(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, 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 (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : 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 (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : 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_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , 1 1 1 array_tmp3 : array_const_2D0 array_tmp2 , 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 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 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_2D0 array_tmp2 , array_tmp4 : array_tmp3 , 2 1 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 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 3.0 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 4.0 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 5.0 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 then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D2 array_x , 1 1 1 array_tmp2 : array_const_0D3 + array_tmp1 , 1 1 1 array_tmp3 : array_const_2D0 array_tmp2 , 1 1 1 array_tmp4 : array_tmp3 + array_const_0D0 , 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 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D2 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_const_2D0 array_tmp2 , array_tmp4 : array_tmp3 , 2 1 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 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 3.0 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 4.0 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 5.0 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 then (temporary : array_tmp4 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := 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 > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%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) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) 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) (%o54) 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) (%i55) exact_soln_y(x) := block(0.6 x + 0.2 x x) (%o55) exact_soln_y(x) := block(0.6 x + 0.2 x x) (%i56) 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, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/mult_c_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.2 * x * x + 0.6 * 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_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), 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(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T00:44:53-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_c_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "mult_c_lin diffeq.max"), logitem_str(html_log_file, "mult_c_lin maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) 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, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/mult_c_linpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:0.1,"), omniout_str(ALWAYS, "x_end:5.0,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h:0.05,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:1000000,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.2 * x * x + 0.6 * 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_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), glob_h : 0.05, 1 + 0 glob_look_poles : true, glob_max_iter : 1000000, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), 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(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-13T00:44:53-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mult_c_lin"), logitem_str(html_log_file, "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "mult_c_lin diffeq.max"), logitem_str(html_log_file, "mult_c_lin maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/mult_c_linpostode.ode#################" "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:0.1," "x_end:5.0," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h:0.05," "glob_look_poles:true," "glob_max_iter:1000000," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (0.2 * x * x + 0.6 * x) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_value3 = 0.0 "" value3 = 0.0 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = 6.200E-2 " " y[1] (numeric) = 6.200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = 0.1 " " y[1] (analytic) = 6.200E-2 " " y[1] (numeric) = 6.200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.101 " " y[1] (analytic) = 6.26402000000000100E-2 " " y[1] (numeric) = 6.2640200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.21547629283023600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000001 " " y[1] (analytic) = 6.3280800E-2 " " y[1] (numeric) = 6.3280800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000001 " " y[1] (analytic) = 6.3921800E-2 " " y[1] (numeric) = 6.3921800E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000001 " " y[1] (analytic) = 6.4563200E-2 " " y[1] (numeric) = 6.4563200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000001 " " y[1] (analytic) = 6.520500E-2 " " y[1] (numeric) = 6.520500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = 6.58472000000000100E-2 " " y[1] (numeric) = 6.5847200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.10757447663901500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = 6.6489800E-2 " " y[1] (numeric) = 6.64897999999999900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.087205527436457300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000001 " " y[1] (analytic) = 6.7132800E-2 " " y[1] (numeric) = 6.71327999999999900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.067214209419904200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = 6.7776200E-2 " " y[1] (numeric) = 6.7776200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = 6.84200000000000100E-2 " " y[1] (numeric) = 6.84200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.02832326919240800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = 6.9064200E-2 " " y[1] (numeric) = 6.90642000000000000E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 2.009403975983860600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = 6.97088000000000200E-2 " " y[1] (numeric) = 6.97087999999999900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.981645877655175500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000002 " " y[1] (analytic) = 7.03538000000000100E-2 " " y[1] (numeric) = 7.0353800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.97257117708133120000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000002 " " y[1] (analytic) = 7.0999200E-2 " " y[1] (numeric) = 7.0999200E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000002 " " y[1] (analytic) = 7.164500E-2 " " y[1] (numeric) = 7.164500E-2 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = 7.22912000000000100E-2 " " y[1] (numeric) = 7.2291200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.919706383047238600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000002 " " y[1] (analytic) = 7.29378000000000100E-2 " " y[1] (numeric) = 7.2937800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.902688017436014500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000002 " " y[1] (analytic) = 7.35848000000000200E-2 " " y[1] (numeric) = 7.35848000000000000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.77191697410727600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000002 " " y[1] (analytic) = 7.42322000000000100E-2 " " y[1] (numeric) = 7.4232200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.8695105099693200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (analytic) = 7.48800000000000100E-2 " " y[1] (numeric) = 7.48800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.85333704698376800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = 7.55282000000000200E-2 " " y[1] (numeric) = 7.5528200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.837431291598959600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12200000000000003 " " y[1] (analytic) = 7.61768000000000200E-2 " " y[1] (numeric) = 7.6176800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.821786660481203600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12300000000000003 " " y[1] (analytic) = 7.68258000000000100E-2 " " y[1] (numeric) = 7.6825800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.80639678438941800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12400000000000003 " " y[1] (analytic) = 7.74752000000000100E-2 " " y[1] (numeric) = 7.7475200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.791255499542363800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000003 " " y[1] (analytic) = 7.81250000000000100E-2 " " y[1] (numeric) = 7.812500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.7763568394002502000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000003 " " y[1] (analytic) = 7.87752000000000200E-2 " " y[1] (numeric) = 7.8775200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.76169502683769190000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = 7.94258000000000100E-2 " " y[1] (numeric) = 7.9425800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.747264466686448400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = 8.00768000000000100E-2 " " y[1] (numeric) = 8.0076800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.73305973862772400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = 8.07282000000000200E-2 " " y[1] (numeric) = 8.0728200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.719075590415053700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = 8.13800000000000200E-2 " " y[1] (numeric) = 8.13800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.41061386281996900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = 8.20322000000000100E-2 " " y[1] (numeric) = 8.2032200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.691748826413829500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = 8.26848000000000100E-2 " " y[1] (numeric) = 8.2684800E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.67839648977979680000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13300000000000003 " " y[1] (analytic) = 8.33378000000000300E-2 " " y[1] (numeric) = 