(%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_0D3 + array_const_0D0 , 1 1 1 array_tmp2 : array_const_0D1 array_x , 1 1 1 array_tmp3 : array_const_0D2 + array_tmp2 , 1 1 1 array_tmp4 : array_tmp1 - array_tmp3 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 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_tmp2 : array_const_0D1 array_x , array_tmp3 : array_tmp2 , 2 1 2 2 2 array_tmp4 : - array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 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 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 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 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 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 (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 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_0D3 + array_const_0D0 , 1 1 1 array_tmp2 : array_const_0D1 array_x , 1 1 1 array_tmp3 : array_const_0D2 + array_tmp2 , 1 1 1 array_tmp4 : array_tmp1 - array_tmp3 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp4 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_tmp2 : array_const_0D1 array_x , array_tmp3 : array_tmp2 , 2 1 2 2 2 array_tmp4 : - array_tmp3 , if not array_y_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : array_tmp4 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 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 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 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 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 (order_d : 1, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 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) (%i52) exact_soln_y(x) := block(0.1 x - 0.05 x x) (%o52) exact_soln_y(x) := block(0.1 x - 0.05 x x) (%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/sub_c_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 0.3 - (0.1 * x + 0.2) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), 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, " (- 0.05 * x * x + 0.1 * 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_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_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_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_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_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, 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 ) = 0.3 - (0.1 * x + 0.2) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T03:41:31-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sub_c_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 0.3 - (0.1 * x + 0.2) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "sub_c_lin diffeq.max"), logitem_str(html_log_file, "sub_c_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/sub_c_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 0.3 - (0.1 * x + 0.2) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), 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, " (- 0.05 * x * x + 0.1 * 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_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_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_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_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_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, 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 ) = 0.3 - (0.1 * x + 0.2) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-12-15T03:41:31-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "sub_c_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 0.3 - (0.1 * x + 0.2) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 151 "), logitem_str(html_log_file, "sub_c_lin diffeq.max"), logitem_str(html_log_file, "sub_c_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/sub_c_linpostode.ode#################" "diff ( y , x , 1 ) = 0.3 - (0.1 * x + 0.2) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "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(" " (- 0.05 * x * x + 0.1 * 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) = 9.500000000000002000E-3 " " y[1] (numeric) = 9.500000000000002000E-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) = 9.589950000000002000E-3 " " y[1] (numeric) = 9.589950000000002000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10200000000000001 " " y[1] (analytic) = 9.6798000E-3 " " y[1] (numeric) = 9.679800000000003000E-3 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.792106733586238400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10300000000000001 " " y[1] (analytic) = 9.769550000000002000E-3 " " y[1] (numeric) = 9.769550000000002000E-3 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10400000000000001 " " y[1] (analytic) = 9.859200000000002000E-3 " " y[1] (numeric) = 9.859200000000002000E-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) = 9.948750000000003000E-3 " " y[1] (numeric) = 9.948750000000003000E-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) = 1.003820000000000300E-2 " " y[1] (numeric) = 1.003820000000000300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10700000000000001 " " y[1] (analytic) = 1.01275500E-2 " " y[1] (numeric) = 1.012755000000000200E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.712875745838635000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10800000000000001 " " y[1] (analytic) = 1.021680000000000100E-2 " " y[1] (numeric) = 1.021680000000000400E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.697912728033050500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10900000000000001 " " y[1] (analytic) = 1.030595000000000100E-2 " " y[1] (numeric) = 1.030595000000000300E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.683225200953630800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11000000000000001 " " y[1] (analytic) = 1.039500000000000300E-2 " " y[1] (numeric) = 1.039500000000000300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11100000000000002 " " y[1] (analytic) = 1.048395000000000300E-2 " " y[1] (numeric) = 1.048395000000000300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11200000000000002 " " y[1] (analytic) = 1.057280000000000200E-2 " " y[1] (numeric) = 1.057280000000000200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11300000000000002 " " y[1] (analytic) = 1.066155000000000300E-2 " " y[1] (numeric) = 1.066155000000000300E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11400000000000002 " " y[1] (analytic) = 1.075020000000000100E-2 " " y[1] (numeric) = 1.075020000000000100E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11500000000000002 " " y[1] (analytic) = 1.083875000000000300E-2 " " y[1] (numeric) = 1.083875000000000100E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.6004829671104200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11600000000000002 " " y[1] (analytic) = 1.092720000000000100E-2 " " y[1] (numeric) = 1.092720000000000100E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11700000000000002 " " y[1] (analytic) = 1.101555000000000200E-2 " " y[1] (numeric) = 1.10155500E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.5747951541019800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11800000000000002 " " y[1] (analytic) = 1.110380000000000300E-2 " " y[1] (numeric) = 1.1103800E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.562279108032211300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.11900000000000002 " " y[1] (analytic) = 1.119195000000000300E-2 " " y[1] (numeric) = 1.11919500E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.54997429042910900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12000000000000002 " " y[1] (analytic) = 1.128000000000000400E-2 " " y[1] (numeric) = 1.12800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.075750843930508000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12100000000000002 " " y[1] (analytic) = 1.136795000000000300E-2 " " y[1] (numeric) = 1.13679500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.0519547956787396000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12200000000000003 " " y[1] (analytic) = 1.145580000000000200E-2 " " y[1] (numeric) = 1.1455800E-2 " " absolute error = 1.734723475976807000000000000000000E-18 " " relative error = 1.514275280623620400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12300000000000003 " " y[1] (analytic) = 1.154355000000000200E-2 " " y[1] (numeric) = 1.15435500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 3.00552858691963300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12400000000000003 " " y[1] (analytic) = 1.163120000000000300E-2 " " y[1] (numeric) = 1.1631200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.98287962716969300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12500000000000003 " " y[1] (analytic) = 