(%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 # 0.0 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 # 0.0 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, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < 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 - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 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 : false, if (not found) 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 : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) 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 > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, 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"))), if (not found) 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 : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, 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"))), if (not found) 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, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found 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")), 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, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < 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 - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc 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 (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 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 (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 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 : false, if (not found) 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 : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) 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 > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, 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"))), if (not found) 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 : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, 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"))), if (not found) 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, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found 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")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_const_0D2 array_x , 1 1 1 array_tmp4 : array_const_0D3 + array_tmp3 , 1 1 1 array_tmp5 : array_tmp2 array_tmp4 , 1 1 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_0D2 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp5 : array_tmp2 array_tmp4 + array_tmp2 array_tmp4 , 2 2 1 1 2 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary array_y_higher : temporary, temporary : ---------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp5 : array_tmp2 array_tmp4 , array_tmp6 : array_tmp5 , 3 2 2 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp6 : array_tmp5 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, array_tmp6 : array_tmp5 , 2, 4 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp6 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_const_0D2 array_x , 1 1 1 array_tmp4 : array_const_0D3 + array_tmp3 , 1 1 1 array_tmp5 : array_tmp2 array_tmp4 , 1 1 1 array_tmp6 : array_tmp5 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_0D2 array_x , array_tmp4 : array_tmp3 , 2 1 2 2 2 array_tmp5 : array_tmp2 array_tmp4 + array_tmp2 array_tmp4 , 2 2 1 1 2 array_tmp6 : array_tmp5 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(1, 2), array_y : temporary, 2 3 temporary array_y_higher : temporary, temporary : ---------, 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp5 : array_tmp2 array_tmp4 , array_tmp6 : array_tmp5 , 3 2 2 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp6 : array_tmp5 , if not array_y_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(3, 4), array_y : temporary, 4 5 temporary 3.0 array_y_higher : temporary, temporary : -------------, 1, 5 glob_h array_y_higher : temporary, 0)), kkk : 5, array_tmp6 : array_tmp5 , 2, 4 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp6 : array_tmp5 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp6 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, 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() := 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 (%o27) 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 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 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, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 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, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) 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, "")) (%o34) 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, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) 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()) (%o37) 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()) (%i38) 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 (%o38) 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 (%i39) 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 (%o39) 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 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) 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 (%o41) 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 (%i42) 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) (%o42) 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) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) 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) (%o51) 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) 2.0 x x x (%i52) exact_soln_y(x) := block(0.035 x x + --------- + 0.06 x) 300.0 2.0 x x x (%o52) exact_soln_y(x) := block(0.035 x x + --------- + 0.06 x) 300.0 (%i53) 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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], 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_log10normmin, 0.1, float), 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_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, 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_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), 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-51, 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_log10abserr, 0.0, float), define_variable(glob_log10relerr, 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/mult_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 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_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), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, 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_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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(), 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 : 1, 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 display_alot(current_iter)), 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 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);"), 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, "2012-12-15T02:04:25-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);"), 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, " 151 "), logitem_str(html_log_file, "mult_lin_lin diffeq.max"), logitem_str(html_log_file, "mult_lin_lin maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) 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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], 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_log10normmin, 0.1, float), 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_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, 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_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), 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-51, 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_log10abserr, 0.0, float), define_variable(glob_log10relerr, 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/mult_lin_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 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_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), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, 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_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), 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(), 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 : 1, 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 display_alot(current_iter)), 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 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);"), 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, "2012-12-15T02:04:25-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_lin_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);"), 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, " 151 "), logitem_str(html_log_file, "mult_lin_lin diffeq.max"), logitem_str(html_log_file, "mult_lin_lin maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/mult_lin_linpostode.ode#################" "diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.05," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (0.06 * x + 2.0/300.0 * x * x * x + 0.035 * x * x) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_value3 = 0.0 "" value3 = 0.0 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = 6.356666666666667000E-3 " " y[1] (numeric) = 6.356666666666667000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.101 " " y[1] (analytic) = 6.423903673333334000E-3 " " y[1] (numeric) = 6.4239036733333330000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.35020975110346500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10200000000000001 " " y[1] (analytic) = 6.49121472000E-3 " " y[1] (numeric) = 6.49121472000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10300000000000001 " " y[1] (analytic) = 6.558599846666667000E-3 " " y[1] (numeric) = 6.5585998466666660000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.322480038829065300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10400000000000001 " " y[1] (analytic) = 6.626059093333333000E-3 " " y[1] (numeric) = 6.626059093333333000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10500000000000001 " " y[1] (analytic) = 6.6935925000E-3 " " y[1] (numeric) = 6.6935925000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10600000000000001 " " y[1] (analytic) = 6.761200106666667000E-3 " " y[1] (numeric) = 6.761200106666666000E-3 " " absolute error = 8.6736173798840350000000000000000000E-19 " " relative error = 1.282851748660964700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10700000000000001 " " y[1] (analytic) = 6.828881953333334000E-3 " " y[1] (numeric) = 6.828881953333332000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.540274510280630700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10800000000000001 " " y[1] (analytic) = 6.896638080000000000E-3 " " y[1] (numeric) = 6.896638079999999000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.515317544366206000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10900000000000001 " " y[1] (analytic) = 6.9644685266666670000E-3 " " y[1] (numeric) = 6.964468526666666000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.49081960717407400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11000000000000001 " " y[1] (analytic) = 7.032373333333335000E-3 " " y[1] (numeric) = 7.032373333333332000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.70015226812741800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11100000000000002 " " y[1] (analytic) = 7.100352540000001000E-3 " " y[1] (numeric) = 7.100352539999999000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.6647267854748100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11200000000000002 " " y[1] (analytic) = 7.168406186666668000E-3 " " y[1] (numeric) = 7.168406186666665000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.6299355061730800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11300000000000002 " " y[1] (analytic) = 7.236534313333334000E-3 " " y[1] (numeric) = 7.236534313333332000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 2.397174394351415700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11400000000000002 " " y[1] (analytic) = 7.304736960000001000E-3 " " y[1] (numeric) = 7.304736959999998000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.749585058232697600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11500000000000002 " " y[1] (analytic) = 7.373014166666667000E-3 " " y[1] (numeric) = 7.373014166666665000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.52920142989717200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11600000000000002 " " y[1] (analytic) = 7.441365973333334000E-3 " " y[1] (numeric) = 7.441365973333331000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.496784358261600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11700000000000002 " " y[1] (analytic) = 7.509792420000001000E-3 " " y[1] (numeric) = 7.509792419999998000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.61989727267802850000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11800000000000002 " " y[1] (analytic) = 7.578293546666668000E-3 " " y[1] (numeric) = 7.578293546666665000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.578137453489986600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11900000000000002 " " y[1] (analytic) = 7.646869393333335000E-3 " " y[1] (numeric) = 7.646869393333332000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.53708148197003950000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12000000000000002 " " y[1] (analytic) = 7.715520000000001000E-3 " " y[1] (numeric) = 7.715519999999998000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.49671176013232200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12100000000000002 " " y[1] (analytic) = 7.784245406666668000E-3 " " y[1] (numeric) = 7.784245406666666000E-3 " " absolute error = 2.6020852139652106000000000000000000E-18 " " relative error = 3.3427584538081300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12200000000000003 " " y[1] (analytic) = 7.853045653333335000E-3 " " y[1] (numeric) = 7.853045653333331000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.417963558483782300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12300000000000003 " " y[1] (analytic) = 7.921920780000001000E-3 " " y[1] (numeric) = 7.921920779999998000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.379552697260895600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12400000000000003 " " y[1] (analytic) = 7.990870826666668000E-3 " " y[1] (numeric) = 7.990870826666665000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 4.34176327863488700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12500000000000003 " " y[1] (analytic) = 8.059895833333336000E-3 " " y[1] (numeric) = 8.05989583333333000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.4568705794031700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12600000000000003 " " y[1] (analytic) = 8.128995840000002000E-3 " " y[1] (numeric) = 8.128995839999996000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.4019843660424600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12700000000000003 " " y[1] (analytic) = 8.198170886666668000E-3 " " y[1] (numeric) = 8.198170886666664000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.34796529600813100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12800000000000003 " " y[1] (analytic) = 8.267421013333335000E-3 " " y[1] (numeric) = 8.26742101333332900E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.2947930431235600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12900000000000003 " " y[1] (analytic) = 8.336746260000002000E-3 " " y[1] (numeric) = 8.336746259999996000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.24244791148341900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13000000000000003 " " y[1] (analytic) = 8.406146666666667000E-3 " " y[1] (numeric) = 8.406146666666663000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.19091081121245400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13100000000000003 " " y[1] (analytic) = 8.475622273333335000E-3 " " y[1] (numeric) = 8.475622273333329000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 8.18688431377943600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13200000000000003 " " y[1] (analytic) = 8.545173120000003000E-3 " " y[1] (numeric) = 8.545173119999996000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 8.1202496502577890000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13300000000000003 " " y[1] (analytic) = 8.614799246666668000E-3 " " y[1] (numeric) = 8.614799246666662000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 6.04096541186850700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13400000000000004 " " y[1] (analytic) = 8.684500693333337000E-3 " " y[1] (numeric) = 8.68450069333332900E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 7.98997449471548200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13500000000000004 " " y[1] (analytic) = 8.754277500000001000E-3 " " y[1] (numeric) = 8.754277499999996000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.94471722872666600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13600000000000004 " " y[1] (analytic) = 8.82412970666667000E-3 " " y[1] (numeric) = 8.824129706666662000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 7.86354477389975700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13700000000000004 " " y[1] (analytic) = 8.894057353333336000E-3 " " y[1] (numeric) = 8.89405735333333000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.85128948598469500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13800000000000004 " " y[1] (analytic) = 8.964060480000002000E-3 " " y[1] (numeric) = 8.964060479999998000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.80559495280248300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13900000000000004 " " y[1] (analytic) = 9.034139126666668000E-3 " " y[1] (numeric) = 9.034139126666664000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.76056041971827200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14000000000000004 " " y[1] (analytic) = 9.104293333333338000E-3 " " y[1] (numeric) = 9.10429333333333100E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 7.62156232214313400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14100000000000004 " " y[1] (analytic) = 9.174523140000004000E-3 " " y[1] (numeric) = 9.174523139999998000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.67241517462717900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14200000000000004 " " y[1] (analytic) = 9.244828586666668000E-3 " " y[1] (numeric) = 9.244828586666665000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.752851574725155600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14300000000000004 " " y[1] (analytic) = 9.315209713333337000E-3 " " y[1] (numeric) = 