8.3337800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.33049055958147500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13400000000000004 " " y[1] (analytic) = 8.39912000000000200E-2 " " y[1] (numeric) = 8.3991200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.652290693288636600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = 8.46450000000000300E-2 " " y[1] (numeric) = 8.464500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.279056721085581400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = 8.52992000000000200E-2 " " y[1] (numeric) = 8.52992000000000000E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.25390808068878800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = 8.59538000000000200E-2 " " y[1] (numeric) = 8.5953800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.2291272306319100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = 8.66088000000000300E-2 " " y[1] (numeric) = 8.6608800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.20470617484931100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = 8.72642000000000100E-2 " " y[1] (numeric) = 8.7264200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.590318573689377400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (analytic) = 8.79200000000000200E-2 " " y[1] (numeric) = 8.79200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.156912604143415300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14100000000000004 " " y[1] (analytic) = 8.85762000000000200E-2 " " y[1] (numeric) = 8.8576200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.133525215083612400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14200000000000004 " " y[1] (analytic) = 8.92328000000000200E-2 " " y[1] (numeric) = 8.92327999999999900E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.665701784931477500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = 8.98898000000000300E-2 " " y[1] (numeric) = 8.98898000000000000E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.631600406658303300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = 9.05472000000000300E-2 " " y[1] (numeric) = 9.0547200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.065315726563484000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = 9.12050000000000200E-2 " " y[1] (numeric) = 9.120500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 3.043207676731418700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14600000000000005 " " y[1] (analytic) = 9.18632000000000300E-2 " " y[1] (numeric) = 9.18631999999999900E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.53210463204453500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14700000000000005 " " y[1] (analytic) = 9.25218000000000300E-2 " " y[1] (numeric) = 9.25217999999999900E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.499843650193074400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14800000000000005 " " y[1] (analytic) = 9.31808000000000400E-2 " " y[1] (numeric) = 9.3180800E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.46801953014390900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14900000000000005 " " y[1] (analytic) = 9.38402000000000300E-2 " " y[1] (numeric) = 9.3840200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.957748983445144000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (analytic) = 9.45000000000000300E-2 " " y[1] (numeric) = 9.4500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.93709794874379900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15100000000000005 " " y[1] (analytic) = 9.51602000000000300E-2 " " y[1] (numeric) = 9.5160200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.91672102576801100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15200000000000005 " " y[1] (analytic) = 9.58208000000000400E-2 " " y[1] (numeric) = 9.5820800E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.34491920579282930000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15300000000000005 " " y[1] (analytic) = 9.64818000000000400E-2 " " y[1] (numeric) = 9.64818000000000000E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.31515202073793800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = 9.71432000000000300E-2 " " y[1] (numeric) = 9.7143200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.857181523321128400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = 9.78050000000000300E-2 " " y[1] (numeric) = 9.780500E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.837848332460396500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = 9.84672000000000300E-2 " " y[1] (numeric) = 9.8467200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.81876356955706100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = 9.91298000000000300E-2 " " y[1] (numeric) = 9.9129800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.799922487045158000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = 9.97928000000000400E-2 " " y[1] (numeric) = 9.9792800E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.17198068632640300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = 0.10045620000000004 " " y[1] (numeric) = 0.1004562 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.14442945516985100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = 0.10112000000000003 " " y[1] (numeric) = 0.10112 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.7448156265455800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = 0.10178420000000003 " " y[1] (numeric) = 0.1017842 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.72690413793387430000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = 0.10244880000000003 " " y[1] (numeric) = 0.1024488 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.70921432126378300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = 0.10311380000000005 " " y[1] (numeric) = 0.1031138 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.037613144258417000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = 0.10377920000000003 " " y[1] (numeric) = 0.1037792 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.67448348181802400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = 0.10444500000000004 " " y[1] (numeric) = 0.104445 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.98615189079834900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = 0.10511120000000004 " " y[1] (numeric) = 0.1051112 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.96088746236779250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = 0.10577780000000005 " " y[1] (numeric) = 0.1057778 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.93592638752586600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000007 " " y[1] (analytic) = 0.10644480000000005 " " y[1] (numeric) = 0.1064448 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.91126324850470400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = 0.10711220000000003 " " y[1] (numeric) = 0.1071122 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.591261837179043000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (analytic) = 0.10778000000000004 " " y[1] (numeric) = 0.10778 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.862809744242285400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000007 " " y[1] (analytic) = 0.10844820000000005 " " y[1] (numeric) = 0.1084482 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 5.118678892896129000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = 0.10911680000000004 " " y[1] (numeric) = 0.1091168 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.815486105113360400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000007 " " y[1] (analytic) = 0.10978580000000004 " " y[1] (numeric) = 0.1097858 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.79223573754013330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000007 " " y[1] (analytic) = 0.11045520000000005 " " y[1] (numeric) = 0.1104552 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.769253364571641400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000007 " " y[1] (analytic) = 0.11112500000000004 " " y[1] (numeric) = 0.111125 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.74653439131098830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = 0.11179520000000005 " " y[1] (numeric) = 0.1117952 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.965432436388843600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000007 " " y[1] (analytic) = 0.11246580000000005 " " y[1] (numeric) = 0.11246579999999999 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.935825044703172600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = 0.11313680000000005 " " y[1] (numeric) = 0.1131368 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.906551292882404500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000008 " " y[1] (analytic) = 0.11380820000000004 " " y[1] (numeric) = 0.1138082 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.658204191213230000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (analytic) = 0.11448000000000004 " " y[1] (numeric) = 0.11448 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.63673684691154350000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000008 " " y[1] (analytic) = 0.11515220000000005 " " y[1] (numeric) = 0.1151522 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.82067656816437760000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = 0.11582480000000005 " " y[1] (numeric) = 0.11582479999999999 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.792682675148829000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000008 " " y[1] (analytic) = 0.11649780000000005 " " y[1] (numeric) = 0.1164978 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.764995667837315000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = 0.11717120000000004 " " y[1] (numeric) = 0.1171712 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.55320790633221800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = 0.11784500000000005 " " y[1] (numeric) = 0.117845 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.532891800538279000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = 0.11851920000000005 " " y[1] (numeric) = 0.1185192 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.512794840282701400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000008 " " y[1] (analytic) = 0.11919380000000006 " " y[1] (numeric) = 0.1191938 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.657218012284012000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = 0.11986880000000005 " " y[1] (numeric) = 0.1198688 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.630992487724729400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = 0.12054420000000005 " " y[1] (numeric) = 0.1205442 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.453784041326198300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = 0.12122000000000005 " " y[1] (numeric) = 0.12122000000000001 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.43452923803360450000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = 0.12189620000000005 " " y[1] (numeric) = 0.12189620000000001 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.415476727202600000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = 0.12257280000000007 " " y[1] (numeric) = 0.12257280000000001 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.528831129847551400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = 0.12324980000000005 " " y[1] (numeric) = 0.1232498 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.377966002658288600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = 0.12392720000000006 " " y[1] (numeric) = 0.1239272 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.47933554790698130000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = 0.12460500000000005 " " y[1] (numeric) = 0.12460500000000001 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 3.34122735230876400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = 0.12528320000000007 " " y[1] (numeric) = 0.1252832 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.43085355668260400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = 0.12596180000000007 " " y[1] (numeric) = 0.1259618 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.40698300844047930000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = 0.12664080000000005 " " y[1] (numeric) = 0.12664080000000003 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.19167721742352400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = 0.12732020000000005 " " y[1] (numeric) = 0.12732020000000002 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.179982093621350100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = 0.12800000000000006 " " y[1] (numeric) = 0.12800000000000003 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.16840434497100800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = 0.12868020000000005 " " y[1] (numeric) = 0.12868020000000002 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.156942219209241300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = 0.12936080000000005 " " y[1] (numeric) = 0.12936080000000003 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.145593998771567800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = 0.13004180000000007 " " y[1] (numeric) = 0.1300418 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.26871599987525500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = 0.13072320000000007 " " y[1] (numeric) = 0.1307232 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.246465144003344600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = 0.13140500000000005 " " y[1] (numeric) = 0.13140500000000002 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.112216096467326400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = 0.13208720000000007 " " y[1] (numeric) = 0.13208720000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.20261397253161530000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = 0.13276980000000008 " " y[1] (numeric) = 0.13276980000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.181007369993612300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = 0.13345280000000007 " " y[1] (numeric) = 0.1334528 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.1596093323825200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = 0.13413620000000007 " " y[1] (numeric) = 0.1341362 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.138416865190589500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = 0.13482000000000005 " " y[1] (numeric) = 0.13482000000000002 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.058713515474625800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = 0.13550420000000005 " " y[1] (numeric) = 0.13550420000000002 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.04831847393873420000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = 0.13618880000000008 " " y[1] (numeric) = 0.13618880000000003 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.076043788568355000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = 0.13687380000000007 " " y[1] (numeric) = 0.13687380000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.05564477871278500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = 0.13755920000000008 " " y[1] (numeric) = 0.13755920000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.035437195858786500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = 0.13824500000000006 " " y[1] (numeric) = 0.138245 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 4.01541836820556300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = 0.13893120000000006 " " y[1] (numeric) = 0.1389312 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.99558567343100800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = 0.13961780000000007 " " y[1] (numeric) = 0.13961780000000001 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.975936537551645000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = 0.14030480000000006 " " y[1] (numeric) = 0.1403048 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.956468433813939400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = 0.1409922000000001 " " y[1] (numeric) = 0.1409922 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.90576832242398400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = 0.14168000000000008 " " y[1] (numeric) = 0.14168 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.87709816818793600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = 0.14236820000000006 " " y[1] (numeric) = 0.1423682 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.89912573392497800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = 0.14305680000000007 " " y[1] (numeric) = 0.1430568 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.8803573986876400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = 0.14374580000000006 " " y[1] (numeric) = 0.1437458 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.861758133542531600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = 0.1444352000000001 " " y[1] (numeric) = 0.1444352 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.76498851020296200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = 0.1451250000000001 " " y[1] (numeric) = 0.145125 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.73758669056928100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = 0.14581520000000006 " " y[1] (numeric) = 0.1458152 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.80695230889905900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = 0.14650580000000007 " " y[1] (numeric) = 0.14650580000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.789007072160815400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = 0.14719680000000007 " " y[1] (numeric) = 0.14719680000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.77121997429684600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = 0.14788820000000008 " " y[1] (numeric) = 0.14788820000000003 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.75358894294864600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = 0.14858000000000007 " " y[1] (numeric) = 0.14858000000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.736111941799556000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = 0.14927220000000008 " " y[1] (numeric) = 0.14927220000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.718786969794630000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = 0.1499648000000001 " " y[1] (numeric) = 0.1499648 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.55241809057103300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = 0.15065780000000006 " " y[1] (numeric) = 0.1506578 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.684585280765934600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = 0.1513512000000001 " " y[1] (numeric) = 0.15135120000000002 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.50155709679782400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = 0.1520450000000001 " " y[1] (numeric) = 0.152045 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.47645281639558600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = 0.15273920000000007 " " y[1] (numeric) = 0.15273920000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.634374884198542400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = 0.1534338000000001 " " y[1] (numeric) = 0.1534338 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.42688291933633200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = 0.15412880000000007 " " y[1] (numeric) = 0.1541288 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.60160795589518700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = 0.1548242000000001 " " y[1] (numeric) = 0.15482420000000002 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.378146752696715000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = 0.15552000000000007 " " y[1] (numeric) = 0.15552000000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.569389868265033000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = 0.15621620000000008 " " y[1] (numeric) = 0.15621620000000003 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.55348236810636760000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = 0.1569128000000001 " " y[1] (numeric) = 0.15691280000000002 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.30656051302931900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = 0.15760980000000008 " " y[1] (numeric) = 0.15760980000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.52206215801668400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = 0.1583072000000001 " " y[1] (numeric) = 0.1583072 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.25981931629683900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = 0.1590050000000001 " " y[1] (numeric) = 0.159005 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.236736382307896000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = 0.15970320000000007 " " y[1] (numeric) = 0.15970320000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.47589473669017270000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = 0.1604018000000001 " " y[1] (numeric) = 0.1604018 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.1911341921902800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = 0.1611008000000001 " " y[1] (numeric) = 0.16110080000000002 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 5.168610388457828000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = 0.16180020000000012 " " y[1] (numeric) = 0.1618002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.8616912996717900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = 0.16250000000000006 " " y[1] (numeric) = 0.1625 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.4160708450004800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = 0.16320020000000007 " " y[1] (numeric) = 0.16320020000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.401414411946664400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = 0.16390080000000007 " " y[1] (numeric) = 0.1639008 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.386874940894602500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = 0.16460180000000008 " " y[1] (numeric) = 0.16460180000000002 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.37245104435418100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = 0.16530320000000007 " " y[1] (numeric) = 0.1653032 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.35814135668624700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = 0.16600500000000007 " " y[1] (numeric) = 0.166005 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.343944533674154700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = 0.16670720000000008 " " y[1] (numeric) = 0.1667072 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.99478887815803350000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = 0.16740980000000008 " " y[1] (numeric) = 0.1674098 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.97382631404414200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = 0.1681128000000001 " " y[1] (numeric) = 0.1681128 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.95302718453839900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = 0.16881620000000008 " " y[1] (numeric) = 0.1688162 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.93238959571929100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = 0.16952000000000006 " " y[1] (numeric) = 0.16952 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.27460778853573660000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = 0.17022420000000008 " " y[1] (numeric) = 0.1702242 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.8915916095882200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = 0.17092880000000008 " " y[1] (numeric) = 0.1709288 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.871427567904689000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = 0.1716338000000001 " " y[1] (numeric) = 0.1716338 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.851417777086255400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = 0.17233920000000008 " " y[1] (numeric) = 0.1723392 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.83156048344698700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = 0.17304500000000006 " " y[1] (numeric) = 0.173045 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.20790263984846700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = 0.17375120000000008 " " y[1] (numeric) = 0.1737512 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.79229650482337400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = 0.17445780000000008 " " y[1] (numeric) = 0.1744578 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.772886442846734400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000001 " " y[1] (analytic) = 0.1751648000000001 " " y[1] (numeric) = 0.1751648 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.753622123102740300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.26900000000000013 " " y[1] (analytic) = 0.1758722000000001 " " y[1] (numeric) = 0.1758722 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.73450191939867100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = 0.17658000000000007 " " y[1] (numeric) = 0.17658000000000001 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 3.1436828197563600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27100000000000013 " " y[1] (analytic) = 0.1772882000000001 " " y[1] (numeric) = 0.1772882 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.6966874753585797000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = 0.1779968000000001 " " y[1] (numeric) = 0.1779968 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.67799010133253530000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = 0.1787058000000001 " " y[1] (numeric) = 0.1787058 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.21257410014199800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27400000000000013 " " y[1] (analytic) = 0.17941520000000008 " " y[1] (numeric) = 0.1794152 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.641007386603069300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27500000000000013 " " y[1] (analytic) = 0.1801250000000001 " " y[1] (numeric) = 0.180125 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.62271904771057300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = 0.18083520000000008 " " y[1] (numeric) = 0.1808352 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.60456409188513600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = 0.1815458000000001 " " y[1] (numeric) = 0.1815458 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.5865410737613704000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = 0.1822568000000001 " " y[1] (numeric) = 0.1822568 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 6.09153142502861800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27900000000000014 " " y[1] (analytic) = 0.18296820000000008 " " y[1] (numeric) = 0.1829682 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.55088517277246600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = 0.1836800000000001 " " y[1] (numeric) = 0.18368 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.53324950168154940000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28100000000000014 " " y[1] (analytic) = 0.1843922000000001 " " y[1] (numeric) = 0.1843922 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.515740191119076400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = 0.1851048000000001 " " y[1] (numeric) = 0.1851048 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.49835589605924350000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = 0.18581780000000012 " " y[1] (numeric) = 0.1858178 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.97479372065085200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = 0.1865312000000001 " " y[1] (numeric) = 0.1865312 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.46395706706903200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28500000000000014 " " y[1] (analytic) = 0.18724500000000008 " " y[1] (numeric) = 0.187245 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.446939936814693000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28600000000000014 " " y[1] (analytic) = 0.1879592000000001 " " y[1] (numeric) = 0.1879592 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.90672350502213100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28700000000000014 " " y[1] (analytic) = 0.18867380000000009 " " y[1] (numeric) = 0.1886738 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.413263889680851000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28800000000000014 " " y[1] (analytic) = 0.1893888000000001 " " y[1] (numeric) = 0.1893888 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.86213664496082000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = 0.1901042000000001 " " y[1] (numeric) = 0.1901042 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.84007625620662700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = 0.1908200000000001 " " y[1] (numeric) = 0.19082 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.81816908408529400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = 0.1915362000000001 " " y[1] (numeric) = 0.1915362 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.79641354806640100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = 0.19225280000000008 " " y[1] (numeric) = 0.1922528 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.3311060669538600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = 0.1929698000000001 " " y[1] (numeric) = 0.1929698 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.75335117010618200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = 0.19368720000000011 " " y[1] (numeric) = 0.1936872 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.73204127389500100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = 0.1944050000000001 " " y[1] (numeric) = 0.194405 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.71087690453000700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = 0.1951232000000001 " " y[1] (numeric) = 0.1951232 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.68985658612177300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = 0.1958418000000001 " " y[1] (numeric) = 0.1958418 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.251734146994497500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = 0.19656080000000012 " " y[1] (numeric) = 0.1965608 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.64824229767662700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = 0.1972802000000001 " " y[1] (numeric) = 0.19728020000000002 