1.171875000000000300E-2 " " y[1] (numeric) = 1.17187500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.9605947323337495000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12600000000000003 " " y[1] (analytic) = 1.180620000000000300E-2 " " y[1] (numeric) = 1.1806200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.938665236870130500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12700000000000003 " " y[1] (analytic) = 1.189355000000000300E-2 " " y[1] (numeric) = 1.18935500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.91708274817326500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12800000000000003 " " y[1] (analytic) = 1.198080000000000300E-2 " " y[1] (numeric) = 1.1980800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.89583913591213700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.12900000000000003 " " y[1] (analytic) = 1.206795000000000200E-2 " " y[1] (numeric) = 1.20679500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.874926521864619700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13000000000000003 " " y[1] (analytic) = 1.215500000000000500E-2 " " y[1] (numeric) = 1.215500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.28150590533148400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13100000000000003 " " y[1] (analytic) = 1.224195000000000300E-2 " " y[1] (numeric) = 1.22419500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.834063978331567400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13200000000000003 " " y[1] (analytic) = 1.232880000000000200E-2 " " y[1] (numeric) = 1.2328800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.814099467874905400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13300000000000003 " " y[1] (analytic) = 1.241555000000000400E-2 " " y[1] (numeric) = 1.24155500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.191655164636620700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13400000000000004 " " y[1] (analytic) = 1.250220000000000200E-2 " " y[1] (numeric) = 1.2502200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.775069149392598000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13500000000000004 " " y[1] (analytic) = 1.258875000000000400E-2 " " y[1] (numeric) = 1.25887500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.133985048499985700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13600000000000004 " " y[1] (analytic) = 1.267520000000000300E-2 " " y[1] (numeric) = 1.2675200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.10578959537555200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13700000000000004 " " y[1] (analytic) = 1.276155000000000500E-2 " " y[1] (numeric) = 1.27615500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.718672067228207000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13800000000000004 " " y[1] (analytic) = 1.284780000000000400E-2 " " y[1] (numeric) = 1.2847800E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 4.0506315695530903000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.13900000000000004 " " y[1] (analytic) = 1.293395000000000200E-2 " " y[1] (numeric) = 1.29339500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.68243417668509100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14000000000000004 " " y[1] (analytic) = 1.302000000000000700E-2 " " y[1] (numeric) = 1.30200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.99705870040738800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14100000000000004 " " y[1] (analytic) = 1.310595000000000500E-2 " " y[1] (numeric) = 1.31059500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.97084562960366800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14200000000000004 " " y[1] (analytic) = 1.319180000000000400E-2 " " y[1] (numeric) = 1.3191800E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.63000269254659200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14300000000000004 " " y[1] (analytic) = 1.327755000000000500E-2 " " y[1] (numeric) = 1.32775500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.61301742561964600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14400000000000004 " " y[1] (analytic) = 1.336320000000000300E-2 " " y[1] (numeric) = 1.3363200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.596269570128123000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14500000000000005 " " y[1] (analytic) = 1.344875000000000700E-2 " " y[1] (numeric) = 1.34487500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.86963132479257840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14600000000000005 " " y[1] (analytic) = 1.353420000000000500E-2 " " y[1] (numeric) = 1.353420000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.56346658979002300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14700000000000005 " " y[1] (analytic) = 1.361955000000000500E-2 " " y[1] (numeric) = 1.361955000000000200E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.5474020448205800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14800000000000005 " " y[1] (analytic) = 1.370480000000000600E-2 " " y[1] (numeric) = 1.370480000000000000E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.531556062075779000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.14900000000000005 " " y[1] (analytic) = 1.378995000000000400E-2 " " y[1] (numeric) = 1.37899500E-2 " " absolute error = 3.469446951953614000000000000000000E-18 " " relative error = 2.515924243346504600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15000000000000005 " " y[1] (analytic) = 1.387500000000000400E-2 " " y[1] (numeric) = 1.387500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.75075346157147300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15100000000000005 " " y[1] (analytic) = 1.395995000000000400E-2 " " y[1] (numeric) = 1.39599500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.727929131501487300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15200000000000005 " " y[1] (analytic) = 1.404480000000000500E-2 " " y[1] (numeric) = 1.4044800E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.705407288057089000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15300000000000005 " " y[1] (analytic) = 1.412955000000000500E-2 " " y[1] (numeric) = 1.41295500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.683182003623908000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15400000000000005 " " y[1] (analytic) = 1.421420000000000500E-2 " " y[1] (numeric) = 1.4214200E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.661247504559116400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15500000000000005 " " y[1] (analytic) = 1.429875000000000500E-2 " " y[1] (numeric) = 1.429875000000000000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.85279755496615100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15600000000000006 " " y[1] (analytic) = 1.438320000000000700E-2 " " y[1] (numeric) = 1.438320000000000000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.824304677615013400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15700000000000006 " " y[1] (analytic) = 1.446755000000000400E-2 " " y[1] (numeric) = 1.44675500E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.59713318974561700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15800000000000006 " " y[1] (analytic) = 1.455180000000000400E-2 " " y[1] (numeric) = 1.455179999999999800E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.57630700527111430000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.15900000000000006 " " y[1] (analytic) = 1.463595000000000600E-2 " " y[1] (numeric) = 1.463594999999999800E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 5.92624146699328200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16000000000000006 " " y[1] (analytic) = 1.472000000000000500E-2 " " y[1] (numeric) = 1.472000000000000000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.713922489067408600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16100000000000006 " " y[1] (analytic) = 1.480395000000000500E-2 " " y[1] (numeric) = 1.480395000000000000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.68719085372973200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16200000000000006 " " y[1] (analytic) = 1.488780000000000400E-2 " " y[1] (numeric) = 1.488779999999999800E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.66079199338198140000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16300000000000006 " " y[1] (analytic) = 1.497155000000000300E-2 " " y[1] (numeric) = 1.497154999999999700E-2 " " absolute error = 5.204170427930421000000000000000000E-18 " " relative error = 3.47603984085176230000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16400000000000006 " " y[1] (analytic) = 1.505520000000000700E-2 " " y[1] (numeric) = 1.505519999999999600E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 