9.315209713333331000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.586745320914703000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14400000000000004 " " y[1] (analytic) = 9.385666560000002000E-3 " " y[1] (numeric) = 9.385666559999999000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.69653761911781900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14500000000000005 " " y[1] (analytic) = 9.45619916666667000E-3 " " y[1] (numeric) = 9.456199166666666000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.50344841114942600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14600000000000005 " " y[1] (analytic) = 9.526807573333336000E-3 " " y[1] (numeric) = 9.526807573333332000E-3 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.64177288692699940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14700000000000005 " " y[1] (analytic) = 9.597491820000004000E-3 " " y[1] (numeric) = 9.597491819999998000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.422427573301563000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14800000000000005 " " y[1] (analytic) = 9.66825194666666900E-3 " " y[1] (numeric) = 9.668251946666664000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.382741840653694000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14900000000000005 " " y[1] (analytic) = 9.739087993333336000E-3 " " y[1] (numeric) = 9.739087993333331000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.34359113655489500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15000000000000005 " " y[1] (analytic) = 9.810000000000003000E-3 " " y[1] (numeric) = 9.809999999999998000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.30496475833885800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15100000000000005 " " y[1] (analytic) = 9.88098800666666900E-3 " " y[1] (numeric) = 9.880988006666664000E-3 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.2668522868555100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15200000000000005 " " y[1] (analytic) = 9.952052053333337000E-3 " " y[1] (numeric) = 9.95205205333333000E-3 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.9723247695264190000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15300000000000005 " " y[1] (analytic) = 1.002319218000000300E-2 " " y[1] (numeric) = 1.002319217999999800E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.19212874947631700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.00944084266666700E-2 " " y[1] (numeric) = 1.009440842666666500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.15549818073778800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.016570083333333800E-2 " " y[1] (numeric) = 1.016570083333333100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.82578999487629200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.023706944000000300E-2 " " y[1] (numeric) = 1.023706943999999800E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.083652561343200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.030851428666666900E-2 " " y[1] (numeric) = 1.030851428666666500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 5.04841947462947700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.038003541333333700E-2 " " y[1] (numeric) = 1.03800354133333300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.68484607961365700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.045163286000000400E-2 " " y[1] (numeric) = 1.045163285999999700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.63905247807109200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.052330666666667100E-2 " " y[1] (numeric) = 1.052330666666666400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.59383416610548200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.059505687333333900E-2 " " y[1] (numeric) = 1.059505687333333000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.54918042145833700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16200000000000006 " " y[1] (analytic) = 1.066688352000000300E-2 " " y[1] (numeric) = 1.066688351999999800E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.87881058996547500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16300000000000006 " " y[1] (analytic) = 1.073878664666667200E-2 " " y[1] (numeric) = 1.073878664666666500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.46152506071164700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16400000000000006 " " y[1] (analytic) = 1.081076629333333800E-2 " " y[1] (numeric) = 1.081076629333333000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.41850329165493800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16500000000000006 " " y[1] (analytic) = 1.088282250000000600E-2 " " y[1] (numeric) = 1.088282249999999900E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 6.37600576863881000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16600000000000006 " " y[1] (analytic) = 1.09549553066666700E-2 " " y[1] (numeric) = 1.095495530666666500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.750517261136983400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16700000000000007 " " y[1] (analytic) = 1.102716475333333800E-2 " " y[1] (numeric) = 1.102716475333333200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.71940933534822100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16800000000000007 " " y[1] (analytic) = 1.109945088000000300E-2 " " y[1] (numeric) = 1.109945087999999900E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.68867377692329560000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16900000000000007 " " y[1] (analytic) = 1.11718137266666710E-2 " " y[1] (numeric) = 1.117181372666666600E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.65830397396286300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17000000000000007 " " y[1] (analytic) = 1.124425333333333700E-2 " " y[1] (numeric) = 1.124425333333333200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.62829347014334400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17100000000000007 " " y[1] (analytic) = 1.131676974000000400E-2 " " y[1] (numeric) = 1.13167697400E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.598635960167923000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17200000000000007 " " y[1] (analytic) = 1.138936298666667200E-2 " " y[1] (numeric) = 1.138936298666666700E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.56932528537623400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17300000000000007 " " y[1] (analytic) = 1.146203311333333800E-2 " " y[1] (numeric) = 1.146203311333333400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.02690361967087800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17400000000000007 " " y[1] (analytic) = 1.153478016000000500E-2 " " y[1] (numeric) = 1.15347801600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.00781367640179900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17500000000000007 " " y[1] (analytic) = 1.160760416666667300E-2 " " y[1] (numeric) = 1.160760416666666700E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.48341479706478500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17600000000000007 " " y[1] (analytic) = 1.168050517333333900E-2 " " y[1] (numeric) = 1.168050517333333500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.970288442553309000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17700000000000007 " " y[1] (analytic) = 1.175348322000000500E-2 " " y[1] (numeric) = 1.175348322000000100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.95184575245738300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17800000000000007 " " y[1] (analytic) = 1.182653834666667200E-2 " " y[1] (numeric) = 1.182653834666666800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.933611552472142300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17900000000000008 " " y[1] (analytic) = 1.189967059333333900E-2 " " y[1] (numeric) = 1.189967059333333500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.91558234720995900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18000000000000008 " " y[1] (analytic) = 1.197288000000000500E-2 " " y[1] (numeric) = 1.197288000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.89775471895952600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18100000000000008 " " y[1] (analytic) = 1.204616660666667400E-2 " " y[1] (numeric) = 1.204616660666667000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.32018798831015070000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18200000000000008 " " y[1] (analytic) = 1.21195304533333400E-2 " " y[1] (numeric) = 1.211953045333333500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.86269089822649200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18300000000000008 " " y[1] (analytic) = 1.219297158000000500E-2 " " y[1] (numeric) = 1.219297158000000300E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.422724119871037000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18400000000000008 " " y[1] (analytic) = 1.226649002666667200E-2 " " y[1] (numeric) = 1.22664900266666710E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.414197111158623200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18500000000000008 " " y[1] (analytic) = 1.234008583333333900E-2 " " y[1] (numeric) = 1.234008583333333600E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.405762892905436700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18600000000000008 " " y[1] (analytic) = 1.241375904000000700E-2 " " y[1] (numeric) = 