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.220734105444271500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = 0.1980000000000001 " " y[1] (numeric) = 0.198 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.205390244792257500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = 0.19872020000000012 " " y[1] (numeric) = 0.1987202 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.58686547530223800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = 0.1994408000000001 " " y[1] (numeric) = 0.1994408 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.56667955917322800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30300000000000016 " " y[1] (analytic) = 0.2001618000000001 " " y[1] (numeric) = 0.2001618 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.54662790115374600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30400000000000016 " " y[1] (analytic) = 0.2008832000000001 " " y[1] (numeric) = 0.2008832 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.145031881555386600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = 0.2016050000000001 " " y[1] (numeric) = 0.201605 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.13019155511454100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30600000000000016 " " y[1] (analytic) = 0.20232720000000012 " " y[1] (numeric) = 0.2023272 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.48726530404787800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30700000000000016 " " y[1] (analytic) = 0.2030498000000001 " " y[1] (numeric) = 0.2030498 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.467737592576579000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30800000000000016 " " y[1] (analytic) = 0.20377280000000011 " " y[1] (numeric) = 0.2037728 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.44833768110933300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30900000000000016 " " y[1] (analytic) = 0.20449620000000013 " " y[1] (numeric) = 0.20449620000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.429064327968715000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = 0.2052200000000001 " " y[1] (numeric) = 0.20522 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.05743723062502170000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = 0.20594420000000013 " " y[1] (numeric) = 0.20594420000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.39089240981370600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = 0.2066688000000001 " " y[1] (numeric) = 0.2066688 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 4.028993580399495000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31300000000000017 " " y[1] (analytic) = 0.20739380000000013 " " y[1] (numeric) = 0.20739380000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.35321222054447100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = 0.20811920000000012 " " y[1] (numeric) = 0.2081192 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.33455358575833400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = 0.20884500000000011 " " y[1] (numeric) = 0.208845 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.31601438686660400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31600000000000017 " " y[1] (analytic) = 0.20957120000000012 " " y[1] (numeric) = 0.2095712 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.29759348911088900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = 0.21029780000000012 " " y[1] (numeric) = 0.2102978 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.27928977205256600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = 0.21102480000000012 " " y[1] (numeric) = 0.2110248 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.261102129347621000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = 0.2117522000000001 " " y[1] (numeric) = 0.2117522 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.243029468525738000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = 0.2124800000000001 " " y[1] (numeric) = 0.21248 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.22507071077351300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = 0.21320820000000013 " " y[1] (numeric) = 0.21320820000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.20722479072172600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = 0.21393680000000012 " " y[1] (numeric) = 0.2139368 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.18949065623658800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = 0.21466580000000013 " " y[1] (numeric) = 0.21466580000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.17186726821485300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = 0.21539520000000012 " " y[1] (numeric) = 0.2153952 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.154353600382720000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = 0.21612500000000012 " " y[1] (numeric) = 0.216125 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.136948639098465000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = 0.21685520000000014 " " y[1] (numeric) = 0.2168552 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.39956422894837100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = 0.2175858000000001 " " y[1] (numeric) = 0.2175858 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.10246084360815800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = 0.21831680000000014 " " y[1] (numeric) = 0.2183168 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.35672005444127400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = 0.21904820000000014 " " y[1] (numeric) = 0.2190482 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.33549502247197100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = 0.21978000000000011 " " y[1] (numeric) = 0.21978 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 5.051519813564274000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = 0.22051220000000013 " " y[1] (numeric) = 0.2205122 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.29343311064623600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = 0.22124480000000013 " " y[1] (numeric) = 0.2212448 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.27259389048440800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = 0.22197780000000014 " " y[1] (numeric) = 0.2219778 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.25188095738152500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = 0.22271120000000014 " " y[1] (numeric) = 0.2227112 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.23129317601200500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = 0.22344500000000012 " " y[1] (numeric) = 0.223445 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.968663539686079500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = 0.22417920000000013 " " y[1] (numeric) = 0.2241792 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.19048859475564700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = 0.22491380000000014 " " y[1] (numeric) = 0.2249138 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.17026959120091600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = 0.22564880000000015 " " y[1] (numeric) = 0.2256488 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.15017133165097500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = 0.22638420000000015 " " y[1] (numeric) = 0.2263842 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.13019274658498600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = 0.22712000000000013 " " y[1] (numeric) = 0.22712000000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.88826622325271200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = 0.22785620000000015 " " y[1] (numeric) = 0.2278562 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.09059038455589400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = 0.22859280000000012 " " y[1] (numeric) = 0.2285928 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.856771624588158700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = 0.22932980000000014 " " y[1] (numeric) = 0.2293298 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.05145419732387400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = 0.23006720000000014 " " y[1] (numeric) = 0.2300672 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 6.03205837590688700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = 0.23080500000000012 " " y[1] (numeric) = 0.230805 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.81022085580969200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = 0.23154320000000014 " " y[1] (numeric) = 0.2315432 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.99360629369139300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = 0.23228180000000015 " " y[1] (numeric) = 0.2322818 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.97454807385445100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = 0.23302080000000014 " " y[1] (numeric) = 0.2330208 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.95560044760572900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = 0.23376020000000014 " " y[1] (numeric) = 0.2337602 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.93676246333398400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = 0.23450000000000013 " " y[1] (numeric) = 0.23450000000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.73442654424373500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3510000000000002 " " y[1] (analytic) = 0.23524020000000015 " " y[1] (numeric) = 0.2352402 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.89941166850497900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3520000000000002 " " y[1] (analytic) = 0.23598080000000013 " " y[1] (numeric) = 0.23598080000000002 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.704717606793248000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3530000000000002 " " y[1] (analytic) = 0.23672180000000015 " " y[1] (numeric) = 0.2367218 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.86248829124079300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3540000000000002 " " y[1] (analytic) = 0.23746320000000015 " " y[1] (numeric) = 0.2374632 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.8441846180016300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3550000000000002 " " y[1] (analytic) = 0.23820500000000014 " " y[1] (numeric) = 0.238205 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.82598510015089900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3560000000000002 " " y[1] (analytic) = 0.23894720000000014 " " y[1] (numeric) = 0.2389472 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.80788885905105800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3570000000000002 " " y[1] (analytic) = 0.23968980000000015 " " y[1] (numeric) = 0.2396898 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.78989502591034200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3580000000000002 " " y[1] (analytic) = 0.24043280000000017 " " y[1] (numeric) = 0.2404328 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.92640328997430300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3590000000000002 " " y[1] (analytic) = 0.24117620000000015 " " y[1] (numeric) = 0.2411762 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.75421115674533800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = 0.24192000000000013 " " y[1] (numeric) = 0.24192 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.73651943114023200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3610000000000002 " " y[1] (analytic) = 0.24266420000000016 " " y[1] (numeric) = 0.2426642 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.86271208088269100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3620000000000002 " " y[1] (analytic) = 0.24340880000000015 " " y[1] (numeric) = 0.2434088 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.70143224395110200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3630000000000002 " " y[1] (analytic) = 0.24415380000000017 " " y[1] (numeric) = 0.2441538 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.82084217791299400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3640000000000002 " " y[1] (analytic) = 0.24489920000000015 " " y[1] (numeric) = 0.2448992 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.6667346434020400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3650000000000002 " " y[1] (analytic) = 0.24564500000000014 " " y[1] (numeric) = 0.245645 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.64952993458627300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3660000000000002 " " y[1] (analytic) = 0.24639120000000017 " " y[1] (numeric) = 0.2463912 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.758904282854801000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3670000000000002 " " y[1] (analytic) = 0.24713780000000016 " " y[1] (numeric) = 0.24713780000000002 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.61540476924794500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3680000000000002 " " y[1] (analytic) = 0.24788480000000016 " " y[1] (numeric) = 0.24788480000000002 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.598482766113311000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3690000000000002 " " y[1] (analytic) = 0.24863220000000016 " " y[1] (numeric) = 0.24863220000000003 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.58165346556658700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = 0.24938000000000016 " " y[1] (numeric) = 0.24938000000000002 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 5.56491611509120500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3710000000000002 " " y[1] (analytic) = 0.2501282000000002 " " y[1] (numeric) = 0.2501282 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.6579239643420200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3720000000000002 " " y[1] (analytic) = 0.2508768000000002 " " y[1] (numeric) = 0.2508768 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.63805715370147200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3730000000000002 " " y[1] (analytic) = 0.2516258000000002 " " y[1] (numeric) = 0.2516258 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.61829803198930100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3740000000000002 " " y[1] (analytic) = 0.25237520000000013 " " y[1] (numeric) = 0.2523752 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.399097156238631600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3750000000000002 " " y[1] (analytic) = 0.25312500000000016 " " y[1] (numeric) = 0.25312500000000004 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.386066270124072700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3760000000000002 " " y[1] (analytic) = 0.2538752000000002 " " y[1] (numeric) = 0.2538752 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.55965819795605600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3770000000000002 " " y[1] (analytic) = 0.2546258000000002 " " y[1] (numeric) = 0.2546258 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.54032127513289500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3780000000000002 " " y[1] (analytic) = 0.2553768000000001 " " y[1] (numeric) = 0.2553768 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.347391872030489400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3790000000000002 " " y[1] (analytic) = 0.25612820000000014 " " y[1] (numeric) = 0.25612820000000003 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.33463798451383330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = 0.25688000000000016 " " y[1] (numeric) = 0.25688000000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.32195198001072800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3810000000000002 " " y[1] (analytic) = 0.2576322000000002 " " y[1] (numeric) = 0.25763220000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.46399998500860400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38200000000000023 " " y[1] (analytic) = 0.2583848000000002 " " y[1] (numeric) = 0.2583848 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.44517222738231300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38300000000000023 " " y[1] (analytic) = 0.25913780000000014 " " y[1] (numeric) = 0.25913780000000003 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.284295940712454000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38400000000000023 " " y[1] (analytic) = 0.25989120000000016 " " y[1] (numeric) = 0.25989120000000004 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.27187617212570400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38500000000000023 " " y[1] (analytic) = 0.2606450000000002 " " y[1] (numeric) = 0.26064500000000007 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.25952166596388100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38600000000000023 " " y[1] (analytic) = 0.26139920000000016 " " y[1] (numeric) = 0.26139920000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.2472319143484600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38700000000000023 " " y[1] (analytic) = 0.26215380000000016 " " y[1] (numeric) = 0.26215380000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.235006414651078500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38800000000000023 " " y[1] (analytic) = 0.26290880000000016 " " y[1] (numeric) = 0.26290880000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.22284466942588400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38900000000000023 " " y[1] (analytic) = 0.2636642000000002 " " y[1] (numeric) = 0.26366420000000007 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.210746186342916000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = 0.26442000000000015 " " y[1] (numeric) = 0.26442000000000004 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.19871047812251700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39100000000000024 " " y[1] (analytic) = 0.2651762000000002 " " y[1] (numeric) = 0.26517620000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.28010559370612200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39200000000000024 " " y[1] (analytic) = 0.2659328000000002 " " y[1] (numeric) = 0.2659328 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.26223819302370100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39300000000000024 " " y[1] (analytic) = 0.26668980000000014 " " y[1] (numeric) = 0.26668980000000003 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.16297520424536600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39400000000000024 " " y[1] (analytic) = 0.26744720000000016 " " y[1] (numeric) = 0.26744720000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.15118582144496540000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39500000000000024 " " y[1] (analytic) = 0.2682050000000002 " " y[1] (numeric) = 0.268205 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.2091852759558310000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39600000000000024 " " y[1] (analytic) = 0.2689632000000002 " " y[1] (numeric) = 0.2689632 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.19168175028306300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39700000000000024 " " y[1] (analytic) = 0.2697218000000002 " " y[1] (numeric) = 0.2697218 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.17426747462657400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39800000000000024 " " y[1] (analytic) = 0.2704808000000002 " " y[1] (numeric) = 0.2704808 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.15694177530432300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39900000000000024 " " y[1] (analytic) = 0.27124020000000015 " " y[1] (numeric) = 0.27124020000000004 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.09313599025939330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = 0.2720000000000002 " " y[1] (numeric) = 0.272 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.1225534446240200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40100000000000025 " " y[1] (analytic) = 0.2727602000000002 " " y[1] (numeric) = 0.2727602 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.1054894993394690000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40200000000000025 " " y[1] (analytic) = 0.2735208000000002 " " y[1] (numeric) = 0.2735208 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.08851150237105800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40300000000000025 " " y[1] (analytic) = 0.2742818000000002 " " y[1] (numeric) = 0.2742818 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.07161881297896400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40400000000000025 " " y[1] (analytic) = 0.27504320000000015 " " y[1] (numeric) = 0.27504320000000004 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 4.03654053117894200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40500000000000025 " " y[1] (analytic) = 0.2758050000000002 " " y[1] (numeric) = 0.275805 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.03808682561133400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40600000000000025 " " y[1] (analytic) = 0.2765672000000002 " " y[1] (numeric) = 0.2765672 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.0214462775691890000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40700000000000025 " " y[1] (analytic) = 0.2773298000000002 " " y[1] (numeric) = 0.2773298 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 6.00488853681693700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40800000000000025 " " y[1] (analytic) = 0.2780928000000002 " " y[1] (numeric) = 0.27809280000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.98841299356809600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40900000000000025 " " y[1] (analytic) = 0.27885620000000017 " " y[1] (numeric) = 0.27885620000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.98134602933395750000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = 0.2796200000000002 " " y[1] (numeric) = 0.27962000000000004 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.95570609018573000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41100000000000025 " " y[1] (analytic) = 0.2803842000000002 " " y[1] (numeric) = 0.28038420000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.93947354001307400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41200000000000025 " " y[1] (analytic) = 0.2811488000000002 " " y[1] (numeric) = 0.28114880000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.92332080712325100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41300000000000026 " " y[1] (analytic) = 0.28191380000000016 " " y[1] (numeric) = 0.28191380000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.938164873891082400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41400000000000026 " " y[1] (analytic) = 0.2826792000000002 " " y[1] (numeric) = 0.2826792000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.92750165072334900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41500000000000026 " " y[1] (analytic) = 0.28344500000000017 " " y[1] (numeric) = 0.28344500000000006 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.91689048889610300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41600000000000026 " " y[1] (analytic) = 0.2842112000000002 " " y[1] (numeric) = 0.28421120000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.85949651856694500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41700000000000026 " " y[1] (analytic) = 0.28497780000000017 " " y[1] (numeric) = 0.28497780000000006 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.89582284874525600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41800000000000026 " " y[1] (analytic) = 0.2857448000000002 " " y[1] (numeric) = 0.2857448000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.88536562913885330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41900000000000026 " " y[1] (analytic) = 0.28651220000000016 " " y[1] (numeric) = 0.28651220000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.874958988221639500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42000000000000026 " " y[1] (analytic) = 0.2872800000000002 " " y[1] (numeric) = 0.28728000000000004 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.79690384620486600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42100000000000026 " " y[1] (analytic) = 0.2880482000000002 " " y[1] (numeric) = 0.28804820000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.78144399769807100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42200000000000026 " " y[1] (analytic) = 0.2888168000000002 " " y[1] (numeric) = 0.28881680000000004 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.76605840428165400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42300000000000026 " " y[1] (analytic) = 0.28958580000000017 " " y[1] (numeric) = 0.28958580000000006 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.83383102564129830000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42400000000000027 " " y[1] (analytic) = 0.29035520000000015 " " y[1] (numeric) = 0.29035520000000004 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.82367191848176300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42500000000000027 " " y[1] (analytic) = 0.2911250000000002 " " y[1] (numeric) = 0.291125 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.72034190446623800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42600000000000027 " " y[1] (analytic) = 0.2918952000000002 " " y[1] (numeric) = 0.2918952 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.70524810595629400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42700000000000027 " " y[1] (analytic) = 0.2926658000000002 " " y[1] (numeric) = 0.29266580000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.69022597426051800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42800000000000027 " " y[1] (analytic) = 0.29343680000000016 " " y[1] (numeric) = 0.29343680000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.783516670796423500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.42900000000000027 " " y[1] (analytic) = 0.2942082000000002 " " y[1] (numeric) = 0.29420820000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.660394703267052000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.43000000000000027 " " y[1] (analytic) = 0.29498000000000024 " " y[1] (numeric) = 0.29498 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.52744609549905500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.43100000000000027 " " y[1] (analytic) = 0.2957522000000002 " " y[1] (numeric) = 0.2957522 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.63084412199717800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4320000000000003 " " y[1] (analytic) = 0.2965248000000002 " " y[1] (numeric) = 0.29652480000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.61617286964777900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4330000000000003 " " y[1] (analytic) = 0.29729780000000017 " " y[1] (numeric) = 0.29729780000000006 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.734380222878056500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4340000000000003 " " y[1] (analytic) = 0.2980712000000002 " " y[1] (numeric) = 0.29807120000000004 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.587036040173400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4350000000000003 " " y[1] (analytic) = 0.29884500000000025 " " y[1] (numeric) = 0.298845 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.43009268768194600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4360000000000003 " " y[1] (analytic) = 0.2996192000000002 " " y[1] (numeric) = 0.29961920000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.558170293952236000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4370000000000003 " " y[1] (analytic) = 0.3003938000000002 " " y[1] (numeric) = 0.30039380000000004 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.543837911893433000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4380000000000003 " " y[1] (analytic) = 0.3011688000000002 " " y[1] (numeric) = 0.30116880000000007 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.686381273973784500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4390000000000003 " " y[1] (analytic) = 0.30194420000000016 " " y[1] (numeric) = 0.30194420000000005 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.6769145578062300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4400000000000003 " " y[1] (analytic) = 0.3027200000000002 " " y[1] (numeric) = 0.30272000000000004 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.5012372388270800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4410000000000003 " " y[1] (analytic) = 0.3034962000000002 " " y[1] (numeric) = 0.30349620000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.48716767108693200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4420000000000003 " " y[1] (analytic) = 0.30427280000000023 " " y[1] (numeric) = 0.30427280000000007 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.4731626913011400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4430000000000003 " " y[1] (analytic) = 0.3050498000000002 " " y[1] (numeric) = 0.3050498000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.63948124085036600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4440000000000003 " " y[1] (analytic) = 0.3058272000000002 " " y[1] (numeric) = 0.3058272000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.630229831176416000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4450000000000003 " " y[1] (analytic) = 0.30660500000000024 " " y[1] (numeric) = 0.30660500000000007 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.43153091742709200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4460000000000003 " " y[1] (analytic) = 0.30738320000000025 " " y[1] (numeric) = 0.3073832000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.41777994678217100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4470000000000003 " " y[1] (analytic) = 0.3081618000000002 " " y[1] (numeric) = 0.3081618000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.602727608110920500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4480000000000003 " " y[1] (analytic) = 0.30894080000000024 " " y[1] (numeric) = 0.30894080000000007 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.39046489469093600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4490000000000003 " " y[1] (analytic) = 0.3097202000000002 " " y[1] (numeric) = 0.30972020000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.37689997919972200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4500000000000003 " " y[1] (analytic) = 0.3105000000000002 " " y[1] (numeric) = 