5.76121033256551400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16500000000000006 " " y[1] (analytic) = 1.513875000000000600E-2 " " y[1] (numeric) = 1.513874999999999800E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 5.72941450244176900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16600000000000006 " " y[1] (analytic) = 1.522220000000000500E-2 " " y[1] (numeric) = 1.522219999999999700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.55840410972607470000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16700000000000007 " " y[1] (analytic) = 1.530555000000000400E-2 " " y[1] (numeric) = 1.530554999999999800E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.533580239787022300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16800000000000007 " " y[1] (analytic) = 1.538880000000000500E-2 " " y[1] (numeric) = 1.538879999999999700E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.5090545746953803000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.16900000000000007 " " y[1] (analytic) = 1.547195000000000700E-2 " " y[1] (numeric) = 1.547194999999999800E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 5.60602728155405800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17000000000000007 " " y[1] (analytic) = 1.555500000000000800E-2 " " y[1] (numeric) = 1.555499999999999700E-2 " " absolute error = 8.673617379884035000000000000000000E-18 " " relative error = 5.57609603335521100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17100000000000007 " " y[1] (analytic) = 1.563795000000000600E-2 " " y[1] (numeric) = 1.563794999999999800E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.43721453509393900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17200000000000007 " " y[1] (analytic) = 1.572080000000000700E-2 " " y[1] (numeric) = 1.572079999999999600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.62074503578751600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17300000000000007 " " y[1] (analytic) = 1.580355000000000500E-2 " " y[1] (numeric) = 1.580354999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.58607772042410600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17400000000000007 " " y[1] (analytic) = 1.588620000000000600E-2 " " y[1] (numeric) = 1.588619999999999500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.5518128034777600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17500000000000007 " " y[1] (analytic) = 1.596875000000000700E-2 " " y[1] (numeric) = 1.596874999999999800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.51794339310267600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17600000000000007 " " y[1] (analytic) = 1.605120000000000400E-2 " " y[1] (numeric) = 1.605120000000000000E-2 " " absolute error = 6.938893903907228000000000000000000E-18 " " relative error = 4.32297516939993700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17700000000000007 " " y[1] (analytic) = 1.613355000000000800E-2 " " y[1] (numeric) = 1.613354999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.45136430349231200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17800000000000007 " " y[1] (analytic) = 1.621580000000000500E-2 " " y[1] (numeric) = 1.621579999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.41864160624874400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.17900000000000008 " " y[1] (analytic) = 1.62979500000000080E-2 " " y[1] (numeric) = 1.629794999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.51505116153531500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18000000000000008 " " y[1] (analytic) = 1.63800000000000080E-2 " " y[1] (numeric) = 1.637999999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.4723979290686500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18100000000000008 " " y[1] (analytic) = 1.646195000000000600E-2 " " y[1] (numeric) = 1.646194999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.32266581775600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18200000000000008 " " y[1] (analytic) = 1.654380000000000800E-2 " " y[1] (numeric) = 1.654379999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.29138460079355400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18300000000000008 " " y[1] (analytic) = 1.662555000000000600E-2 " " y[1] (numeric) = 1.662554999999999400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.26044904130139400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18400000000000008 " " y[1] (analytic) = 1.67072000000000080E-2 " " y[1] (numeric) = 1.670719999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.30647134637428700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18500000000000008 " " y[1] (analytic) = 1.67887500000000080E-2 " " y[1] (numeric) = 1.678874999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.26612333128699300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18600000000000008 " " y[1] (analytic) = 1.68702000000000070E-2 " " y[1] (numeric) = 1.687019999999999600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.22621415739851800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18700000000000008 " " y[1] (analytic) = 1.695155000000000700E-2 " " y[1] (numeric) = 1.695154999999999600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.140052594518400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18800000000000008 " " y[1] (analytic) = 1.703280000000001000E-2 " " y[1] (numeric) = 1.703279999999999800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 6.11076326608710100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.18900000000000008 " " y[1] (analytic) = 1.71139500000000100E-2 " " y[1] (numeric) = 1.711394999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.1090501069679700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.19000000000000009 " " y[1] (analytic) = 1.71950000000000100E-2 " " y[1] (numeric) = 1.719499999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.07082745438467600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1910000000000001 " " y[1] (analytic) = 1.72759500000000100E-2 " " y[1] (numeric) = 1.727594999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 8.03300994030108400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1920000000000001 " " y[1] (analytic) = 1.735680000000000600E-2 " " y[1] (numeric) = 1.735679999999999400E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.99669343188885100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1930000000000001 " " y[1] (analytic) = 1.74375500000000100E-2 " " y[1] (numeric) = 1.743754999999999600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.95856516988593500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1940000000000001 " " y[1] (analytic) = 1.751820000000001000E-2 " " y[1] (numeric) = 1.751819999999999800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.94144424419223300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1950000000000001 " " y[1] (analytic) = 1.75987500000000100E-2 " " y[1] (numeric) = 1.759874999999999600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.8856667705458900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1960000000000001 " " y[1] (analytic) = 1.76792000000000100E-2 " " y[1] (numeric) = 1.767919999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.84978268689445600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1970000000000001 " " y[1] (analytic) = 1.775955000000000700E-2 " " y[1] (numeric) = 1.775954999999999600E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.86070078119143800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1980000000000001 " " y[1] (analytic) = 1.78398000000000100E-2 " " y[1] (numeric) = 1.783979999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.77911625007816700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1990000000000001 " " y[1] (analytic) = 1.79199500000000120E-2 " " y[1] (numeric) = 1.791994999999999600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.74432284008295100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2000000000000001 " " y[1] (analytic) = 1.80000000000000100E-2 " " y[1] (numeric) = 1.800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.78241158658935300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2010000000000001 " " y[1] (analytic) = 1.807995000000000900E-2 " " y[1] (numeric) = 1.807994999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.75684161508236400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2020000000000001 " " y[1] (analytic) = 1.815980000000000600E-2 " " y[1] (numeric) = 1.815979999999999800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.73152835155719700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2030000000000001 " " y[1] (analytic) = 1.82395500000000100E-2 " " y[1] (numeric) = 1.823954999999999600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.60862401090731300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2040000000000001 " " y[1] (analytic) = 1.83192000000000100E-2 " " y[1] (numeric) = 1.831919999999999700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.57554249520418300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2050000000000001 " " y[1] (analytic) = 1.83987500000000080E-2 " " y[1] (numeric) = 1.83987500E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.65709130014856300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2060000000000001 " " y[1] (analytic) = 1.847820000000000600E-2 " " y[1] (numeric) = 1.847819999999999700E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.63276772405366200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2070000000000001 " " y[1] (analytic) = 1.85575500000000100E-2 " " y[1] (numeric) = 1.855754999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.4782435223477500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2080000000000001 " " y[1] (analytic) = 1.86368000000000100E-2 " " y[1] (numeric) = 1.863679999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.44644349234549400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2090000000000001 " " y[1] (analytic) = 1.87159500000000100E-2 " " y[1] (numeric) = 1.871594999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.4149523843643790000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2100000000000001 " " y[1] (analytic) = 1.87950000000000100E-2 " " y[1] (numeric) = 1.879499999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.38376579293133700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2110000000000001 " " y[1] (analytic) = 1.887395000000000600E-2 " " y[1] (numeric) = 1.887394999999999800E-2 " " absolute error = 1.040834085586084300000000000000000E-17 " " relative error = 5.514659547079884000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2120000000000001 " " y[1] (analytic) = 1.89528000000000090E-2 " " y[1] (numeric) = 1.895279999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.32228895351317500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2130000000000001 " " y[1] (analytic) = 1.90315500000000100E-2 " " y[1] (numeric) = 1.903154999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 9.11498788052894200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2140000000000001 " " y[1] (analytic) = 1.91102000000000100E-2 " " y[1] (numeric) = 1.911019999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 9.07747420736991800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2150000000000001 " " y[1] (analytic) = 1.91887500000000100E-2 " " y[1] (numeric) = 1.918874999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 9.04031516371210300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2160000000000001 " " y[1] (analytic) = 1.92672000000000100E-2 " " y[1] (numeric) = 1.926719999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.20280466690253500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2170000000000001 " " y[1] (analytic) = 1.93455500000000100E-2 " " y[1] (numeric) = 1.934554999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.17363311346250100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2180000000000001 " " y[1] (analytic) = 1.942380000000001300E-2 " " y[1] (numeric) = 1.942379999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.93091710158056600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2190000000000001 " " y[1] (analytic) = 1.95019500000000120E-2 " " y[1] (numeric) = 1.950194999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.89512831269081300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2200000000000001 " " y[1] (analytic) = 1.95800000000000100E-2 " " y[1] (numeric) = 1.957999999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.8596704595342500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2210000000000001 " " y[1] (analytic) = 1.96579500000000100E-2 " " y[1] (numeric) = 1.965794999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.82453905914302400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22200000000000011 " " y[1] (analytic) = 1.973580000000001000E-2 " " y[1] (numeric) = 1.973579999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 7.03178376747557800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22300000000000011 " " y[1] (analytic) = 1.981355000000001300E-2 " " y[1] (numeric) = 1.981354999999999600E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.75523808694961700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22400000000000012 " " y[1] (analytic) = 1.98912000000000120E-2 " " y[1] (numeric) = 1.989119999999999500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.72105994599021700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22500000000000012 " " y[1] (analytic) = 1.99687500000000100E-2 " " y[1] (numeric) = 1.996874999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.68719111600278500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22600000000000012 " " y[1] (analytic) = 2.00462000000000100E-2 " " y[1] (numeric) = 2.004619999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.65362750035820300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22700000000000012 " " y[1] (analytic) = 2.01235500000000120E-2 " " y[1] (numeric) = 2.012354999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.62036507463547100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22800000000000012 " " y[1] (analytic) = 2.020080000000001300E-2 " " y[1] (numeric) = 2.020079999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.58739988503824700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.22900000000000012 " " y[1] (analytic) = 2.02779500000000100E-2 " " y[1] (numeric) = 2.027794999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 6.84378243748231400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23000000000000012 " " y[1] (analytic) = 2.035500000000001200E-2 " " y[1] (numeric) = 2.035499999999999500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.52234574294672600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23100000000000012 " " y[1] (analytic) = 2.04319500000000100E-2 " " y[1] (numeric) = 2.043194999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.49024922230529300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23200000000000012 " " y[1] (analytic) = 2.050880000000000800E-2 " " y[1] (numeric) = 2.050879999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 6.76674783888596700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23300000000000012 " " y[1] (analytic) = 2.05855500000000100E-2 " " y[1] (numeric) = 2.058554999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.426898848837200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23400000000000012 " " y[1] (analytic) = 2.066220000000001400E-2 " " y[1] (numeric) = 2.066219999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.39563781193099500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23500000000000013 " " y[1] (analytic) = 2.07387500000000100E-2 " " y[1] (numeric) = 2.073874999999999700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 6.69171854996778900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23600000000000013 " " y[1] (analytic) = 2.08152000000000100E-2 " " y[1] (numeric) = 2.081519999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 6.6671412274753310000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23700000000000013 " " y[1] (analytic) = 2.08915500000000100E-2 " " y[1] (numeric) = 2.089154999999999500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 6.6427755756822490000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23800000000000013 " " y[1] (analytic) = 2.096780000000001100E-2 " " y[1] (numeric) = 2.096779999999999500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.27327366713153500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.23900000000000013 " " y[1] (analytic) = 2.104395000000001000E-2 " " y[1] (numeric) = 2.104394999999999500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.24333585651365800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24000000000000013 " " y[1] (analytic) = 2.11200000000000100E-2 " " y[1] (numeric) = 2.111999999999999700E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 6.57092225748790200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24100000000000013 " " y[1] (analytic) = 2.119595000000001300E-2 " " y[1] (numeric) = 2.119594999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.18422140067704400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24200000000000013 " " y[1] (analytic) = 2.12718000000000100E-2 " " y[1] (numeric) = 2.127179999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.15503848276500400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24300000000000013 " " y[1] (analytic) = 2.134755000000001500E-2 " " y[1] (numeric) = 2.134754999999999300E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 