1.241375904000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.79483993589230540000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18700000000000008 " " y[1] (analytic) = 1.248750968666667300E-2 " " y[1] (numeric) = 1.24875096866666700E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.389166871140872000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18800000000000008 " " y[1] (analytic) = 1.25613378133333400E-2 " " y[1] (numeric) = 1.256133781333333700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.762004337046759500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18900000000000008 " " y[1] (analytic) = 1.263524346000000600E-2 " " y[1] (numeric) = 1.263524346000000400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.372924456476445600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19000000000000009 " " y[1] (analytic) = 1.270922666666667300E-2 " " y[1] (numeric) = 1.27092266666666700E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.364932360933164300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1910000000000001 " " y[1] (analytic) = 1.278328747333333800E-2 " " y[1] (numeric) = 1.278328747333333800E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.357024536603388400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1920000000000001 " " y[1] (analytic) = 1.285742592000000400E-2 " " y[1] (numeric) = 1.285742592000000400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.349199666224331000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1930000000000001 " " y[1] (analytic) = 1.293164204666667500E-2 " " y[1] (numeric) = 1.29316420466666700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.682912919668942000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1940000000000001 " " y[1] (analytic) = 1.30059358933333400E-2 " " y[1] (numeric) = 1.300593589333333700E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.333793654069909700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1950000000000001 " " y[1] (analytic) = 1.308030750000000500E-2 " " y[1] (numeric) = 1.308030750000000500E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.326210011482380200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1960000000000001 " " y[1] (analytic) = 1.315475690666667300E-2 " " y[1] (numeric) = 1.31547569066666700E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.318704319878134800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1970000000000001 " " y[1] (analytic) = 1.32292841533333400E-2 " " y[1] (numeric) = 1.322928415333333700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.622550783353934000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1980000000000001 " " y[1] (analytic) = 1.330388928000000600E-2 " " y[1] (numeric) = 1.330388928000000300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.607844126581315700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1990000000000001 " " y[1] (analytic) = 1.337857232666667000E-2 " " y[1] (numeric) = 1.33785723266666680E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.296643194520159200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2000000000000001 " " y[1] (analytic) = 1.345333333333334200E-2 " " y[1] (numeric) = 1.345333333333333700E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.868313003912600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2010000000000001 " " y[1] (analytic) = 1.352817234000000500E-2 " " y[1] (numeric) = 1.352817234000000300E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.282304388485345500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2020000000000001 " " y[1] (analytic) = 1.360308938666667200E-2 " " y[1] (numeric) = 1.36030893866666700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.550484565185801600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2030000000000001 " " y[1] (analytic) = 1.36780845133333380E-2 " " y[1] (numeric) = 1.367808451333333600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.536500595950852400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2040000000000001 " " y[1] (analytic) = 1.375315776000000700E-2 " " y[1] (numeric) = 1.375315776000000000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.783982208846864000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2050000000000001 " " y[1] (analytic) = 1.382830916666667500E-2 " " y[1] (numeric) = 1.382830916666667000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.76341775788116200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2060000000000001 " " y[1] (analytic) = 1.39035387733333400E-2 " " y[1] (numeric) = 1.390353877333333500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.743054565296640700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2070000000000001 " " y[1] (analytic) = 1.397884662000000700E-2 " " y[1] (numeric) = 1.397884662000000200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.72288971286417800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2080000000000001 " " y[1] (analytic) = 1.405423274666667300E-2 " " y[1] (numeric) = 1.40542327466666700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.46861355898384700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2090000000000001 " " y[1] (analytic) = 1.412969719333334300E-2 " " y[1] (numeric) = 1.412969719333333500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.910858179735889700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2100000000000001 " " y[1] (analytic) = 1.420524000000000500E-2 " " y[1] (numeric) = 1.420524000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.44237123199158400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2110000000000001 " " y[1] (analytic) = 1.428086120666667300E-2 " " y[1] (numeric) = 1.428086120666666700E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.644157276383990000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2120000000000001 " " y[1] (analytic) = 1.43565608533333420E-2 " " y[1] (numeric) = 1.435656085333333600E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.624942269319399400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2130000000000001 " " y[1] (analytic) = 1.44323389800000100E-2 " " y[1] (numeric) = 1.443233898000000300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.807878967867219600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2140000000000001 " " y[1] (analytic) = 1.450819562666667300E-2 " " y[1] (numeric) = 1.45081956266666700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.391370395899973200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2150000000000001 " " y[1] (analytic) = 1.45841308333333420E-2 " " y[1] (numeric) = 1.458413083333333600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.378919245584304200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2160000000000001 " " y[1] (analytic) = 1.466014464000000800E-2 " " y[1] (numeric) = 1.466014464000000600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.366584394049752500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2170000000000001 " " y[1] (analytic) = 1.473623708666667600E-2 " " y[1] (numeric) = 1.473623708666667000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.354364232571125300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2180000000000001 " " y[1] (analytic) = 1.481240821333334500E-2 " " y[1] (numeric) = 1.481240821333334000E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.51338577291294400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2190000000000001 " " y[1] (analytic) = 1.488865806000000700E-2 " " y[1] (numeric) = 1.488865806000000400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.330261691800592200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2200000000000001 " " y[1] (analytic) = 1.496498666666667700E-2 " " y[1] (numeric) = 1.496498666666667100E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.47756435996184330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2210000000000001 " " y[1] (analytic) = 1.504139407333334200E-2 " " y[1] (numeric) = 1.504139407333333600E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.4598989977643200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22200000000000011 " " y[1] (analytic) = 1.51178803200000100E-2 " " y[1] (numeric) = 1.511788032000000400E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.44239424957322200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22300000000000011 " " y[1] (analytic) = 1.519444544666667400E-2 " " y[1] (numeric) = 1.519444544666667000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.283365302229397300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22400000000000012 " " y[1] (analytic) = 1.527108949333334000E-2 " " y[1] (numeric) = 1.527108949333333700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.27190532376109500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22500000000000012 " " y[1] (analytic) = 1.534781250000000800E-2 " " y[1] (numeric) = 1.534781250000000500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.390822260781735700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22600000000000012 " " y[1] (analytic) = 1.542461450666667600E-2 " " y[1] (numeric) = 1.54246145066666700E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.37393872999621870000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22700000000000012 " " y[1] (analytic) = 1.550149555333334400E-2 " " y[1] (numeric) = 1.550149555333333600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.47627384082636640000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22800000000000012 " " y[1] (analytic) = 1.55784556800000080E-2 " " y[1] (numeric) = 1.557845568000000300E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.45416031373093400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22900000000000012 " " y[1] (analytic) = 1.565549492666667700E-2 " " y[1] (numeric) = 1.56554949266666700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.432241801623219600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23000000000000012 " " y[1] (analytic) = 1.573261333333334200E-2 " " y[1] (numeric) = 1.573261333333333700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.410515759136789400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23100000000000012 " " y[1] (analytic) = 1.58098109400000080E-2 " " y[1] (numeric) = 1.580981094000000200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.38897968498238370000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23200000000000012 " " y[1] (analytic) = 1.588708778666667600E-2 " " y[1] (numeric) = 1.588708778666666800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.55144668149696900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23300000000000012 " " y[1] (analytic) = 1.59644439133333430E-2 " " y[1] (numeric) = 1.596444391333333400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.34646765122331300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23400000000000012 " " y[1] (analytic) = 1.60418793600000100E-2 " " y[1] (numeric) = 1.60418793600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.48823035149719300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23500000000000013 " " y[1] (analytic) = 1.611939416666667600E-2 " " y[1] (numeric) = 1.61193941666666670E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.30468653608345900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23600000000000013 " " y[1] (analytic) = 1.619698837333334300E-2 " " y[1] (numeric) = 1.619698837333333500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.28406426180523500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23700000000000013 " " y[1] (analytic) = 1.62746620200000100E-2 " " y[1] (numeric) = 1.62746620200E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.39542673332938100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23800000000000013 " " y[1] (analytic) = 1.635241514666667700E-2 " " y[1] (numeric) = 1.635241514666666600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.36501749894877600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23900000000000013 " " y[1] (analytic) = 1.643024779333334000E-2 " " y[1] (numeric) = 1.643024779333333600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.22324361213999470000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24000000000000013 " " y[1] (analytic) = 1.650816000000000800E-2 " " y[1] (numeric) = 1.65081600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.20331151618788800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24100000000000013 " " y[1] (analytic) = 1.65861518066666770E-2 " " y[1] (numeric) = 1.658615180666666900E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.27531990372672700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24200000000000013 " " y[1] (analytic) = 1.666422325333334300E-2 " " y[1] (numeric) = 1.666422325333333500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.16394679693170900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24300000000000013 " " y[1] (analytic) = 1.67423743800000100E-2 " " y[1] (numeric) = 1.67423743800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.21676508936173700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24400000000000013 " " y[1] (analytic) = 1.682060522666667700E-2 " " y[1] (numeric) = 1.682060522666666800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.18785157585168200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24500000000000013 " " y[1] (analytic) = 1.689891583333334400E-2 " " y[1] (numeric) = 1.689891583333333300E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.15917669424108600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24600000000000014 " " y[1] (analytic) = 1.69773062400000120E-2 " " y[1] (numeric) = 1.69773062400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.13073753204609400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24700000000000014 " " y[1] (analytic) = 1.705577648666667700E-2 " " y[1] (numeric) = 1.705577648666666800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.1025312239507500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24800000000000014 " " y[1] (analytic) = 1.713432661333334500E-2 " " y[1] (numeric) = 1.713432661333333400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.07455495085603700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24900000000000014 " " y[1] (analytic) = 1.721295666000000600E-2 " " y[1] (numeric) = 1.72129566600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.03120395930121670000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2500000000000001 " " y[1] (analytic) = 1.729166666666667700E-2 " " y[1] (numeric) = 1.729166666666666600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.01928145881108500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2510000000000001 " " y[1] (analytic) = 1.73704566733333400E-2 " " y[1] (numeric) = 1.737045667333333400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.994652549670517600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2520000000000001 " " y[1] (analytic) = 1.74493267200000080E-2 " " y[1] (numeric) = 1.744932671999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.96489539274374900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2530000000000001 " " y[1] (analytic) = 1.752827684666667700E-2 " " y[1] (numeric) = 1.752827684666666600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.93802856202615300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2540000000000001 " " y[1] (analytic) = 1.760730709333334400E-2 " " y[1] (numeric) = 1.760730709333333300E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.91137577182472800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2550000000000001 " " y[1] (analytic) = 1.76864175000000100E-2 " " y[1] (numeric) = 1.7686417500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.88493450177846200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2560000000000001 " " y[1] (analytic) = 1.776560810666667500E-2 " " y[1] (numeric) = 1.776560810666666700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.905801513939372600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2570000000000001 " " y[1] (analytic) = 1.784487895333334300E-2 " " y[1] (numeric) = 1.784487895333333500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.83267663685474900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2580000000000001 " " y[1] (analytic) = 1.79242300800000100E-2 " " y[1] (numeric) = 1.79242300800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.80685519512190800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2590000000000001 " " y[1] (analytic) = 1.800366152666667600E-2 " " y[1] (numeric) = 1.800366152666666400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.78123557835399600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2600000000000001 " " y[1] (analytic) = 1.808317333333334400E-2 " " y[1] (numeric) = 1.808317333333333600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.75581545561739800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2610000000000001 " " y[1] (analytic) = 1.81627655400000120E-2 " " y[1] (numeric) = 1.81627655400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.73059253170364800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2620000000000001 " " y[1] (analytic) = 1.82424381866666800E-2 " " y[1] (numeric) = 1.824243818666666800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.70556454644766500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2630000000000001 " " y[1] (analytic) = 1.832219131333334400E-2 " " y[1] (numeric) = 1.832219131333333300E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.68072927406152100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2640000000000001 " " y[1] (analytic) = 1.84020249600000100E-2 " " y[1] (numeric) = 1.84020249600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.656084522483354000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2650000000000001 " " y[1] (analytic) = 1.848193916666667800E-2 " " y[1] (numeric) = 1.848193916666666700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.63162813274103300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2660000000000001 " " y[1] (analytic) = 1.856193397333334400E-2 " " y[1] (numeric) = 1.856193397333333300E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.607357978330163000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2670000000000001 " " y[1] (analytic) = 1.864200942000000800E-2 " " y[1] (numeric) = 1.86420094200E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.72218130973738400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2680000000000001 " " y[1] (analytic) = 1.872216554666667500E-2 " " y[1] (numeric) = 1.87221655466666700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.706245352126287000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.26900000000000013 " " y[1] (analytic) = 1.880240239333334500E-2 " " y[1] (numeric) = 1.880240239333333700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.690429424256716500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27000000000000013 " " y[1] (analytic) = 1.88827200000000080E-2 " " y[1] (numeric) = 