(%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 : ln(array_const_0D1 ), 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : exp(array_const_0D1 ), array_tmp4 : array_tmp3 + array_tmp2 , 1 1 1 1 1 array_tmp5 : sqrt(array_const_0D1 ), array_tmp6 : array_tmp5 + array_tmp4 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 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 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 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_tmp6 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_tmp6 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_tmp6 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_tmp6 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 : ln(array_const_0D1 ), 1 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 array_tmp3 : exp(array_const_0D1 ), array_tmp4 : array_tmp3 + array_tmp2 , 1 1 1 1 1 array_tmp5 : sqrt(array_const_0D1 ), array_tmp6 : array_tmp5 + array_tmp4 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp6 expt(glob_h, 1) factorial_3(0, 1), 1 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 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp6 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_tmp6 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_tmp6 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_tmp6 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_tmp6 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((sqrt(0.1) + exp(0.1) + ln(0.1)) x) (%o55) exact_soln_y(x) := block((sqrt(0.1) + exp(0.1) + ln(0.1)) 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/ln_c_exp_c_sqrt_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1);"), 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, " ((ln(0.1) + exp(0.1) + sqrt(0.1)) * x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_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 ) = ln(0.1) + exp(0.1) + sqrt(0.1);"), 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, "2013-01-13T00:31:55-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "ln_c_exp_c_sqrt_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1);"), 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, "ln_c_exp_c_sqrt_c diffeq.max"), logitem_str(html_log_file, "ln_c_e\ xp_c_sqrt_c 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/ln_c_exp_c_sqrt_cpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1);"), 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, " ((ln(0.1) + exp(0.1) + sqrt(0.1)) * x) "), omniout_str(ALWAYS, "));"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_y_init, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_complex_pole, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_norms : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_1st_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp5 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp5, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp5 : 0.0, term : 1 + term), term array(array_tmp6, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_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 ) = ln(0.1) + exp(0.1) + sqrt(0.1);"), 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, "2013-01-13T00:31:55-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "ln_c_exp_c_sqrt_c"), logitem_str(html_log_file, "diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1);"), 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, "ln_c_exp_c_sqrt_c diffeq.max"), logitem_str(html_log_file, "ln_c_e\ xp_c_sqrt_c 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/ln_c_exp_c_sqrt_cpostode.ode#################" "diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1);" "!" "/* 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(" " ((ln(0.1) + exp(0.1) + sqrt(0.1)) * x) " "));" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Optimize" min_size = 0.0 "" min_size = 1. "" opt_iter = 1 glob_desired_digits_correct = 10. "" desired_abs_gbl_error = 1.0000000000E-10 "" range = 4.9 "" estimated_steps = 4900. "" step_error = 2.040816326530612300000000000000E-14 "" est_needed_step_err = 2.040816326530612300000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" max_value3 = 0.0 "" value3 = 0.0 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = -8.81186408901559700E-2 " " y[1] (numeric) = -8.81186408901559700E-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) = -8.81186408901559700E-2 " " y[1] (numeric) = -8.81186408901559700E-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) = -8.89998272990575400E-2 " " y[1] (numeric) = -8.89998272990575300E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.559305026647103700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10200000000000001 " " y[1] (analytic) = -8.9881013707959100E-2 " " y[1] (numeric) = -8.98810137079590900E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.544017722464289300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10300000000000001 " " y[1] (analytic) = -9.07622001168606600E-2 " " y[1] (numeric) = -9.07622001168606500E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.529027259139393300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10400000000000001 " " y[1] (analytic) = -9.16433865257622200E-2 " " y[1] (numeric) = -9.1643386525762200E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.514325073955360700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10500000000000001 " " y[1] (analytic) = -9.25245729346637700E-2 " " y[1] (numeric) = -9.25245729346637600E-2 " " absolute error = 1.387778780781445700000000000000000E-17 " " relative error = 1.49990293039388100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10600000000000001 " " y[1] (analytic) = -9.34057593435653400E-2 " " y[1] (numeric) = -9.34057593435653200E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.97150580549731100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10700000000000001 " " y[1] (analytic) = -9.4286945752466900E-2 " " y[1] (numeric) = -9.42869457524668800E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.943734723202943700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10800000000000001 " " y[1] (analytic) = -9.51681321613684600E-2 " " y[1] (numeric) = -9.51681321613684400E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.91647792021032400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.10900000000000001 " " y[1] (analytic) = -9.60493185702700100E-2 " " y[1] (numeric) = -9.60493185702699900E-2 " " absolute error = 2.775557561562891400000000000000000E-17 " " relative error = 2.88972124204325660000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11000000000000001 " " y[1] (analytic) = -9.69305049791716000E-2 " " y[1] (numeric) = -9.69305049791715500E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.295176573400658600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11100000000000002 " " y[1] (analytic) = -9.78116913880731500E-2 " " y[1] (numeric) = -9.78116913880731100E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.256481288955607500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11200000000000002 " " y[1] (analytic) = -9.8692877796974710E-2 " " y[1] (numeric) = -9.86928777969746700E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.2184769917327897000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11300000000000002 " " y[1] (analytic) = -9.95740642058762700E-2 " " y[1] (numeric) = -9.95740642058762200E-2 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.181145336938694000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11400000000000002 " " y[1] (analytic) = -0.10045525061477782 " " y[1] (numeric) = -0.10045525061477778 " " absolute error = 4.16333634234433700000000000000000E-17 " " relative error = 4.14446862345677570000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11500000000000002 " " y[1] (analytic) = -0.1013364370236794 " " y[1] (numeric) = -0.10133643702367934 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 5.47790635448200000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11600000000000002 " " y[1] (analytic) = -0.10221762343258095 " " y[1] (numeric) = -0.1022176234325809 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 5.43068302383991300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11700000000000002 " " y[1] (analytic) = -0.10309880984148251 " " y[1] (numeric) = -0.10309880984148245 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 5.384266929619059000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11800000000000002 " " y[1] (analytic) = -0.10397999625038407 " " y[1] (numeric) = -0.10397999625038401 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 5.33863754885957600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.11900000000000002 " " y[1] (analytic) = -0.10486118265928562 " " y[1] (numeric) = -0.10486118265928557 " " absolute error = 5.55111512312578300000000000000000E-17 " " relative error = 5.29377504844899100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12000000000000002 " " y[1] (analytic) = -0.1057423690681872 " " y[1] (numeric) = -0.10574236906818713 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 6.56207532047322700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12100000000000002 " " y[1] (analytic) = -0.10662355547708875 " " y[1] (numeric) = -0.10662355547708868 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 6.50784329303130100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12200000000000003 " " y[1] (analytic) = -0.10750474188599031 " " y[1] (numeric) = -0.10750474188599024 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 6.45450031521956900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12300000000000003 " " y[1] (analytic) = -0.10838592829489187 " " y[1] (numeric) = -0.1083859282948918 " " absolute error = 6.93889390390722800000000000000000E-17 " " relative error = 6.40202470290071200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12400000000000003 " " y[1] (analytic) = -0.10926711470379344 " " y[1] (numeric) = -0.10926711470379336 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.62047456571084500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12500000000000003 " " y[1] (analytic) = -0.110148301112695 " " y[1] (numeric) = -0.11014830111269491 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.55951076918515800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12600000000000003 " " y[1] (analytic) = -0.11102948752159655 " " y[1] (numeric) = -0.11102948752159647 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.49951465196940400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12700000000000003 " " y[1] (analytic) = -0.11191067393049811 " " y[1] (numeric) = -0.11191067393049803 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.44046335549720300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12800000000000003 " " y[1] (analytic) = -0.11279186033939967 " " y[1] (numeric) = -0.11279186033939959 " " absolute error = 8.32667268468867400000000000000000E-17 " " relative error = 7.38233473553238200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.12900000000000003 " " y[1] (analytic) = -0.11367304674830124 " " y[1] (numeric) = -0.11367304674830114 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 8.54595855689536700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13000000000000003 " " y[1] (analytic) = -0.1145542331572028 " " y[1] (numeric) = -0.1145542331572027 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 8.48022041415001700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13100000000000003 " " y[1] (analytic) = -0.11543541956610436 " " y[1] (numeric) = -0.11543541956610426 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 8.41548590717177400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13200000000000003 " " y[1] (analytic) = -0.11631660597500591 " " y[1] (numeric) = -0.11631660597500582 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 8.35173222605683500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13300000000000003 " " y[1] (analytic) = -0.11719779238390747 " " y[1] (numeric) = -0.11719779238390737 " " absolute error = 9.7144514654701200000000000000000E-17 " " relative error = 8.28893724691355100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13400000000000004 " " y[1] (analytic) = -0.11807897879280904 " " y[1] (numeric) = -0.11807897879280893 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 9.40237657858850500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13500000000000004 " " y[1] (analytic) = -0.1189601652017106 " " y[1] (numeric) = -0.11896016520171049 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 9.33272934467303400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13600000000000004 " " y[1] (analytic) = -0.11984135161061216 " " y[1] (numeric) = -0.11984135161061205 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 9.26410633478573300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13700000000000004 " " y[1] (analytic) = -0.12072253801951371 " " y[1] (numeric) = -0.1207225380195136 " " absolute error = 1.11022302462515650000000000000000E-16 " " relative error = 9.1964851206632100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13800000000000004 " " y[1] (analytic) = -0.12160372442841529 " " y[1] (numeric) = -0.12160372442841516 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.02710744146537470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.13900000000000004 " " y[1] (analytic) = -0.12248491083731684 " " y[1] (numeric) = -0.12248491083731672 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.0197181792965590000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14000000000000004 " " y[1] (analytic) = -0.1233660972462184 " " y[1] (numeric) = -0.12336609724621828 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.01243447801586950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14100000000000004 " " y[1] (analytic) = -0.12424728365511996 " " y[1] (numeric) = -0.12424728365511983 " " absolute error = 1.2490009027033011000000000000000E-16 " " relative error = 1.00525409164696270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14200000000000004 " " y[1] (analytic) = -0.12512847006402153 " " y[1] (numeric) = -0.1251284700640214 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.10908315275603840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14300000000000004 " " y[1] (analytic) = -0.1260096564729231 " " y[1] (numeric) = -0.12600965647292295 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.10132732651298910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14400000000000004 " " y[1] (analytic) = -0.12689084288182464 " " y[1] (numeric) = -0.1268908428818245 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.09367922007887110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14500000000000005 " " y[1] (analytic) = -0.1277720292907262 " " y[1] (numeric) = -0.12777202929072606 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.08613660476798250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14600000000000005 " " y[1] (analytic) = -0.12865321569962776 " " y[1] (numeric) = -0.12865321569962762 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.07869731295450330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14700000000000005 " " y[1] (analytic) = -0.12953440210852932 " " y[1] (numeric) = -0.12953440210852918 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.07135923599562910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14800000000000005 " " y[1] (analytic) = -0.13041558851743087 " " y[1] (numeric) = -0.13041558851743074 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.06412032223890190000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.14900000000000005 " " y[1] (analytic) = -0.13129677492633243 " " y[1] (numeric) = -0.1312967749263323 " " absolute error = 1.38777878078144570000000000000000E-16 " " relative error = 1.05697857510978170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15000000000000005 " " y[1] (analytic) = -0.13217796133523402 " " y[1] (numeric) = -0.13217796133523385 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.25991846153085950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15100000000000005 " " y[1] (analytic) = -0.13305914774413558 " " y[1] (numeric) = -0.1330591477441354 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.25157463065979400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15200000000000005 " " y[1] (analytic) = -0.13394033415303713 " " y[1] (numeric) = -0.13394033415303697 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.24334058703703260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15300000000000005 " " y[1] (analytic) = -0.1348215205619387 " " y[1] (numeric) = -0.13482152056193852 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.2352141779714310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15400000000000005 " " y[1] (analytic) = -0.13570270697084025 " " y[1] (numeric) = -0.13570270697084008 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.22719330668590230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15500000000000005 " " y[1] (analytic) = -0.1365838933797418 " " y[1] (numeric) = -0.13658389337974164 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.21927593051373520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15600000000000006 " " y[1] (analytic) = -0.13746507978864336 " " y[1] (numeric) = -0.1374650797886432 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.21146005916428820000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15700000000000006 " " y[1] (analytic) = -0.13834626619754492 " " y[1] (numeric) = -0.13834626619754475 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.20374375305496130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15800000000000006 " " y[1] (analytic) = -0.13922745260644648 " " y[1] (numeric) = -0.1392274526064463 " " absolute error = 1.66533453693773480000000000000000E-16 " " relative error = 1.19612512170651250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.15900000000000006 " " y[1] (analytic) = -0.14010863901534806 " " y[1] (numeric) = -0.14010863901534787 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.3867027092320780000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16000000000000006 " " y[1] (analytic) = -0.14098982542424962 " " y[1] (numeric) = -0.14098982542424943 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.37803581729937760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16100000000000006 " " y[1] (analytic) = -0.14187101183315118 " " y[1] (numeric) = -0.14187101183315098 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.36947658862049960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16200000000000006 " " y[1] (analytic) = -0.14275219824205274 " " y[1] (numeric) = -0.14275219824205254 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.36102302943148400000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16300000000000006 " " y[1] (analytic) = -0.1436333846509543 " " y[1] (numeric) = -0.1436333846509541 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.35267319489509460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16400000000000006 " " y[1] (analytic) = -0.14451457105985585 " " y[1] (numeric) = -0.14451457105985566 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.3444251876091490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16500000000000006 " " y[1] (analytic) = -0.1453957574687574 " " y[1] (numeric) = -0.14539575746875721 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.33627715616909360000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16600000000000006 " " y[1] (analytic) = -0.14627694387765897 " " y[1] (numeric) = -0.14627694387765877 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.32822729378253260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16700000000000007 " " y[1] (analytic) = -0.14715813028656052 " " y[1] (numeric) = -0.14715813028656033 " " absolute error = 1.9428902930940240000000000000000E-16 " " relative error = 1.32027383693353570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16800000000000007 " " y[1] (analytic) = -0.1480393166954621 " " y[1] (numeric) = -0.1480393166954619 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.49990293039388020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.16900000000000007 " " y[1] (analytic) = -0.14892050310436367 " " y[1] (numeric) = -0.14892050310436344 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.49102776512527730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17000000000000007 " " y[1] (analytic) = -0.14980168951326522 " " y[1] (numeric) = -0.149801689513265 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.48225701356571730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17100000000000007 " " y[1] (analytic) = -0.15068287592216678 " " y[1] (numeric) = -0.15068287592216656 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.47358884389574200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17200000000000007 " " y[1] (analytic) = -0.15156406233106834 " " y[1] (numeric) = -0.15156406233106812 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.46502146689634850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17300000000000007 " " y[1] (analytic) = -0.1524452487399699 " " y[1] (numeric) = -0.15244524873996967 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.45655313471775650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17400000000000007 " " y[1] (analytic) = -0.15332643514887145 " " y[1] (numeric) = -0.15332643514887123 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.44818213969064330000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17500000000000007 " " y[1] (analytic) = -0.154207621557773 " " y[1] (numeric) = -0.1542076215577728 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.43990681317812500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17600000000000007 " " y[1] (analytic) = -0.15508880796667457 " " y[1] (numeric) = -0.15508880796667435 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.4317255244668858000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17700000000000007 " " y[1] (analytic) = -0.15596999437557615 " " y[1] (numeric) = -0.1559699943755759 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.60159126465787230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17800000000000007 " " y[1] (analytic) = -0.1568511807844777 " " y[1] (numeric) = -0.15685118078447746 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.59259356092383920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.17900000000000008 " " y[1] (analytic) = -0.15773236719337927 " " y[1] (numeric) = -0.15773236719337902 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.5836963901924211000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18000000000000008 " " y[1] (analytic) = -0.15861355360228083 " " y[1] (numeric) = -0.15861355360228058 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.57489807691357430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18100000000000008 " " y[1] (analytic) = -0.15949474001118238 " " y[1] (numeric) = -0.15949474001118213 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.56619698256598580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18200000000000008 " " y[1] (analytic) = -0.16037592642008394 " " y[1] (numeric) = -0.1603759264200837 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.55759150463979900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18300000000000008 " " y[1] (analytic) = -0.1612571128289855 " " y[1] (numeric) = -0.16125711282898525 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.5490800756526960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18400000000000008 " " y[1] (analytic) = -0.16213829923788706 " " y[1] (numeric) = -0.1621382992378868 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.5406611621980620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18500000000000008 " " y[1] (analytic) = -0.16301948564678861 " " y[1] (numeric) = -0.16301948564678836 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.53233326402401840000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18600000000000008 " " y[1] (analytic) = -0.16390067205569017 " " y[1] (numeric) = -0.16390067205568992 " " absolute error = 2.4980018054066022000000000000000E-16 " " relative error = 1.52409491314216880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18700000000000008 " " y[1] (analytic) = -0.16478185846459176 " " y[1] (numeric) = -0.16478185846459148 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.6843829699610420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18800000000000008 " " y[1] (analytic) = -0.16566304487349331 " " y[1] (numeric) = -0.16566304487349304 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.67542348607827070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.18900000000000008 " " y[1] (analytic) = -0.16654423128239487 " " y[1] (numeric) = -0.1665442312823946 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.66655881154875600000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.19000000000000009 " " y[1] (analytic) = -0.16742541769129643 " " y[1] (numeric) = -0.16742541769129615 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.65778744938271000000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1910000000000001 " " y[1] (analytic) = -0.168306604100198 " " y[1] (numeric) = -0.1683066041001977 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.64910793394091560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1920000000000001 " " y[1] (analytic) = -0.16918779050909954 " " y[1] (numeric) = -0.16918779050909927 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.64051883011830680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1930000000000001 " " y[1] (analytic) = -0.1700689769180011 " " y[1] (numeric) = -0.17006897691800082 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.6320187325529270000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1940000000000001 " " y[1] (analytic) = -0.17095016332690266 " " y[1] (numeric) = -0.17095016332690238 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.62360626485935520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1950000000000001 " " y[1] (analytic) = -0.17183134973580422 " " y[1] (numeric) = -0.17183134973580394 " " absolute error = 2.77555756156289140000000000000000E-16 " " relative error = 1.61528007888571750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1960000000000001 " " y[1] (analytic) = -0.1727125361447058 " " y[1] (numeric) = -0.1727125361447055 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.76774273939278750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1970000000000001 " " y[1] (analytic) = -0.17359372255360736 " " y[1] (numeric) = -0.17359372255360705 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.75876942599485440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1980000000000001 " " y[1] (analytic) = -0.17447490896250892 " " y[1] (numeric) = -0.1744749089625086 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.74988675212619350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.1990000000000001 " " y[1] (analytic) = -0.17535609537141048 " " y[1] (numeric) = -0.17535609537141017 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.74109335136174050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2000000000000001 " " y[1] (analytic) = -0.17623728178031203 " " y[1] (numeric) = -0.17623728178031173 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.73238788460493180000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2010000000000001 " " y[1] (analytic) = -0.1771184681892136 " " y[1] (numeric) = -0.17711846818921329 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.72376903940789220000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2020000000000001 " " y[1] (analytic) = -0.17799965459811515 " " y[1] (numeric) = -0.17799965459811484 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.71523552931181350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2030000000000001 " " y[1] (analytic) = -0.1788808410070167 " " y[1] (numeric) = -0.1788808410070164 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.70678609320682930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2040000000000001 " " y[1] (analytic) = -0.17976202741591826 " " y[1] (numeric) = -0.17976202741591796 " " absolute error = 3.05311331771918050000000000000000E-16 " " relative error = 1.69841949471071730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2050000000000001 " " y[1] (analytic) = -0.18064321382481985 " " y[1] (numeric) = -0.18064321382481952 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.8437831144354040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2060000000000001 " " y[1] (analytic) = -0.1815244002337214 " " y[1] (numeric) = -0.18152440023372107 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.83483271096727070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2070000000000001 " " y[1] (analytic) = -0.18240558664262296 " " y[1] (numeric) = -0.18240558664262263 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.82596878482733230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2080000000000001 " " y[1] (analytic) = -0.18328677305152452 " " y[1] (numeric) = -0.1832867730515242 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.8171900887464318000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2090000000000001 " " y[1] (analytic) = -0.18416795946042608 " " y[1] (numeric) = -0.18416795946042575 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.80849539932659260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2100000000000001 " " y[1] (analytic) = -0.18504914586932764 " " y[1] (numeric) = -0.1850491458693273 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.79988351647265650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2110000000000001 " " y[1] (analytic) = -0.1859303322782292 " " y[1] (numeric) = -0.18593033227822886 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.79135326284008470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2120000000000001 " " y[1] (analytic) = -0.18681151868713075 " " y[1] (numeric) = -0.18681151868713042 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.7829034832983860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2130000000000001 " " y[1] (analytic) = -0.1876927050960323 " " y[1] (numeric) = -0.18769270509603198 " " absolute error = 3.33066907387546960000000000000000E-16 " " relative error = 1.77453304440966130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2140000000000001 " " y[1] (analytic) = -0.1885738915049339 " " y[1] (numeric) = -0.18857389150493353 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.91342757008191260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2150000000000001 " " y[1] (analytic) = -0.18945507791383545 " " y[1] (numeric) = -0.1894550779138351 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.90452790696525260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2160000000000001 " " y[1] (analytic) = -0.190336264322737 " " y[1] (numeric) = -0.19033626432273665 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.89571064813670980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2170000000000001 " " y[1] (analytic) = -0.19121745073163857 " " y[1] (numeric) = -0.1912174507316382 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.88697465436649450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2180000000000001 " " y[1] (analytic) = -0.19209863714054012 " " y[1] (numeric) = -0.19209863714053976 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.8783188073281160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2190000000000001 " " y[1] (analytic) = -0.19297982354944168 " " y[1] (numeric) = -0.19297982354944132 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.86974200912113860000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2200000000000001 " " y[1] (analytic) = -0.19386100995834324 " " y[1] (numeric) = -0.19386100995834288 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.86124318180695160000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2210000000000001 " " y[1] (analytic) = -0.1947421963672448 " " y[1] (numeric) = -0.19474219636724444 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.85282126695714640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22200000000000011 " " y[1] (analytic) = -0.19562338277614635 " " y[1] (numeric) = -0.195623382776146 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.8444752252140960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22300000000000011 " " y[1] (analytic) = -0.1965045691850479 " " y[1] (numeric) = -0.19650456918504755 " " absolute error = 3.6082248300317590000000000000000E-16 " " relative error = 1.83620403586336020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22400000000000012 " " y[1] (analytic) = -0.1973857555939495 " " y[1] (numeric) = -0.1973857555939491 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.96862259614196800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22500000000000012 " " y[1] (analytic) = -0.19826694200285105 " " y[1] (numeric) = -0.19826694200285067 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.9598731623813370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22600000000000012 " " y[1] (analytic) = -0.1991481284117526 " " y[1] (numeric) = -0.19914812841175222 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.95120115723805640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22700000000000012 " " y[1] (analytic) = -0.20002931482065417 " " y[1] (numeric) = -0.20002931482065378 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.94260555742643530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22800000000000012 " " y[1] (analytic) = -0.20091050122955573 " " y[1] (numeric) = -0.20091050122955534 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.93408535761316100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.22900000000000012 " " y[1] (analytic) = -0.20179168763845728 " " y[1] (numeric) = -0.2017916876384569 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.9256395700253310000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23000000000000012 " " y[1] (analytic) = -0.20267287404735884 " " y[1] (numeric) = -0.20267287404735845 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.91726722406869910000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23100000000000012 " " y[1] (analytic) = -0.2035540604562604 " " y[1] (numeric) = -0.20355406045626 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.90896736595584760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23200000000000012 " " y[1] (analytic) = -0.20443524686516196 " " y[1] (numeric) = -0.20443524686516157 " " absolute error = 3.8857805861880480000000000000000E-16 " " relative error = 1.9007390583439690000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23300000000000012 " " y[1] (analytic) = -0.20531643327406354 " " y[1] (numeric) = -0.20531643327406313 