0.31050000000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.36339625422780600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4510000000000003 " " y[1] (analytic) = 0.31128020000000023 " " y[1] (numeric) = 0.31128020000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.34995331196052100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4520000000000003 " " y[1] (analytic) = 0.31206080000000025 " " y[1] (numeric) = 0.3120608000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.33657074819308800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4530000000000003 " " y[1] (analytic) = 0.3128418000000002 " " y[1] (numeric) = 0.31284180000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.323248162290760000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4540000000000003 " " y[1] (analytic) = 0.3136232000000002 " " y[1] (numeric) = 0.31362320000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.309985157149515000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4550000000000003 " " y[1] (analytic) = 0.31440500000000027 " " y[1] (numeric) = 0.31440500000000005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 7.06237511887632600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4560000000000003 " " y[1] (analytic) = 0.3151872000000002 " " y[1] (numeric) = 0.31518720000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.28363631815547600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4570000000000003 " " y[1] (analytic) = 0.31596980000000024 " " y[1] (numeric) = 0.3159698000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.270549707401573000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4580000000000003 " " y[1] (analytic) = 0.3167528000000002 " " y[1] (numeric) = 0.31675280000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.25752112353145300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4590000000000003 " " y[1] (analytic) = 0.3175362000000002 " " y[1] (numeric) = 0.31753620000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.24455018652277700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4600000000000003 " " y[1] (analytic) = 0.31832000000000027 " " y[1] (numeric) = 0.31832000000000005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.97551535954483400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4610000000000003 " " y[1] (analytic) = 0.3191042000000002 " " y[1] (numeric) = 0.31910420000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.21877974949165100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4620000000000003 " " y[1] (analytic) = 0.3198888000000002 " " y[1] (numeric) = 0.3198888000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.47065300387245800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4630000000000003 " " y[1] (analytic) = 0.32067380000000023 " " y[1] (numeric) = 0.32067380000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.1932354215958200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4640000000000003 " " y[1] (analytic) = 0.3214592000000002 " " y[1] (numeric) = 0.32145920000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.1805471330039200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4650000000000003 " " y[1] (analytic) = 0.3222450000000002 " " y[1] (numeric) = 0.32224500000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.167914279314602000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4660000000000003 " " y[1] (analytic) = 0.32303120000000024 " " y[1] (numeric) = 0.3230312000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.15533650290663400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4670000000000003 " " y[1] (analytic) = 0.3238178000000002 " " y[1] (numeric) = 0.3238178000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.42854229948185600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4680000000000003 " " y[1] (analytic) = 0.32460480000000025 " " y[1] (numeric) = 0.3246048000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.130344766737070000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4690000000000003 " " y[1] (analytic) = 0.3253922000000002 " " y[1] (numeric) = 0.3253922000000001 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 3.41195340461497200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4700000000000003 " " y[1] (analytic) = 0.32618000000000025 " " y[1] (numeric) = 0.3261800000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.10556912421893900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4710000000000003 " " y[1] (analytic) = 0.32696820000000026 " " y[1] (numeric) = 0.3269682000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.0932614760020500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4720000000000003 " " y[1] (analytic) = 0.32775680000000024 " " y[1] (numeric) = 0.32775680000000007 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.081006822551762000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4730000000000003 " " y[1] (analytic) = 0.3285458000000002 " " y[1] (numeric) = 0.32854580000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.06880482702178400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4740000000000003 " " y[1] (analytic) = 0.3293352000000002 " " y[1] (numeric) = 0.32933520000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.05665515540924200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4750000000000003 " " y[1] (analytic) = 0.3301250000000003 " " y[1] (numeric) = 0.33012500000000006 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.72607663536633400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4760000000000003 " " y[1] (analytic) = 0.33091520000000024 " " y[1] (numeric) = 0.3309152000000001 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.03251146196286400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4770000000000003 " " y[1] (analytic) = 0.3317058000000002 " " y[1] (numeric) = 0.33170580000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 5.020516786072880000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4780000000000003 " " y[1] (analytic) = 0.33249680000000026 " " y[1] (numeric) = 0.33249680000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.67809750124004700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4790000000000003 " " y[1] (analytic) = 0.3332882000000002 " " y[1] (numeric) = 0.33328820000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.996680161307042000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4800000000000003 " " y[1] (analytic) = 0.33408000000000027 " " y[1] (numeric) = 0.33408000000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.64645009952799200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4810000000000003 " " y[1] (analytic) = 0.33487220000000023 " " y[1] (numeric) = 0.33487220000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.97304505103061300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4820000000000003 " " y[1] (analytic) = 0.33566480000000026 " " y[1] (numeric) = 0.33566480000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.61506970421179500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4830000000000003 " " y[1] (analytic) = 0.33645780000000025 " " y[1] (numeric) = 0.33645780000000003 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.59947859508773900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4840000000000003 " " y[1] (analytic) = 0.3372512000000002 " " y[1] (numeric) = 0.33725120000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.9379647483470300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4850000000000003 " " y[1] (analytic) = 0.33804500000000026 " " y[1] (numeric) = 0.33804500000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.56849250617613500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4860000000000003 " " y[1] (analytic) = 0.33883920000000023 " " y[1] (numeric) = 0.33883920000000006 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.91482253805856500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4870000000000003 " " y[1] (analytic) = 0.33963380000000026 " " y[1] (numeric) = 0.33963380000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.53776523199490600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4880000000000003 " " y[1] (analytic) = 0.34042880000000025 " " y[1] (numeric) = 0.34042880000000003 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.52249765369531400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4890000000000003 " " y[1] (analytic) = 0.3412242000000002 " " y[1] (numeric) = 0.34122420000000003 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.880470192142684600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4900000000000003 " " y[1] (analytic) = 0.34202000000000027 " " y[1] (numeric) = 0.34202000000000005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.49215264969975800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4910000000000003 " " y[1] (analytic) = 0.34281620000000024 " " y[1] (numeric) = 0.34281620000000007 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.85780583571527150000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4920000000000003 " " y[1] (analytic) = 0.3436128000000003 " " y[1] (numeric) = 0.34361280000000005 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.46205859982605800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4930000000000003 " " y[1] (analytic) = 0.34440980000000027 " " y[1] (numeric) = 0.34440980000000004 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.44710472596979300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.4940000000000003 " " y[1] (analytic) = 0.3452072000000002 " " y[1] (numeric) = 0.34520720000000005 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 4.82415933658896350000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.49500000000000033 " " y[1] (analytic) = 0.3460050000000003 " " y[1] (numeric) = 0.34600500000000006 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 6.41738139405589900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = 2.0 * (0.2 * x + 0.3);" Iterations = 396 "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 34 Minutes 7 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 34 Minutes 0 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 37 Minutes 1 Seconds "Time to Timeout " Unknown Percent Done = 8.102040816326538 "%" (%o57) true (%o57) diffeq.max