1.888272000000000600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.837366095537937600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27100000000000013 " " y[1] (analytic) = 1.896311840666667600E-2 " " y[1] (numeric) = 1.896311840666667400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.829576168618920200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27200000000000013 " " y[1] (analytic) = 1.904359765333334400E-2 " " y[1] (numeric) = 1.90435976533333400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.821844283370653300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27300000000000013 " " y[1] (analytic) = 1.91241577800000100E-2 " " y[1] (numeric) = 1.91241577800000100E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27400000000000013 " " y[1] (analytic) = 1.920479882666667700E-2 " " y[1] (numeric) = 1.920479882666667500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.806552093186282200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27500000000000013 " " y[1] (analytic) = 1.928552083333334400E-2 " " y[1] (numeric) = 1.92855208333333420E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.798990539035366700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27600000000000013 " " y[1] (analytic) = 1.936632384000001000E-2 " " y[1] (numeric) = 1.93663238400000080E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.79148452779028400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27700000000000014 " " y[1] (analytic) = 1.944720788666667600E-2 " " y[1] (numeric) = 1.944720788666667600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27800000000000014 " " y[1] (analytic) = 1.952817301333334400E-2 " " y[1] (numeric) = 1.95281730133333410E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.776636733802370300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27900000000000014 " " y[1] (analytic) = 1.960921926000001000E-2 " " y[1] (numeric) = 1.96092192600000080E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.76929377246078680000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28000000000000014 " " y[1] (analytic) = 1.96903466666666800E-2 " " y[1] (numeric) = 1.969034666666667500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.52400799304052700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28100000000000014 " " y[1] (analytic) = 1.977155527333334700E-2 " " y[1] (numeric) = 1.977155527333334000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.754766837504680400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28200000000000014 " " y[1] (analytic) = 1.98528451200000120E-2 " " y[1] (numeric) = 1.985284512000000700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.74758173500202700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28300000000000014 " " y[1] (analytic) = 1.993421624666667800E-2 " " y[1] (numeric) = 1.993421624666667500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.74044813652192680000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28400000000000014 " " y[1] (analytic) = 2.001566869333334400E-2 " " y[1] (numeric) = 2.001566869333334400E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28500000000000014 " " y[1] (analytic) = 2.009720250000000800E-2 " " y[1] (numeric) = 2.009720250000000800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28600000000000014 " " y[1] (analytic) = 2.017881770666668000E-2 " " y[1] (numeric) = 2.017881770666667400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.71935095622940200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28700000000000014 " " y[1] (analytic) = 2.026051435333334500E-2 " " y[1] (numeric) = 2.026051435333334200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.712418002548295000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28800000000000014 " " y[1] (analytic) = 2.03422924800000100E-2 " " y[1] (numeric) = 2.03422924800000100E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28900000000000015 " " y[1] (analytic) = 2.042415212666667800E-2 " " y[1] (numeric) = 2.042415212666667800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29000000000000015 " " y[1] (analytic) = 2.050609333333334200E-2 " " y[1] (numeric) = 2.050609333333334200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29100000000000015 " " y[1] (analytic) = 2.058811614000000700E-2 " " y[1] (numeric) = 2.058811614000000700E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29200000000000015 " " y[1] (analytic) = 2.067022058666667700E-2 " " y[1] (numeric) = 2.067022058666667400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.678476016937903400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29300000000000015 " " y[1] (analytic) = 2.075240671333334300E-2 " " y[1] (numeric) = 2.07524067133333400E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.671828718412938200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29400000000000015 " " y[1] (analytic) = 2.083467456000001300E-2 " " y[1] (numeric) = 2.08346745600000100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.665227331467188700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29500000000000015 " " y[1] (analytic) = 2.091702416666667600E-2 " " y[1] (numeric) = 2.091702416666667600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29600000000000015 " " y[1] (analytic) = 2.099945557333334800E-2 " " y[1] (numeric) = 2.099945557333334200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.652160428558620800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29700000000000015 " " y[1] (analytic) = 2.108196882000001300E-2 " " y[1] (numeric) = 2.10819688200000080E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.6456939964080700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29800000000000015 " " y[1] (analytic) = 2.116456394666667600E-2 " " y[1] (numeric) = 2.116456394666667600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29900000000000015 " " y[1] (analytic) = 2.124724099333334400E-2 " " y[1] (numeric) = 2.124724099333334400E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30000000000000016 " " y[1] (analytic) = 2.133000000000001300E-2 " " y[1] (numeric) = 2.13300000000000100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.626557408323306100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30100000000000016 " " y[1] (analytic) = 2.14128410066666800E-2 " " y[1] (numeric) = 2.141284100666667700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.620264658423156400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30200000000000016 " " y[1] (analytic) = 2.149576405333334400E-2 " " y[1] (numeric) = 2.149576405333334000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.614014251061528200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30300000000000016 " " y[1] (analytic) = 2.157876918000001300E-2 " " y[1] (numeric) = 2.15787691800000100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.607805766405446300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30400000000000016 " " y[1] (analytic) = 2.16618564266666800E-2 " " y[1] (numeric) = 2.166185642666667600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.20327758029323400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30500000000000016 " " y[1] (analytic) = 2.174502583333334500E-2 " " y[1] (numeric) = 2.17450258333333420E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.59551291341086230000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30600000000000016 " " y[1] (analytic) = 2.182827744000001300E-2 " " y[1] (numeric) = 2.18282774400000100E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.589427732669322400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30700000000000016 " " y[1] (analytic) = 2.19116112866666820E-2 " " y[1] (numeric) = 2.191161128666667400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.166765699302806500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30800000000000016 " " y[1] (analytic) = 2.199502741333334600E-2 " " y[1] (numeric) = 2.19950274133333400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.154755742518821600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30900000000000016 " " y[1] (analytic) = 2.207852586000001400E-2 " " y[1] (numeric) = 2.207852586000000600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.14282481896969560000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31000000000000016 " " y[1] (analytic) = 2.21621066666666800E-2 " " y[1] (numeric) = 2.216210666666667600E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.130972162652658000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31100000000000017 " " y[1] (analytic) = 2.22457698733333500E-2 " " y[1] (numeric) = 2.22457698733333430E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.119197017418166600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31200000000000017 " " y[1] (analytic) = 2.232951552000001500E-2 " " y[1] (numeric) = 2.23295155200000100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 3.10749863681199300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31300000000000017 " " y[1] (analytic) = 2.24133436466666800E-2 " " y[1] (numeric) = 2.241334364666667800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.547938141960176200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31400000000000017 " " y[1] (analytic) = 2.24972542933333500E-2 " " y[1] (numeric) = 2.249725429333334600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.54216461560899100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31500000000000017 " " y[1] (analytic) = 2.258124750000001500E-2 " " y[1] (numeric) = 