9.75132121096878600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24400000000000013 " " y[1] (analytic) = 2.14232000000000100E-2 " " y[1] (numeric) = 2.142319999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.0974059709884900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24500000000000013 " " y[1] (analytic) = 2.14987500000000100E-2 " " y[1] (numeric) = 2.149874999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.0689504086368100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24600000000000014 " " y[1] (analytic) = 2.157420000000001300E-2 " " y[1] (numeric) = 2.157419999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.04073141055893700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24700000000000014 " " y[1] (analytic) = 2.16495500000000120E-2 " " y[1] (numeric) = 2.164954999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 8.0127461123986700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24800000000000014 " " y[1] (analytic) = 2.172480000000001400E-2 " " y[1] (numeric) = 2.172479999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 9.58199003522318900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.24900000000000014 " " y[1] (analytic) = 2.179995000000001200E-2 " " y[1] (numeric) = 2.17999499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 9.54895846629082900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2500000000000001 " " y[1] (analytic) = 2.18750000000000080E-2 " " y[1] (numeric) = 2.18749999999999920E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.93016446160825800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2510000000000001 " " y[1] (analytic) = 2.19499500000000100E-2 " " y[1] (numeric) = 2.194994999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.90308623015909500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2520000000000001 " " y[1] (analytic) = 2.20248000000000100E-2 " " y[1] (numeric) = 2.202479999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.87622805190878600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2530000000000001 " " y[1] (analytic) = 2.20995500000000100E-2 " " y[1] (numeric) = 2.209954999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.84958732633382200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2540000000000001 " " y[1] (analytic) = 2.21742000000000080E-2 " " y[1] (numeric) = 2.21741999999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.82316149388391200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2550000000000001 " " y[1] (analytic) = 2.224875000000001000E-2 " " y[1] (numeric) = 2.22487499999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.79694803517863500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2560000000000001 " " y[1] (analytic) = 2.23232000000000100E-2 " " y[1] (numeric) = 2.23231999999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.77094447022293700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2570000000000001 " " y[1] (analytic) = 2.239755000000001300E-2 " " y[1] (numeric) = 2.239754999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 9.29417802916911700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2580000000000001 " " y[1] (analytic) = 2.24718000000000100E-2 " " y[1] (numeric) = 2.247179999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.71955729392752800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2590000000000001 " " y[1] (analytic) = 2.25459500000000100E-2 " " y[1] (numeric) = 2.25459499999999920E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.6941689127173900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2600000000000001 " " y[1] (analytic) = 2.262000000000000700E-2 " " y[1] (numeric) = 2.26199999999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.66898088407076300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2610000000000001 " " y[1] (analytic) = 2.269395000000000700E-2 " " y[1] (numeric) = 2.26939499999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.64399091377572700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2620000000000001 " " y[1] (analytic) = 2.27678000000000100E-2 " " y[1] (numeric) = 2.27677999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 9.1430360911997100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2630000000000001 " " y[1] (analytic) = 2.28415500000000100E-2 " " y[1] (numeric) = 2.28415499999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.59459614595684900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2640000000000001 " " y[1] (analytic) = 2.29152000000000100E-2 " " y[1] (numeric) = 2.291519999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.57018693258975000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2650000000000001 " " y[1] (analytic) = 2.29887500000000080E-2 " " y[1] (numeric) = 2.298874999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.54596694460032200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2660000000000001 " " y[1] (analytic) = 2.30622000000000080E-2 " " y[1] (numeric) = 2.30621999999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.52193405649420400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2670000000000001 " " y[1] (analytic) = 2.31355500000000100E-2 " " y[1] (numeric) = 2.31355499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.99770340956738600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2680000000000001 " " y[1] (analytic) = 2.320880000000001300E-2 " " y[1] (numeric) = 2.32087999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.96930548400678900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.26900000000000013 " " y[1] (analytic) = 2.32819500000000100E-2 " " y[1] (numeric) = 2.328194999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.4509372109157800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27000000000000013 " " y[1] (analytic) = 2.33550000000000120E-2 " " y[1] (numeric) = 2.335499999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.42763209581163000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27100000000000013 " " y[1] (analytic) = 2.34279500000000080E-2 " " y[1] (numeric) = 2.342794999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.40450391936471800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27200000000000013 " " y[1] (analytic) = 2.350080000000001300E-2 " " y[1] (numeric) = 2.350079999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.85786088631947600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27300000000000013 " " y[1] (analytic) = 2.357355000000001300E-2 " " y[1] (numeric) = 2.35735499999999930E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.83052476683472500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27400000000000013 " " y[1] (analytic) = 2.36462000000000100E-2 " " y[1] (numeric) = 2.364619999999999200E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.33616173413405200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27500000000000013 " " y[1] (analytic) = 2.37187500000000100E-2 " " y[1] (numeric) = 2.371874999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.313722164856100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27600000000000013 " " y[1] (analytic) = 2.37912000000000100E-2 " " y[1] (numeric) = 2.379119999999999600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.83316007927908300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27700000000000014 " " y[1] (analytic) = 2.38635500000000100E-2 " " y[1] (numeric) = 2.386354999999999400E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.26934373124202500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27800000000000014 " " y[1] (analytic) = 2.39358000000000100E-2 " " y[1] (numeric) = 2.393579999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.24740128166514700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.27900000000000014 " " y[1] (analytic) = 2.40079500000000100E-2 " " y[1] (numeric) = 2.400794999999999500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.22562099628167400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28000000000000014 " " y[1] (analytic) = 2.40800000000000130E-2 " " y[1] (numeric) = 2.407999999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.20400114608308200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28100000000000014 " " y[1] (analytic) = 2.41519500000000080E-2 " " y[1] (numeric) = 2.415194999999999400E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 5.74603202135415600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28200000000000014 " " y[1] (analytic) = 2.42238000000000120E-2 " " y[1] (numeric) = 2.422379999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.16123595792900500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28300000000000014 " " y[1] (analytic) = 2.429555000000001300E-2 " " y[1] (numeric) = 2.429554999999999400E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.56810474005390900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28400000000000014 " " y[1] (analytic) = 2.436720000000001000E-2 " " y[1] (numeric) = 2.43671999999999920E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.5429108439712700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28500000000000014 " " y[1] (analytic) = 2.44387500000000100E-2 " " y[1] (numeric) = 2.44387499999999920E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.09824960759779600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28600000000000014 " " y[1] (analytic) = 2.45102000000000100E-2 " " y[1] (numeric) = 2.451019999999999300E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 7.07755740865764600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28700000000000014 " " y[1] (analytic) = 2.458155000000001300E-2 " " y[1] (numeric) = 2.458154999999999400E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.46841704925916900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28800000000000014 " " y[1] (analytic) = 2.465280000000001400E-2 " " y[1] (numeric) = 2.465279999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.44394215331389400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.28900000000000015 " " y[1] (analytic) = 2.472395000000001000E-2 " " y[1] (numeric) = 2.47239499999999920E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.41964237580227900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29000000000000015 " " y[1] (analytic) = 2.47950000000000110E-2 " " y[1] (numeric) = 2.47949999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.39551591519325500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29100000000000015 " " y[1] (analytic) = 2.48659500000000120E-2 " " y[1] (numeric) = 2.48659499999999920E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.3715609947424800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29200000000000015 " " y[1] (analytic) = 2.493680000000001200E-2 " " y[1] (numeric) = 2.49367999999999920E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.34777586206797800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29300000000000015 " " y[1] (analytic) = 2.50075500000000100E-2 " " y[1] (numeric) = 2.500754999999999500E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.93679899061206100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29400000000000015 " " y[1] (analytic) = 2.507820000000001000E-2 " " y[1] (numeric) = 2.50781999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.30070806984619100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29500000000000015 " " y[1] (analytic) = 2.51487500000000100E-2 " " y[1] (numeric) = 2.51487499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.27742202364796500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29600000000000015 " " y[1] (analytic) = 2.52192000000000100E-2 " " y[1] (numeric) = 2.52191999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.25429899113440300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29700000000000015 " " y[1] (analytic) = 2.528955000000001600E-2 " " y[1] (numeric) = 2.52895499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 9.6032268916114700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29800000000000015 " " y[1] (analytic) = 2.535980000000001000E-2 " " y[1] (numeric) = 2.53597999999999930E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.20853544259878800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.29900000000000015 " " y[1] (analytic) = 2.542995000000001000E-2 " " y[1] (numeric) = 2.542994999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.18589171890690900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30000000000000016 " " y[1] (analytic) = 2.550000000000001000E-2 " " y[1] (numeric) = 2.54999999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.16340459283202900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30100000000000016 " " y[1] (analytic) = 2.55699500000000140E-2 " " y[1] (numeric) = 2.55699499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.1410725135253200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30200000000000016 " " y[1] (analytic) = 2.56398000000000100E-2 " " y[1] (numeric) = 2.56397999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.11889395070229700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30300000000000016 " " y[1] (analytic) = 2.57095500000000140E-2 " " y[1] (numeric) = 2.57095499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.09686739430354600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30400000000000016 " " y[1] (analytic) = 2.577920000000001300E-2 " " y[1] (numeric) = 2.57791999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.07499135416214400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30500000000000016 " " y[1] (analytic) = 2.58487500000000100E-2 " " y[1] (numeric) = 2.584874999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.71105363306467900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30600000000000016 " " y[1] (analytic) = 2.59182000000000100E-2 " " y[1] (numeric) = 2.591819999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.69307079958024200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30700000000000016 " " y[1] (analytic) = 2.598755000000001500E-2 " " y[1] (numeric) = 2.59875499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 8.01025172119791100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30800000000000016 " " y[1] (analytic) = 2.605680000000001300E-2 " " y[1] (numeric) = 2.60567999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.98896323098833100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30900000000000016 " " y[1] (analytic) = 2.612595000000001400E-2 " " y[1] (numeric) = 2.61259499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.96781809339820200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31000000000000016 " " y[1] (analytic) = 2.61950000000000100E-2 " " y[1] (numeric) = 2.619499999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.62234577582289200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31100000000000017 " " y[1] (analytic) = 2.62639500000000140E-2 " " y[1] (numeric) = 2.626394999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.60496032004632400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31200000000000017 " " y[1] (analytic) = 2.633280000000001000E-2 " " y[1] (numeric) = 2.633279999999999500E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.90522911035730100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31300000000000017 " " y[1] (analytic) = 2.64015500000000070E-2 " " y[1] (numeric) = 2.640154999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.57053648735322900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31400000000000017 " " y[1] (analytic) = 2.647020000000001000E-2 " " y[1] (numeric) = 2.647019999999999400E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.86419509928964400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31500000000000017 " " y[1] (analytic) = 2.653875000000001000E-2 " " y[1] (numeric) = 2.653874999999999400E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.84388176222379600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31600000000000017 " " y[1] (analytic) = 2.66072000000000100E-2 " " y[1] (numeric) = 2.660719999999999000E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.51975208205600800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31700000000000017 " " y[1] (analytic) = 2.667555000000001500E-2 " " y[1] (numeric) = 2.667554999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.80365604897431500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.31800000000000017 " " y[1] (analytic) = 2.674380000000001000E-2 " " y[1] (numeric) = 2.67437999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.78374117055978400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3190000000000002 " " y[1] (analytic) = 2.681195000000002000E-2 " " y[1] (numeric) = 2.68119499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 9.05794940825836400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3200000000000002 " " y[1] (analytic) = 2.688000000000001500E-2 " " y[1] (numeric) = 2.68799999999999930E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 9.03501810404586500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3210000000000002 " " y[1] (analytic) = 2.694795000000001000E-2 " " y[1] (numeric) = 2.69479499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.72477376265047100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3220000000000002 " " y[1] (analytic) = 2.701580000000001000E-2 " " y[1] (numeric) = 2.701579999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.70537304530003800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3230000000000002 " " y[1] (analytic) = 2.708355000000001000E-2 " " y[1] (numeric) = 