000000005 " " y[1] (analytic) = 1.2199183364335746 " " y[1] (numeric) = 1.2199183364335748 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.82015958194527700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6770000000000005 " " y[1] (analytic) = 1.2205444040811944 " " y[1] (numeric) = 1.2205444040811946 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.819225946901807400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6780000000000005 " " y[1] (analytic) = 1.221171251184345 " " y[1] (numeric) = 1.2211712511843453 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.81829210857758720000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6790000000000005 " " y[1] (analytic) = 1.2217988771161798 " " y[1] (numeric) = 1.2217988771161798 " " 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] = 0.6800000000000005 " " y[1] (analytic) = 1.2224272812490724 " " y[1] (numeric) = 1.2224272812490724 " " 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] = 0.6810000000000005 " " y[1] (analytic) = 1.223056462954619 " " y[1] (numeric) = 1.223056462954619 " " 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] = 0.6820000000000005 " " y[1] (analytic) = 1.223686421603638 " " y[1] (numeric) = 1.2236864216036378 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.81455478303046290000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6830000000000005 " " y[1] (analytic) = 1.2243171565661706 " " y[1] (numeric) = 1.2243171565661704 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.813619973665953300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6840000000000005 " " y[1] (analytic) = 1.224948667211482 " " y[1] (numeric) = 1.2249486672114818 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.81268497912244590000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6850000000000005 " " y[1] (analytic) = 1.2255809529080617 " " y[1] (numeric) = 1.2255809529080615 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.811749802395046200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6860000000000005 " " y[1] (analytic) = 1.2262140130236237 " " y[1] (numeric) = 1.2262140130236237 " " 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] = 0.6870000000000005 " " y[1] (analytic) = 1.2268478469251085 " " y[1] (numeric) = 1.2268478469251083 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.809878914337661500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6880000000000005 " " y[1] (analytic) = 1.2274824539786817 " " y[1] (numeric) = 1.2274824539786815 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.808943208966534400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6890000000000005 " " y[1] (analytic) = 1.2281178335497365 " " y[1] (numeric) = 1.2281178335497365 " " 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] = 0.6900000000000005 " " y[1] (analytic) = 1.2287539850028937 " " y[1] (numeric) = 1.2287539850028935 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.807071290389413700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6910000000000005 " " y[1] (analytic) = 1.2293909077020015 " " y[1] (numeric) = 1.2293909077020013 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.80613508310453420000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6920000000000005 " " y[1] (analytic) = 1.2300286010101376 " " y[1] (numeric) = 1.2300286010101371 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.61039742885135240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6930000000000005 " " y[1] (analytic) = 1.2306670642896083 " " y[1] (numeric) = 1.2306670642896078 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.60852437459524600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6940000000000005 " " y[1] (analytic) = 1.2313062969019506 " " y[1] (numeric) = 1.2313062969019501 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.60665100931767300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6950000000000005 " " y[1] (analytic) = 1.231946298207932 " " y[1] (numeric) = 1.2319462982079314 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.604777338882898500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6960000000000005 " " y[1] (analytic) = 1.232587067567551 " " y[1] (numeric) = 1.2325870675675505 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.60290336914251830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6970000000000005 " " y[1] (analytic) = 1.2332286043400384 " " y[1] (numeric) = 1.2332286043400382 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.800514552967722700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6980000000000005 " " y[1] (analytic) = 1.233870907883858 " " y[1] (numeric) = 1.2338709078838577 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.799577277543948400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.6990000000000005 " " y[1] (analytic) = 1.2345139775567056 " " y[1] (numeric) = 1.2345139775567053 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.79863986120669120000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7000000000000005 " " y[1] (analytic) = 1.2351578127155118 " " y[1] (numeric) = 1.2351578127155116 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.79770230685634500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7010000000000005 " " y[1] (analytic) = 1.2358024127164418 " " y[1] (numeric) = 1.2358024127164415 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.796764617386938700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7020000000000005 " " y[1] (analytic) = 1.2364477769148952 " " y[1] (numeric) = 1.236447776914895 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.795826795686128200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7030000000000005 " " y[1] (analytic) = 1.237093904665508 " " y[1] (numeric) = 1.2370939046655078 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.794888844635192700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7040000000000005 " " y[1] (analytic) = 1.2377407953221526 " " y[1] (numeric) = 1.2377407953221524 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.79395076710902700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7050000000000005 " " y[1] (analytic) = 1.2383884482379386 " " y[1] (numeric) = 1.2383884482379381 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.58602513195227400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7060000000000005 " " y[1] (analytic) = 1.2390368627652126 " " y[1] (numeric) = 1.2390368627652122 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.58414848819727070000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7070000000000005 " " y[1] (analytic) = 1.2396860382555608 " " y[1] (numeric) = 1.2396860382555601 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.373407412996699000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7080000000000005 " " y[1] (analytic) = 1.240335974059807 " " y[1] (numeric) = 1.2403359740598066 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.58039449905247500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7090000000000005 " " y[1] (analytic) = 1.240986669528016 " " y[1] (numeric) = 1.2409866695280156 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.5785171650470900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7100000000000005 " " y[1] (analytic) = 1.241638124009492 " " y[1] (numeric) = 1.2416381240094918 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.78831980616063800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7110000000000005 " " y[1] (analytic) = 1.2422903368527811 " " y[1] (numeric) = 1.2422903368527807 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.57476184653515400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7120000000000005 " " y[1] (analytic) = 1.2429433074056702 " " y[1] (numeric) = 1.2429433074056697 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.572883873335997400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7130000000000005 " " y[1] (analytic) = 1.2435970350151886 " " y[1] (numeric) = 1.2435970350151881 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.571005698358220600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7140000000000005 " " y[1] (analytic) = 1.244251519027609 " " y[1] (numeric) = 1.2442515190276087 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.56912732722336800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7150000000000005 " " y[1] (analytic) = 1.2449067587884475 " " y[1] (numeric) = 1.244906758788447 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.56724876554010750000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7160000000000005 " " y[1] (analytic) = 1.2455627536424643 " " y[1] (numeric) = 1.2455627536424638 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.565370018904220300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7170000000000005 " " y[1] (analytic) = 1.2462195029336645 " " y[1] (numeric) = 1.246219502933664 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.563491092898593600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7180000000000005 " " y[1] (analytic) = 1.246877006005299 " " y[1] (numeric) = 1.2468770060052985 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.56161199309320940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7190000000000005 " " y[1] (analytic) = 1.2475352621998645 " " y[1] (numeric) = 1.247535262199864 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.559732725045139400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7200000000000005 " " y[1] (analytic) = 1.2481942708591054 " " y[1] (numeric) = 1.248194270859105 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.557853294298535000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7210000000000005 " " y[1] (analytic) = 1.2488540313240126 " " y[1] (numeric) = 1.2488540313240122 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.55597370638462250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7220000000000005 " " y[1] (analytic) = 1.249514542934826 " " y[1] (numeric) = 1.2495145429348256 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.5540939668216900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7230000000000005 " " y[1] (analytic) = 1.2501758050310339 " " y[1] (numeric) = 1.2501758050310334 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.552214081115085400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7240000000000005 " " y[1] (analytic) = 1.2508378169513743 " " y[1] (numeric) = 1.2508378169513739 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.550334054757207600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7250000000000005 " " y[1] (analytic) = 1.2515005780338353 " " y[1] (numeric) = 1.2515005780338349 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.54845389322749700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7260000000000005 " " y[1] (analytic) = 1.2521640876156557 " " y[1] (numeric) = 1.2521640876156555 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.773286800996217200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7270000000000005 " " y[1] (analytic) = 1.2528283450333264 " " y[1] (numeric) = 1.2528283450333262 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.77234659325276300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7280000000000005 " " y[1] (analytic) = 1.2534933496225897 " " y[1] (numeric) = 1.2534933496225895 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.771406326103652800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7290000000000005 " " y[1] (analytic) = 1.2541591007184412 " " y[1] (numeric) = 1.254159100718441 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.770466002262661400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7300000000000005 " " y[1] (analytic) = 1.2548255976551301 " " y[1] (numeric) = 1.2548255976551297 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.53905124887413900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7310000000000005 " " y[1] (analytic) = 1.2554928397661589 " " y[1] (numeric) = 1.2554928397661587 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.768585195327661800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7320000000000005 " " y[1] (analytic) = 1.2561608263842858 " " y[1] (numeric) = 1.2561608263842858 " " 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] = 0.7330000000000005 " " y[1] (analytic) = 1.2568295568415246 " " y[1] (numeric) = 1.2568295568415246 " " 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] = 0.7340000000000005 " " y[1] (analytic) = 1.2574990304691447 " " y[1] (numeric) = 1.2574990304691447 " " 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] = 0.7350000000000005 " " y[1] (analytic) = 1.2581692465976722 " " y[1] (numeric) = 1.2581692465976724 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.764823019839993300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7360000000000005 " " y[1] (analytic) = 1.2588402045568914 " " y[1] (numeric) = 1.2588402045568916 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.763882374595674000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7370000000000005 " " y[1] (analytic) = 1.2595119036758442 " " y[1] (numeric) = 1.2595119036758444 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.762941694135652400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7380000000000005 " " y[1] (analytic) = 1.2601843432828317 " " y[1] (numeric) = 1.260184343282832 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.7620009811151600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7390000000000005 " " y[1] (analytic) = 1.2608575227054142 " " y[1] (numeric) = 1.2608575227054144 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.76106023818291200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7400000000000005 " " y[1] (analytic) = 1.2615314412704124 " " y[1] (numeric) = 1.2615314412704126 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.760119467981103600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7410000000000005 " " y[1] (analytic) = 1.2622060983039078 " " y[1] (numeric) = 1.262206098303908 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.759178673145409800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7420000000000005 " " y[1] (analytic) = 1.2628814931312435 " " y[1] (numeric) = 1.2628814931312438 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.758237856304982500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7430000000000005 " " y[1] (analytic) = 1.2635576250770246 " " y[1] (numeric) = 1.2635576250770248 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.7572970200824500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7440000000000005 " " y[1] (analytic) = 1.2642344934651193 " " y[1] (numeric) = 1.2642344934651195 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.756356167093914300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7450000000000006 " " y[1] (analytic) = 1.2649120976186592 " " y[1] (numeric) = 1.2649120976186594 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.755415299948949200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7460000000000006 " " y[1] (analytic) = 1.2655904368600401 " " y[1] (numeric) = 1.2655904368600404 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.754474421250600300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7470000000000006 " " y[1] (analytic) = 1.266269510510923 " " y[1] (numeric) = 1.2662695105109232 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.753533533595381700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7480000000000006 " " y[1] (analytic) = 1.2669493178922342 " " y[1] (numeric) = 1.2669493178922344 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.752592639573277000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7490000000000006 " " y[1] (analytic) = 1.2676298583241665 " " y[1] (numeric) = 1.2676298583241667 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.751651741767734600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7500000000000006 " " y[1] (analytic) = 1.2683111311261794 " " y[1] (numeric) = 1.2683111311261797 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.75071084275567200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7510000000000006 " " y[1] (analytic) = 1.2689931356170003 " " y[1] (numeric) = 1.2689931356170006 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.749769945107468600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7520000000000006 " " y[1] (analytic) = 1.2696758711146248 " " y[1] (numeric) = 1.2696758711146248 " " 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] = 0.7530000000000006 " " y[1] (analytic) = 1.270359336936317 " " y[1] (numeric) = 1.270359336936317 " " 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] = 0.7540000000000006 " " y[1] (analytic) = 1.2710435323986116 " " y[1] (numeric) = 1.2710435323986116 " " 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] = 0.7550000000000006 " " y[1] (analytic) = 1.2717284568173128 " " y[1] (numeric) = 1.271728456817313 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.746006419332083700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7560000000000006 " " y[1] (analytic) = 1.2724141095074968 " " y[1] (numeric) = 1.272414109507497 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.74506556683009700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7570000000000006 " " y[1] (analytic) = 1.2731004897835105 " " y[1] (numeric) = 1.2731004897835108 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.74412473097696920000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7580000000000006 " " y[1] (analytic) = 1.2737875969589743 " " y[1] (numeric) = 1.2737875969589743 " " 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] = 0.7590000000000006 " " y[1] (analytic) = 1.27447543034678 " " y[1] (numeric) = 1.2744754303467802 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.74224311930920300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7600000000000006 " " y[1] (analytic) = 1.2751639892590951 " " y[1] (numeric) = 1.2751639892590954 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.74130234852417100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7610000000000006 " " y[1] (analytic) = 1.2758532730073608 " " y[1] (numeric) = 1.2758532730073608 " " 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] = 0.7620000000000006 " " y[1] (analytic) = 1.2765432809022927 " " y[1] (numeric) = 1.276543280902293 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.739420889576768800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7630000000000006 " " y[1] (analytic) = 1.2772340122538837 " " y[1] (numeric) = 1.2772340122538839 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.73848020640476100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7640000000000006 " " y[1] (analytic) = 1.2779254663714021 " " y[1] (numeric) = 1.2779254663714024 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.73753955741655700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7650000000000006 " " y[1] (analytic) = 1.2786176425633942 " " y[1] (numeric) = 1.2786176425633944 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.736598945090985500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7660000000000006 " " y[1] (analytic) = 1.2793105401376834 " " y[1] (numeric) = 1.2793105401376836 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.735658371900337700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7670000000000006 " " y[1] (analytic) = 1.2800041584013724 " " y[1] (numeric) = 1.2800041584013726 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.734717840310363300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7680000000000006 " " y[1] (analytic) = 1.2806984966608432 " " y[1] (numeric) = 1.2806984966608432 " " 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] = 0.7690000000000006 " " y[1] (analytic) = 1.2813935542217572 " " y[1] (numeric) = 1.2813935542217572 " " 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] = 0.7700000000000006 " " y[1] (analytic) = 1.282089330389057 " " y[1] (numeric) = 1.282089330389057 " " 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] = 0.7710000000000006 " " y[1] (analytic) = 1.2827858244669668 " " y[1] (numeric) = 1.2827858244669668 " " 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] = 0.7720000000000006 " " y[1] (analytic) = 1.2834830357589921 " " y[1] (numeric) = 1.2834830357589921 " " 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] = 0.7730000000000006 " " y[1] (analytic) = 1.2841809635679222 " " y[1] (numeric) = 1.2841809635679222 " " 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] = 0.7740000000000006 " " y[1] (analytic) = 1.284879607195829 " " y[1] (numeric) = 1.284879607195829 " " 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] = 0.7750000000000006 " " y[1] (analytic) = 1.285578965944069 " " y[1] (numeric) = 1.285578965944069 " " 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] = 0.7760000000000006 " " y[1] (analytic) = 1.2862790391132837 " " y[1] (numeric) = 1.2862790391132837 " " 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] = 0.7770000000000006 " " y[1] (analytic) = 1.2869798260033996 " " y[1] (numeric) = 1.2869798260033996 " " 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] = 0.7780000000000006 " " y[1] (analytic) = 1.28768132591363 " " y[1] (numeric) = 1.2876813259136302 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.724375437125231200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7790000000000006 " " y[1] (analytic) = 1.2883835381424753 " " y[1] (numeric) = 1.2883835381424753 " " 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] = 0.7800000000000006 " " y[1] (analytic) = 1.289086461987723 " " y[1] (numeric) = 1.2890864619877231 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.72249582531994680000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7810000000000006 " " y[1] (analytic) = 1.2897900967464495 " " y[1] (numeric) = 1.2897900967464497 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.721556131382527300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7820000000000006 " " y[1] (analytic) = 1.2904944417150204 " " y[1] (numeric) = 1.2904944417150204 " " 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] = 0.7830000000000006 " " y[1] (analytic) = 1.29119949618909 " " y[1] (numeric) = 1.2911994961890902 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.71967697927690300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7840000000000006 " " y[1] (analytic) = 1.2919052594636047 " " y[1] (numeric) = 1.2919052594636047 " " 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] = 0.7850000000000006 " " y[1] (analytic) = 1.2926117308328007 " " y[1] (numeric) = 1.2926117308328007 " " 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] = 0.7860000000000006 " " y[1] (analytic) = 1.293318909590207 " " y[1] (numeric) = 1.293318909590207 " " 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] = 0.7870000000000006 " " y[1] (analytic) = 1.2940267950286448 " " y[1] (numeric) = 1.2940267950286446 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.71591968402876900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7880000000000006 " " y[1] (analytic) = 1.2947353864402287 " " y[1] (numeric) = 1.2947353864402285 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.714980584067646300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7890000000000006 " " y[1] (analytic) = 1.2954446831163673 " " y[1] (numeric) = 1.2954446831163673 " " 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] = 0.7900000000000006 " " y[1] (analytic) = 1.2961546843477643 " " y[1] (numeric) = 1.2961546843477643 " " 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] = 0.7910000000000006 " " y[1] (analytic) = 1.2968653894244182 " " y[1] (numeric) = 1.2968653894244182 " " 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] = 0.7920000000000006 " " y[1] (analytic) = 1.297576797635624 " " y[1] (numeric) = 1.297576797635624 " " 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] = 0.7930000000000006 " " y[1] (analytic) = 1.2982889082699738 " " y[1] (numeric) = 1.2982889082699738 " " 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] = 0.7940000000000006 " " y[1] (analytic) = 1.2990017206153568 " " y[1] (numeric) = 1.2990017206153568 " " 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] = 0.7950000000000006 " " y[1] (analytic) = 1.2997152339589606 " " y[1] (numeric) = 1.2997152339589608 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.708409651002386600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7960000000000006 " " y[1] (analytic) = 1.3004294475872724 " " y[1] (numeric) = 1.3004294475872724 " " 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] = 0.7970000000000006 " " y[1] (analytic) = 1.3011443607860782 " " y[1] (numeric) = 1.3011443607860782 " " 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] = 0.7980000000000006 " " y[1] (analytic) = 1.3018599728404647 " " y[1] (numeric) = 1.301859972840465 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.7055951450797202000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.7990000000000006 " " y[1] (analytic) = 1.3025762830348204 " " y[1] (numeric) = 1.3025762830348206 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.704657207543334400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8000000000000006 " " y[1] (analytic) = 1.3032932906528352 " " y[1] (numeric) = 1.3032932906528352 " " 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] = 0.8010000000000006 " " y[1] (analytic) = 1.3040109949775007 " " y[1] (numeric) = 1.304010994977501 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.70278169264103800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8020000000000006 " " y[1] (analytic) = 1.3047293952911136 " " y[1] (numeric) = 1.3047293952911139 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.70184411975701920000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8030000000000006 " " y[1] (analytic) = 1.3054484908752733 " " y[1] (numeric) = 1.3054484908752735 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.700906672894887400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8040000000000006 " " y[1] (analytic) = 1.3061682810108841 " " y[1] (numeric) = 1.3061682810108843 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.69996935427940500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8050000000000006 " " y[1] (analytic) = 1.3068887649781562 " " y[1] (numeric) = 1.3068887649781564 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.699032166128864300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8060000000000006 " " y[1] (analytic) = 1.3076099420566054 " " y[1] (numeric) = 1.3076099420566056 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.698095110655094300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8070000000000006 " " y[1] (analytic) = 1.308331811525055 " " y[1] (numeric) = 1.308331811525055 " " 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] = 0.8080000000000006 " " y[1] (analytic) = 1.3090543726616355 " " y[1] (numeric) = 1.3090543726616355 " " 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] = 0.8090000000000006 " " y[1] (analytic) = 1.3097776247437856 " " y[1] (numeric) = 1.3097776247437856 " " 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] = 0.8100000000000006 " " y[1] (analytic) = 1.3105015670482534 " " y[1] (numeric) = 1.3105015670482534 " " 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] = 0.8110000000000006 " " y[1] (analytic) = 1.311226198851097 " " y[1] (numeric) = 1.3112261988510967 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.693411900399701700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8120000000000006 " " y[1] (analytic) = 1.311951519427684 " " y[1] (numeric) = 1.3119515194276838 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.692475687073363700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8130000000000006 " " y[1] (analytic) = 1.3126775280526943 " " y[1] (numeric) = 1.312677528052694 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.691539621725876300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8140000000000006 " " y[1] (analytic) = 1.3134042240001191 " " y[1] (numeric) = 1.3134042240001191 " " 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] = 0.8150000000000006 " " y[1] (analytic) = 1.314131606543263 " " y[1] (numeric) = 1.3141316065432629 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.689667943601973500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8160000000000006 " " y[1] (analytic) = 1.3148596749547432 " " y[1] (numeric) = 1.314859674954743 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.688732335126742500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8170000000000006 " " y[1] (analytic) = 1.3155884285064912 " " y[1] (numeric) = 1.315588428506491 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.687796883232739200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8180000000000006 " " y[1] (analytic) = 1.316317866469754 " " y[1] (numeric) = 1.3163178664697535 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.373723180108995600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8190000000000006 " " y[1] (analytic) = 1.317047988115093 " " y[1] (numeric) = 1.3170479881150925 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.37185291544027600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8200000000000006 " " y[1] (analytic) = 1.317778792712387 " " y[1] (numeric) = 1.3177787927123865 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.36998297670273500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8210000000000006 " " y[1] (analytic) = 1.3185102795308312 " " y[1] (numeric) = 1.318510279530831 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.684056684063487000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8220000000000006 " " y[1] (analytic) = 1.3192424478389395 " " y[1] (numeric) = 1.319242447838939 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.36624409393078800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8230000000000006 " " y[1] (analytic) = 1.319975296904543 " " y[1] (numeric) = 1.3199752969045426 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.36437515831917830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8240000000000006 " " y[1] (analytic) = 1.3207088259947932 " " y[1] (numeric) = 1.3207088259947926 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.04375984822653200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8250000000000006 " " y[1] (analytic) = 1.3214430343761605 " " y[1] (numeric) = 1.32144303437616 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 3.36063831960575200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8260000000000006 " " y[1] (analytic) = 1.3221779213144371 " " y[1] (numeric) = 1.3221779213144365 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.038155637275050000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8270000000000006 " " y[1] (analytic) = 1.3229134860747358 " " y[1] (numeric) = 1.3229134860747351 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.035354328056656000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8280000000000006 " " y[1] (analytic) = 1.323649727921492 " " y[1] (numeric) = 1.3236497279214914 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.03255355796517400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8290000000000006 " " y[1] (analytic) = 1.324386646118464 " " y[1] (numeric) = 1.3243866461184632 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.02975333319322400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8300000000000006 " " y[1] (analytic) = 1.3251242399287335 " " y[1] (numeric) = 1.3251242399287326 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.70260487988577200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8310000000000006 " " y[1] (analytic) = 1.3258625086147067 " " y[1] (numeric) = 1.325862508614706 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.02415454428292700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8320000000000006 " " y[1] (analytic) = 1.3266014514381153 " " y[1] (numeric) = 1.3266014514381146 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.0213559924343900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8330000000000006 " " y[1] (analytic) = 1.3273410676600161 " " y[1] (numeric) = 1.3273410676600155 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.0185580104850400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8340000000000006 " " y[1] (analytic) = 1.3280813565407934 " " y[1] (numeric) = 1.3280813565407927 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.015760604532159000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8350000000000006 " " y[1] (analytic) = 1.3288223173401583 " " y[1] (numeric) = 1.3288223173401574 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.68395170753867700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8360000000000006 " " y[1] (analytic) = 1.3295639493171496 " " y[1] (numeric) = 1.329563949317149 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.010167544909844000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8370000000000006 " " y[1] (analytic) = 1.330306251730136 " " y[1] (numeric) = 1.3303062517301352 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.67649587111990600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8380000000000006 " " y[1] (analytic) = 1.3310492238368146 " " y[1] (numeric) = 1.331049223836814 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.004576861965560000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8390000000000006 " " y[1] (analytic) = 1.3317928648942137 " " y[1] (numeric) = 1.331792864894213 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.001782426789063000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8400000000000006 " " y[1] (analytic) = 1.3325371741586922 " " y[1] (numeric) = 1.3325371741586916 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 4.99898860379383200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8410000000000006 " " y[1] (analytic) = 1.3332821508859412 " " y[1] (numeric) = 1.3332821508859403 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.66159386525910700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8420000000000006 " " y[1] (analytic) = 1.3340277943309835 " " y[1] (numeric) = 1.3340277943309826 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.65787042424815200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8430000000000006 " " y[1] (analytic) = 1.334774103748176 " " y[1] (numeric) = 1.334774103748175 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 6.65414782326113200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8440000000000006 " " y[1] (analytic) = 1.3355210783912095 " " y[1] (numeric) = 1.3355210783912084 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.31303258771886500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8450000000000006 " " y[1] (analytic) = 1.336268717513109 " " y[1] (numeric) = 1.3362687175131078 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.30838146605243100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" " " "TOP MAIN SOLVE Loop" x[1] = 0.8460000000000006 " " y[1] (analytic) = 1.3370170203662357 " " y[1] (numeric) = 1.3370170203662346 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 8.3037314238605900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE for equation 1" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = sin(x);" Iterations = 747 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 36 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 0 Minutes 36 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 3 Minutes 37 Seconds "Time to Timeout " Unknown Percent Done = 83.11111111111119 "%" (%o58) true (%o58) diffeq.max