2.258124750000001200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.536428380209557400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31600000000000017 " " y[1] (analytic) = 2.26653233066666800E-2 " " y[1] (numeric) = 2.26653233066666800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31700000000000017 " " y[1] (analytic) = 2.27494817533333500E-2 " " y[1] (numeric) = 2.274948175333334500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.525066368355954300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31800000000000017 " " y[1] (analytic) = 2.283372288000001500E-2 " " y[1] (numeric) = 2.28337228800000120E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.519439896063769500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3190000000000002 " " y[1] (analytic) = 2.291804672666668300E-2 " " y[1] (numeric) = 2.29180467266666800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.513849322907907500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3200000000000002 " " y[1] (analytic) = 2.300245333333334500E-2 " " y[1] (numeric) = 2.300245333333334500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3210000000000002 " " y[1] (analytic) = 2.308694274000001600E-2 " " y[1] (numeric) = 2.308694274000001000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.50277452975292100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3220000000000002 " " y[1] (analytic) = 2.317151498666668300E-2 " " y[1] (numeric) = 2.31715149866666800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.497289648065738300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3230000000000002 " " y[1] (analytic) = 2.325617011333334600E-2 " " y[1] (numeric) = 2.325617011333334600E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3240000000000002 " " y[1] (analytic) = 2.334090816000001200E-2 " " y[1] (numeric) = 2.334090816000001200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3250000000000002 " " y[1] (analytic) = 2.34257291666666800E-2 " " y[1] (numeric) = 2.34257291666666800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3260000000000002 " " y[1] (analytic) = 2.351063317333334800E-2 " " y[1] (numeric) = 2.351063317333334800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3270000000000002 " " y[1] (analytic) = 2.359562022000001600E-2 " " y[1] (numeric) = 2.359562022000001300E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.470377519050275700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3280000000000002 " " y[1] (analytic) = 2.368069034666668300E-2 " " y[1] (numeric) = 2.36806903466666770E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.46509535877697800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3290000000000002 " " y[1] (analytic) = 2.37658435933333500E-2 " " y[1] (numeric) = 2.376584359333334700E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.459845907984870500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3300000000000002 " " y[1] (analytic) = 2.385108000000001300E-2 " " y[1] (numeric) = 2.385108000000001300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3310000000000002 " " y[1] (analytic) = 2.39363996066666800E-2 " " y[1] (numeric) = 2.39363996066666800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3320000000000002 " " y[1] (analytic) = 2.40218024533333500E-2 " " y[1] (numeric) = 2.402180245333334600E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.444290851485285600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3330000000000002 " " y[1] (analytic) = 2.410728858000002000E-2 " " y[1] (numeric) = 2.41072885800000100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.878338590787808400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3340000000000002 " " y[1] (analytic) = 2.41928580266666800E-2 " " y[1] (numeric) = 2.419285802666667800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 1.43407899477168100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3350000000000002 " " y[1] (analytic) = 2.42785108333333500E-2 " " y[1] (numeric) = 2.427851083333334400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.858039338384966700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3360000000000002 " " y[1] (analytic) = 2.436424704000001400E-2 " " y[1] (numeric) = 2.43642470400000100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.847982083138171400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3370000000000002 " " y[1] (analytic) = 2.44500666866666830E-2 " " y[1] (numeric) = 2.445006668666667400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.837985676207257500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3380000000000002 " " y[1] (analytic) = 2.45359698133333500E-2 " " y[1] (numeric) = 2.45359698133333400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.24207436471687240000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3390000000000002 " " y[1] (analytic) = 2.462195646000001600E-2 " " y[1] (numeric) = 2.462195646000000800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.227259873832478000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3400000000000002 " " y[1] (analytic) = 2.470802666666668500E-2 " " y[1] (numeric) = 2.470802666666667400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.21253424900282100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3410000000000002 " " y[1] (analytic) = 2.479418047333334700E-2 " " y[1] (numeric) = 2.47941804733333400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.798597804581664500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3420000000000002 " " y[1] (analytic) = 2.488041792000001400E-2 " " y[1] (numeric) = 2.48804179200000100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.788897648833072500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3430000000000002 " " y[1] (analytic) = 2.496673904666668300E-2 " " y[1] (numeric) = 2.496673904666667500E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.779255188648131500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3440000000000002 " " y[1] (analytic) = 2.50531438933333500E-2 " " y[1] (numeric) = 2.50531438933333400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.15450487977698700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3450000000000002 " " y[1] (analytic) = 2.513963250000001400E-2 " " y[1] (numeric) = 2.51396325000000100E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.76014134411361200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3460000000000002 " " y[1] (analytic) = 2.522620490666668000E-2 " " y[1] (numeric) = 2.522620490666667000E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.12600345330191400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3470000000000002 " " y[1] (analytic) = 2.531286115333335500E-2 " " y[1] (numeric) = 2.53128611533333440E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.111878460839346600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3480000000000002 " " y[1] (analytic) = 2.539960128000001700E-2 " " y[1] (numeric) = 2.539960128000000600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.09783631684663800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3490000000000002 " " y[1] (analytic) = 2.548642532666668400E-2 " " y[1] (numeric) = 2.548642532666667300E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.08387630766347600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3500000000000002 " " y[1] (analytic) = 2.55733333333333500E-2 " " y[1] (numeric) = 2.55733333333333400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.069997727787083600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3510000000000002 " " y[1] (analytic) = 2.56603253400000200E-2 " " y[1] (numeric) = 2.56603253400000060E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.0561998797560200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3520000000000002 " " y[1] (analytic) = 2.574740138666668500E-2 " " y[1] (numeric) = 2.574740138666667400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.0424820740359500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3530000000000002 " " y[1] (analytic) = 2.58345615133333500E-2 " " y[1] (numeric) = 2.58345615133333430E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.028843628907362600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3540000000000002 " " y[1] (analytic) = 2.59218057600000200E-2 " " y[1] (numeric) = 2.592180576000000500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.35371182714025700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3550000000000002 " " y[1] (analytic) = 2.600913416666668000E-2 " " y[1] (numeric) = 2.600913416666667500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 4.00180213196030800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3560000000000002 " " y[1] (analytic) = 2.609654677333334600E-2 " " y[1] (numeric) = 2.60965467733333400E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 2.65893183652854400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3570000000000002 " " y[1] (analytic) = 2.61840436200000200E-2 " " y[1] (numeric) = 2.618404362000001000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.300093449742903000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3580000000000002 " " y[1] (analytic) = 2.627162474666669000E-2 " " y[1] (numeric) = 2.627162474666667000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.28242464698543400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3590000000000002 " " y[1] (analytic) = 2.63592901933333500E-2 " " y[1] (numeric) = 2.63592901933333400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 