2.70835499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.68609791246778100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3240000000000002 " " y[1] (analytic) = 2.715120000000001400E-2 " " y[1] (numeric) = 2.71511999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.9447717462488910000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3250000000000002 " " y[1] (analytic) = 2.721875000000001400E-2 " " y[1] (numeric) = 2.72187499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.92257310261319400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3260000000000002 " " y[1] (analytic) = 2.72862000000000100E-2 " " y[1] (numeric) = 2.72861999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.62901456110476200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3270000000000002 " " y[1] (analytic) = 2.735355000000001500E-2 " " y[1] (numeric) = 2.73535499999999930E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.87860210600645500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3280000000000002 " " y[1] (analytic) = 2.74208000000000100E-2 " " y[1] (numeric) = 2.74207999999999900E-2 " " absolute error = 1.73472347597680700000000000000000E-17 " " relative error = 6.32630512595112700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3290000000000002 " " y[1] (analytic) = 2.748795000000001700E-2 " " y[1] (numeric) = 2.74879499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.83519093409122400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3300000000000002 " " y[1] (analytic) = 2.755500000000002000E-2 " " y[1] (numeric) = 2.75549999999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 1.00727910054904350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3310000000000002 " " y[1] (analytic) = 2.762195000000001000E-2 " " y[1] (numeric) = 2.76219499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.79232952911553600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3320000000000002 " " y[1] (analytic) = 2.768880000000001300E-2 " " y[1] (numeric) = 2.76887999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.77110191256944600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3330000000000002 " " y[1] (analytic) = 2.77555500000000100E-2 " " y[1] (numeric) = 2.77555499999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.50000692175859500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3340000000000002 " " y[1] (analytic) = 2.782220000000001400E-2 " " y[1] (numeric) = 2.78221999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.48204013763170400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3350000000000002 " " y[1] (analytic) = 2.788875000000002000E-2 " " y[1] (numeric) = 2.78887499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.95224799090274600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3360000000000002 " " y[1] (analytic) = 2.795520000000001300E-2 " " y[1] (numeric) = 2.79551999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.6875174077364090000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3370000000000002 " " y[1] (analytic) = 2.802155000000001000E-2 " " y[1] (numeric) = 2.80215499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.66694692608913100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3380000000000002 " " y[1] (analytic) = 2.80878000000000070E-2 " " y[1] (numeric) = 2.80877999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.4112894964082900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3390000000000002 " " y[1] (analytic) = 2.815395000000001600E-2 " " y[1] (numeric) = 2.81539499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.62618874569120300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3400000000000002 " " y[1] (analytic) = 2.822000000000002000E-2 " " y[1] (numeric) = 2.82199999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.60599881774460900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3410000000000002 " " y[1] (analytic) = 2.82859500000000100E-2 " " y[1] (numeric) = 2.82859499999999930E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.35937160028978200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3420000000000002 " " y[1] (analytic) = 2.835180000000001600E-2 " " y[1] (numeric) = 2.83517999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.56599181134012100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3430000000000002 " " y[1] (analytic) = 2.841755000000001400E-2 " " y[1] (numeric) = 2.84175499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.54617258126590400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3440000000000002 " " y[1] (analytic) = 2.848320000000001400E-2 " " y[1] (numeric) = 2.84831999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.52647478642683600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3450000000000002 " " y[1] (analytic) = 2.854875000000001700E-2 " " y[1] (numeric) = 2.85487499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.50689738208337900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3460000000000002 " " y[1] (analytic) = 2.861420000000001000E-2 " " y[1] (numeric) = 2.861419999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.27494800194367700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3470000000000002 " " y[1] (analytic) = 2.867955000000001500E-2 " " y[1] (numeric) = 2.86795499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.46809962627561700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3480000000000002 " " y[1] (analytic) = 2.87448000000000100E-2 " " y[1] (numeric) = 2.87447999999999900E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.24189478156803200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3490000000000002 " " y[1] (analytic) = 2.880995000000002000E-2 " " y[1] (numeric) = 2.88099499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.42977119490845500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3500000000000002 " " y[1] (analytic) = 2.887500000000002000E-2 " " y[1] (numeric) = 2.88749999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.41078048958451500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3510000000000002 " " y[1] (analytic) = 2.893995000000001400E-2 " " y[1] (numeric) = 2.893994999999999000E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.19306070387878200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3520000000000002 " " y[1] (analytic) = 2.900480000000001400E-2 " " y[1] (numeric) = 2.90047999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.37314122616783600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3530000000000002 " " y[1] (analytic) = 2.906955000000001000E-2 " " y[1] (numeric) = 2.90695499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.35449075189512400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3540000000000002 " " y[1] (analytic) = 2.913420000000001000E-2 " " y[1] (numeric) = 2.91341999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.33595178988106400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3550000000000002 " " y[1] (analytic) = 2.919875000000002000E-2 " " y[1] (numeric) = 2.91987499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.50574103878724200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3560000000000002 " " y[1] (analytic) = 2.926320000000001000E-2 " " y[1] (numeric) = 2.92631999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.299204688371500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3570000000000002 " " y[1] (analytic) = 2.932755000000001300E-2 " " y[1] (numeric) = 2.93275499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.28099471782514500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3580000000000002 " " y[1] (analytic) = 2.939180000000001000E-2 " " y[1] (numeric) = 2.93917999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.2628925971445400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3590000000000002 " " y[1] (analytic) = 2.945595000000001400E-2 " " y[1] (numeric) = 2.945594999999998600E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.42273992712131200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3600000000000002 " " y[1] (analytic) = 2.95200000000000200E-2 " " y[1] (numeric) = 2.951999999999998500E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.05775821705902810000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3610000000000002 " " y[1] (analytic) = 2.95839500000000140E-2 " " y[1] (numeric) = 2.958394999999998700E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.20922448276017600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3620000000000002 " " y[1] (analytic) = 2.964780000000001300E-2 " " y[1] (numeric) = 2.964779999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.36176566747917200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3630000000000002 " " y[1] (analytic) = 2.97115500000000100E-2 " " y[1] (numeric) = 2.97115499999999870E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 