3.94864231150399650000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3600000000000002 " " y[1] (analytic) = 2.64470400000000200E-2 " " y[1] (numeric) = 2.644704000000000500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.24738791479668300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3610000000000002 " " y[1] (analytic) = 2.653487420666668000E-2 " " y[1] (numeric) = 2.653487420666667500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 3.922513735997220600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3620000000000002 " " y[1] (analytic) = 2.66227928533333500E-2 " " y[1] (numeric) = 2.66227928533333440E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 3.90956009506630340000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3630000000000002 " " y[1] (analytic) = 2.671079598000002000E-2 " " y[1] (numeric) = 2.671079598000000700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 3.89667940395868200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3640000000000002 " " y[1] (analytic) = 2.679888362666668600E-2 " " y[1] (numeric) = 2.679888362666667000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.178494746700989000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3650000000000002 " " y[1] (analytic) = 2.688705583333335000E-2 " " y[1] (numeric) = 2.68870558333333400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.161512622966106000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3660000000000002 " " y[1] (analytic) = 2.697531264000001500E-2 " " y[1] (numeric) = 2.697531264000000400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 3.85846903602776400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3670000000000002 " " y[1] (analytic) = 2.706365408666669000E-2 " " y[1] (numeric) = 2.706365408666667000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.12783224444608800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3680000000000002 " " y[1] (analytic) = 2.715208021333335000E-2 " " y[1] (numeric) = 2.71520802133333400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.11113244317818600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3690000000000002 " " y[1] (analytic) = 2.72405910600000200E-2 " " y[1] (numeric) = 2.724059106000001000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.09452521688949200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3700000000000002 " " y[1] (analytic) = 2.732918666666668000E-2 " " y[1] (numeric) = 2.73291866666666700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.07800981312815500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3710000000000002 " " y[1] (analytic) = 2.741786707333335000E-2 " " y[1] (numeric) = 2.741786707333333500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.06158548755676500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3720000000000002 " " y[1] (analytic) = 2.750663232000002400E-2 " " y[1] (numeric) = 2.750663232000001000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.30656437980411300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3730000000000002 " " y[1] (analytic) = 2.759548244666668600E-2 " " y[1] (numeric) = 2.759548244666667500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.02900713355376800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3740000000000002 " " y[1] (analytic) = 2.768441749333335000E-2 " " y[1] (numeric) = 2.76844174933333400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.012851656046708000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3750000000000002 " " y[1] (analytic) = 2.77734375000000200E-2 " " y[1] (numeric) = 2.777343750000000300E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 4.996784358369196000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3760000000000002 " " y[1] (analytic) = 2.78625425066666900E-2 " " y[1] (numeric) = 2.78625425066666700E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.22600566894330900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3770000000000002 " " y[1] (analytic) = 2.79517325533333500E-2 " " y[1] (numeric) = 2.795173255333333600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 4.96491148852219450000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3780000000000002 " " y[1] (analytic) = 2.804100768000002000E-2 " " y[1] (numeric) = 2.804100768000000000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 4.94910452797766500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3790000000000002 " " y[1] (analytic) = 2.813036792666669000E-2 " " y[1] (numeric) = 2.81303679266666700E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.16672871289516500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3800000000000002 " " y[1] (analytic) = 2.82198133333333500E-2 " " y[1] (numeric) = 2.821981333333334000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 4.91774613952600500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3810000000000002 " " y[1] (analytic) = 2.83093439400000200E-2 " " y[1] (numeric) = 2.830934394000000400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.12774170836827200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38200000000000023 " " y[1] (analytic) = 2.839895978666668300E-2 " " y[1] (numeric) = 2.839895978666666700E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.10840498739415100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38300000000000023 " " y[1] (analytic) = 2.848866091333335000E-2 " " y[1] (numeric) = 2.848866091333333600E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.08917169274501200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38400000000000023 " " y[1] (analytic) = 2.85784473600000200E-2 " " y[1] (numeric) = 2.857844736000000300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.07004101421136800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38500000000000023 " " y[1] (analytic) = 2.866831916666668400E-2 " " y[1] (numeric) = 2.866831916666666700E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.05101215000358300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38600000000000023 " " y[1] (analytic) = 2.875827637333336000E-2 " " y[1] (numeric) = 2.875827637333333600E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.23850116797136600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38700000000000023 " " y[1] (analytic) = 2.88483190200000200E-2 " " y[1] (numeric) = 2.884831902000000000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.01325669885359600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38800000000000023 " " y[1] (analytic) = 2.893844714666668500E-2 " " y[1] (numeric) = 2.893844714666667000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 5.99452854945820300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38900000000000023 " " y[1] (analytic) = 2.902866079333335500E-2 " " y[1] (numeric) = 2.902866079333333300E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.17107890712698300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39000000000000024 " " y[1] (analytic) = 2.91189600000000200E-2 " " y[1] (numeric) = 2.91189600E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.14884106840411600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39100000000000024 " " y[1] (analytic) = 2.920934480666668000E-2 " " y[1] (numeric) = 2.920934480666666500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 5.9389331991482310000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39200000000000024 " " y[1] (analytic) = 2.929981525333335600E-2 " " y[1] (numeric) = 2.929981525333333300E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.10471432387391400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39300000000000024 " " y[1] (analytic) = 2.939037138000002400E-2 " " y[1] (numeric) = 2.93903713800E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.26329424343438800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39400000000000024 " " y[1] (analytic) = 2.94810132266666900E-2 " " y[1] (numeric) = 2.948101322666666400E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.23788805254073700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39500000000000024 " " y[1] (analytic) = 2.957174083333335400E-2 " " y[1] (numeric) = 2.957174083333333000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.03938325073411400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39600000000000024 " " y[1] (analytic) = 2.96625542400000200E-2 " " y[1] (numeric) = 2.96625542400E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.01783182368372800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39700000000000024 " " y[1] (analytic) = 2.97534534866666870E-2 " " y[1] (numeric) = 2.975345348666667000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 6.99639177047134700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39800000000000024 " " y[1] (analytic) = 2.984443861333335000E-2 " " y[1] (numeric) = 2.984443861333333500E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 6.97506224909239500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39900000000000024 " " y[1] (analytic) = 2.99355096600000200E-2 " " y[1] (numeric) = 2.993550966000000000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 6.95384242598583200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = (0.1 * x + 0.2) * (0.2 * x + 0.3);" Iterations = 299 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 46 Minutes 15 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 45 Minutes 52 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 48 Minutes 53 Seconds "Time to Timeout " Unknown Percent Done = 6.122448979591842 "%" (%o54) true (%o54) diffeq.max