7.00625908500959300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3640000000000002 " " y[1] (analytic) = 2.977520000000001000E-2 " " y[1] (numeric) = 2.977519999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.32170921291171900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3650000000000002 " " y[1] (analytic) = 2.983875000000002000E-2 " " y[1] (numeric) = 2.983874999999998600E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.0464588016449250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3660000000000002 " " y[1] (analytic) = 2.990220000000001000E-2 " " y[1] (numeric) = 2.990219999999998400E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.28211824401846700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3670000000000002 " " y[1] (analytic) = 2.996555000000001300E-2 " " y[1] (numeric) = 2.996554999999998500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.26249497026715700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3680000000000002 " " y[1] (analytic) = 3.00288000000000100E-2 " " y[1] (numeric) = 3.002879999999999000E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.08761211359604400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3690000000000002 " " y[1] (analytic) = 3.009195000000001000E-2 " " y[1] (numeric) = 3.00919499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.07063971051237600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3700000000000002 " " y[1] (analytic) = 3.015500000000001500E-2 " " y[1] (numeric) = 3.015499999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.20430297318152800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3710000000000002 " " y[1] (analytic) = 3.021795000000001600E-2 " " y[1] (numeric) = 3.021794999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.18512857941352700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3720000000000002 " " y[1] (analytic) = 3.028080000000002000E-2 " " y[1] (numeric) = 3.028079999999998600E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.03118222000681980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3730000000000002 " " y[1] (analytic) = 3.03435500000000100E-2 " " y[1] (numeric) = 3.034354999999998600E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 8.00372028443451500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3740000000000002 " " y[1] (analytic) = 3.040620000000001700E-2 " " y[1] (numeric) = 3.040619999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.12826187278545100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3750000000000002 " " y[1] (analytic) = 3.046875000000001700E-2 " " y[1] (numeric) = 3.04687499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.10952225333461300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3760000000000002 " " y[1] (analytic) = 3.053120000000001400E-2 " " y[1] (numeric) = 3.053119999999998600E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.09088919388327400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3770000000000002 " " y[1] (analytic) = 3.059355000000002000E-2 " " y[1] (numeric) = 3.059354999999998600E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.02064070915544330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3780000000000002 " " y[1] (analytic) = 3.065580000000001600E-2 " " y[1] (numeric) = 3.065579999999999000E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.01856818506065770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3790000000000002 " " y[1] (analytic) = 3.071795000000001600E-2 " " y[1] (numeric) = 3.071794999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.03562106704024900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3800000000000002 " " y[1] (analytic) = 3.078000000000002000E-2 " " y[1] (numeric) = 3.077999999999998500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 9.01740598298534800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.3810000000000002 " " y[1] (analytic) = 3.084195000000001000E-2 " " y[1] (numeric) = 3.08419499999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 7.87438169884695700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38200000000000023 " " y[1] (analytic) = 3.090380000000001500E-2 " " y[1] (numeric) = 3.090379999999998700E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.98128243634404100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38300000000000023 " " y[1] (analytic) = 3.09655500000000200E-2 " " y[1] (numeric) = 3.096554999999998600E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.00837939476555440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38400000000000023 " " y[1] (analytic) = 3.102720000000001600E-2 " " y[1] (numeric) = 3.102719999999999000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.94556247925333200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38500000000000023 " " y[1] (analytic) = 3.10887500000000200E-2 " " y[1] (numeric) = 3.108874999999999000E-2 " " absolute error = 3.12250225675825300000000000000000E-17 " " relative error = 1.00438334019806230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38600000000000023 " " y[1] (analytic) = 3.115020000000001000E-2 " " y[1] (numeric) = 3.11501999999999900E-2 " " absolute error = 2.4286128663675300000000000000000E-17 " " relative error = 7.79645994686239200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38700000000000023 " " y[1] (analytic) = 3.12115500000000200E-2 " " y[1] (numeric) = 3.12115499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.89272580683397500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38800000000000023 " " y[1] (analytic) = 3.12728000000000200E-2 " " y[1] (numeric) = 3.12727999999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.87530877172139900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.38900000000000023 " " y[1] (analytic) = 3.13339500000000100E-2 " " y[1] (numeric) = 3.13339499999999940E-2 " " absolute error = 2.081668171172168500000000000000000E-17 " " relative error = 6.64349107333153900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39000000000000024 " " y[1] (analytic) = 3.13950000000000200E-2 " " y[1] (numeric) = 3.13949999999999950E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.8407630564194610000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39100000000000024 " " y[1] (analytic) = 3.14559500000000160E-2 " " y[1] (numeric) = 3.14559499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.82363292656203300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39200000000000024 " " y[1] (analytic) = 3.15168000000000170E-2 " " y[1] (numeric) = 3.15167999999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.80659699450099500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39300000000000024 " " y[1] (analytic) = 3.15775500000000150E-2 " " y[1] (numeric) = 3.15775499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.78965455382982500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39400000000000024 " " y[1] (analytic) = 3.16382000000000160E-2 " " y[1] (numeric) = 3.16381999999999940E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.77280490534508800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39500000000000024 " " y[1] (analytic) = 3.16987500000000200E-2 " " y[1] (numeric) = 3.16987499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.75604735695536800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39600000000000024 " " y[1] (analytic) = 3.175920000000001500E-2 " " y[1] (numeric) = 3.17591999999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.73938122359155800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39700000000000024 " " y[1] (analytic) = 3.181955000000002000E-2 " " y[1] (numeric) = 3.18195499999999850E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.72280582711851700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39800000000000024 " " y[1] (analytic) = 3.18798000000000200E-2 " " y[1] (numeric) = 3.187979999999998600E-2 " " absolute error = 3.46944695195361400000000000000000E-17 " " relative error = 1.08829006203100780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.39900000000000024 " " y[1] (analytic) = 3.193995000000001700E-2 " " y[1] (numeric) = 3.19399499999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.68992456645326500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.40000000000000024 " " y[1] (analytic) = 3.200000000000002000E-2 " " y[1] (numeric) = 3.19999999999999840E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 8.67361737988403200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = 0.3 - (0.1 * x + 0.2) ;" Iterations = 300 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 46 Minutes 3 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 45 Minutes 36 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 48 Minutes 37 Seconds "Time to Timeout " Unknown Percent Done = 6.142857142857148 "%" (%o54) true (%o54) diffeq.max