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.02776576426640430000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23400000000000012 " " y[1] (analytic) = -0.2061976196829651 " " y[1] (numeric) = -0.20619761968296468 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.01910009860714640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23500000000000013 " " y[1] (analytic) = -0.20707880609186666 " " y[1] (numeric) = -0.20707880609186624 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.01050818329392450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23600000000000013 " " y[1] (analytic) = -0.20795999250076821 " " y[1] (numeric) = -0.2079599925007678 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 2.001989080822340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23700000000000013 " " y[1] (analytic) = -0.20884117890966977 " " y[1] (numeric) = -0.20884117890966936 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 1.99354186951085340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23800000000000013 " " y[1] (analytic) = -0.20972236531857133 " " y[1] (numeric) = -0.2097223653185709 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 1.9851656431683710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.23900000000000013 " " y[1] (analytic) = -0.2106035517274729 " " y[1] (numeric) = -0.21060355172747247 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 1.97685951077017670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24000000000000013 " " y[1] (analytic) = -0.21148473813637444 " " y[1] (numeric) = -0.21148473813637403 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 1.96862259614196800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24100000000000013 " " y[1] (analytic) = -0.212365924545276 " " y[1] (numeric) = -0.2123659245452756 " " absolute error = 4.1633363423443370000000000000000E-16 " " relative error = 1.96045403765175200000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24200000000000013 " " y[1] (analytic) = -0.2132471109541776 " " y[1] (numeric) = -0.21324711095417714 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.08250985377001540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24300000000000013 " " y[1] (analytic) = -0.21412829736307915 " " y[1] (numeric) = -0.2141282973630787 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.07393985437178500000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24400000000000013 " " y[1] (analytic) = -0.2150094837719807 " " y[1] (numeric) = -0.21500948377198026 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.06544010087026100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24500000000000013 " " y[1] (analytic) = -0.21589067018088226 " " y[1] (numeric) = -0.21589067018088182 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.0570097331116072000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24600000000000014 " " y[1] (analytic) = -0.21677185658978382 " " y[1] (numeric) = -0.21677185658978337 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.04864790492822660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24700000000000014 " " y[1] (analytic) = -0.21765304299868538 " " y[1] (numeric) = -0.21765304299868493 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.04035378385564300000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24800000000000014 " " y[1] (analytic) = -0.21853422940758693 " " y[1] (numeric) = -0.2185342294075865 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.0321265508562250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.24900000000000014 " " y[1] (analytic) = -0.2194154158164885 " " y[1] (numeric) = -0.21941541581648805 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.02396540004957350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2500000000000001 " " y[1] (analytic) = -0.22029660222539005 " " y[1] (numeric) = -0.2202966022253896 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.01586953844937520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2510000000000001 " " y[1] (analytic) = -0.2211777886342916 " " y[1] (numeric) = -0.22117778863429116 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 2.0078381857065490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2520000000000001 " " y[1] (analytic) = -0.22205897504319316 " " y[1] (numeric) = -0.22205897504319272 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.9998705738585070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2530000000000001 " " y[1] (analytic) = -0.22294016145209472 " " y[1] (numeric) = -0.22294016145209428 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.9919659470843630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2540000000000001 " " y[1] (analytic) = -0.22382134786099628 " " y[1] (numeric) = -0.22382134786099583 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.98412356146592060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2550000000000001 " " y[1] (analytic) = -0.22470253426989784 " " y[1] (numeric) = -0.2247025342698974 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.97634268475428950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2560000000000001 " " y[1] (analytic) = -0.2255837206787994 " " y[1] (numeric) = -0.22558372067879895 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.9686225961419682000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2570000000000001 " " y[1] (analytic) = -0.22646490708770095 " " y[1] (numeric) = -0.2264649070877005 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.96096258604024830000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2580000000000001 " " y[1] (analytic) = -0.2273460934966025 " " y[1] (numeric) = -0.22734609349660206 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.95336195586179800000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2590000000000001 " " y[1] (analytic) = -0.22822727990550407 " " y[1] (numeric) = -0.22822727990550362 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 1.94582001780827740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2600000000000001 " " y[1] (analytic) = -0.22910846631440565 " " y[1] (numeric) = -0.22910846631440518 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.05948210057928960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2610000000000001 " " y[1] (analytic) = -0.2299896527233072 " " y[1] (numeric) = -0.22998965272330674 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.05159136456174450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2620000000000001 " " y[1] (analytic) = -0.23087083913220877 " " y[1] (numeric) = -0.2308708391322083 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.04376086317028720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2630000000000001 " " y[1] (analytic) = -0.23175202554111032 " " y[1] (numeric) = -0.23175202554110985 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.03598990931792900000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2640000000000001 " " y[1] (analytic) = -0.23263321195001188 " " y[1] (numeric) = -0.2326332119500114 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.0282778263280882000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2650000000000001 " " y[1] (analytic) = -0.23351439835891344 " " y[1] (numeric) = -0.23351439835891297 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.0206239477381710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2660000000000001 " " y[1] (analytic) = -0.234395584767815 " " y[1] (numeric) = -0.23439558476781452 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.01302761710757620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2670000000000001 " " y[1] (analytic) = -0.23527677117671655 " " y[1] (numeric) = -0.23527677117671608 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 2.005488187830020000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.2680000000000001 " " y[1] (analytic) = -0.2361579575856181 " " y[1] (numeric) = -0.23615795758561764 " " absolute error = 4.7184478546569153000000000000000E-16 " " relative error = 1.99800502295005730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.26900000000000013 " " y[1] (analytic) = -0.2370391439945197 " " y[1] (numeric) = -0.2370391439945192 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.10767028880627040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27000000000000013 " " y[1] (analytic) = -0.23792033040342125 " " y[1] (numeric) = -0.23792033040342075 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.09986410255143250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27100000000000013 " " y[1] (analytic) = -0.2388015168123228 " " y[1] (numeric) = -0.2388015168123223 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.09211552652725760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27200000000000013 " " y[1] (analytic) = -0.23968270322122437 " " y[1] (numeric) = -0.23968270322122387 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.08442392532678960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27300000000000013 " " y[1] (analytic) = -0.24056388963012593 " " y[1] (numeric) = -0.24056388963012543 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.07678867285306520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27400000000000013 " " y[1] (analytic) = -0.24144507603902748 " " y[1] (numeric) = -0.24144507603902698 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.06920915214922170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27500000000000013 " " y[1] (analytic) = -0.24232626244792904 " " y[1] (numeric) = -0.24232626244792854 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.06168475523231530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27600000000000013 " " y[1] (analytic) = -0.2432074488568306 " " y[1] (numeric) = -0.2432074488568301 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.0542148829307490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27700000000000014 " " y[1] (analytic) = -0.24408863526573216 " " y[1] (numeric) = -0.24408863526573166 " " absolute error = 4.9960036108132044000000000000000E-16 " " relative error = 2.0467989447252230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27800000000000014 " " y[1] (analytic) = -0.24496982167463374 " " y[1] (numeric) = -0.24496982167463321 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.15273837851495760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.27900000000000014 " " y[1] (analytic) = -0.2458510080835353 " " y[1] (numeric) = -0.24585100808353477 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.14502247034823730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28000000000000014 " " y[1] (analytic) = -0.24673219449243686 " " y[1] (numeric) = -0.24673219449243633 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.13736167581127960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28100000000000014 " " y[1] (analytic) = -0.24761338090133841 " " y[1] (numeric) = -0.2476133809013379 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.12975540650234250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28200000000000014 " " y[1] (analytic) = -0.24849456731023997 " " y[1] (numeric) = -0.24849456731023944 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.12220308236580920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28300000000000014 " " y[1] (analytic) = -0.24937575371914153 " " y[1] (numeric) = -0.249375753719141 " " absolute error = 5.2735593669694940000000000000000E-16 " " relative error = 2.11470413154472870000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28400000000000014 " " y[1] (analytic) = -0.2502569401280431 " " y[1] (numeric) = -0.25025694012804256 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.21816630551207620000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28500000000000014 " " y[1] (analytic) = -0.2511381265369447 " " y[1] (numeric) = -0.2511381265369441 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.2103832658436130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28600000000000014 " " y[1] (analytic) = -0.25201931294584623 " " y[1] (numeric) = -0.2520193129458457 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.20265465302597770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28700000000000014 " " y[1] (analytic) = -0.2529004993547478 " " y[1] (numeric) = -0.25290049935474723 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.19497989813738580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28800000000000014 " " y[1] (analytic) = -0.25378168576364935 " " y[1] (numeric) = -0.2537816857636488 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.1873584401577420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.28900000000000015 " " y[1] (analytic) = -0.2546628721725509 " " y[1] (numeric) = -0.25466287217255035 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.17978972583193650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29000000000000015 " " y[1] (analytic) = -0.25554405858145246 " " y[1] (numeric) = -0.2555440585814519 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.17227320953596450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29100000000000015 " " y[1] (analytic) = -0.256425244990354 " " y[1] (numeric) = -0.25642524499035346 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.16480835314580650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29200000000000015 " " y[1] (analytic) = -0.2573064313992556 " " y[1] (numeric) = -0.257306431399255 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.1573946259090060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29300000000000015 " " y[1] (analytic) = -0.25818761780815713 " " y[1] (numeric) = -0.2581876178081566 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.15003150431887280000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29400000000000015 " " y[1] (analytic) = -0.2590688042170587 " " y[1] (numeric) = -0.25906880421705814 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.14271847199125760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29500000000000015 " " y[1] (analytic) = -0.25994999062596025 " " y[1] (numeric) = -0.2599499906259597 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.13545501954382960000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29600000000000015 " " y[1] (analytic) = -0.2608311770348618 " " y[1] (numeric) = -0.26083117703486125 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.12824064447780320000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29700000000000015 " " y[1] (analytic) = -0.26171236344376336 " " y[1] (numeric) = -0.2617123634437628 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.1210748510620530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29800000000000015 " " y[1] (analytic) = -0.2625935498526649 " " y[1] (numeric) = -0.26259354985266437 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.1139571502195628000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.29900000000000015 " " y[1] (analytic) = -0.2634747362615665 " " y[1] (numeric) = -0.2634747362615659 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.1068870594161532000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30000000000000016 " " y[1] (analytic) = -0.26435592267046804 " " y[1] (numeric) = -0.2643559226704675 " " absolute error = 5.5511151231257830000000000000000E-16 " " relative error = 2.09986410255143250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30100000000000016 " " y[1] (analytic) = -0.26523710907936965 " " y[1] (numeric) = -0.26523710907936904 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.3021765908371183000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30200000000000016 " " y[1] (analytic) = -0.2661182954882712 " " y[1] (numeric) = -0.2661182954882706 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.2945534895429560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30300000000000016 " " y[1] (analytic) = -0.26699948189717276 " " y[1] (numeric) = -0.26699948189717215 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.2869807057490849000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30400000000000016 " " y[1] (analytic) = -0.2678806683060743 " " y[1] (numeric) = -0.2678806683060737 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.27945774290122550000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30500000000000016 " " y[1] (analytic) = -0.2687618547149759 " " y[1] (numeric) = -0.26876185471497527 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.27198411095728750000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30600000000000016 " " y[1] (analytic) = -0.26964304112387744 " " y[1] (numeric) = -0.2696430411238768 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.26455932628095660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30700000000000016 " " y[1] (analytic) = -0.270524227532779 " " y[1] (numeric) = -0.2705242275327784 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.25718291153737040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30800000000000016 " " y[1] (analytic) = -0.27140541394168055 " " y[1] (numeric) = -0.27140541394167994 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.24985439559082040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.30900000000000016 " " y[1] (analytic) = -0.2722866003505821 " " y[1] (numeric) = -0.2722866003505815 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.24257331340444230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31000000000000016 " " y[1] (analytic) = -0.27316778675948367 " " y[1] (numeric) = -0.27316778675948306 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.23533920594184730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31100000000000017 " " y[1] (analytic) = -0.2740489731683852 " " y[1] (numeric) = -0.2740489731683846 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.22815162007065170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31200000000000017 " " y[1] (analytic) = -0.2749301595772868 " " y[1] (numeric) = -0.27493015957728617 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.2210101084678610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31300000000000017 " " y[1] (analytic) = -0.27581134598618834 " " y[1] (numeric) = -0.27581134598618773 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.21391422952706920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31400000000000017 " " y[1] (analytic) = -0.2766925323950899 " " y[1] (numeric) = -0.2766925323950893 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.2068635472674290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31500000000000017 " " y[1] (analytic) = -0.27757371880399145 " " y[1] (numeric) = -0.27757371880399084 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.19985763124435770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31600000000000017 " " y[1] (analytic) = -0.278454905212893 " " y[1] (numeric) = -0.2784549052128924 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.1928960564619390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31700000000000017 " " y[1] (analytic) = -0.27933609162179457 " " y[1] (numeric) = -0.27933609162179396 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.18597840328698030000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.31800000000000017 " " y[1] (analytic) = -0.2802172780306961 " " y[1] (numeric) = -0.2802172780306955 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.1791042573646940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3190000000000002 " " y[1] (analytic) = -0.2810984644395977 " " y[1] (numeric) = -0.2810984644395971 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 2.17227320953596480000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3200000000000002 " " y[1] (analytic) = -0.2819796508484993 " " y[1] (numeric) = -0.28197965084849863 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3623471153703610000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3210000000000002 " " y[1] (analytic) = -0.28286083725740085 " " y[1] (numeric) = -0.2828608372574002 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3549877785623538000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3220000000000002 " " y[1] (analytic) = -0.2837420236663024 " " y[1] (numeric) = -0.28374202366630175 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3476741519208560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3230000000000002 " " y[1] (analytic) = -0.28462321007520397 " " y[1] (numeric) = -0.2846232100752033 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3404058108932370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3240000000000002 " " y[1] (analytic) = -0.2855043964841055 " " y[1] (numeric) = -0.28550439648410486 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3331823361682580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3250000000000002 " " y[1] (analytic) = -0.2863855828930071 " " y[1] (numeric) = -0.2863855828930064 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.32600331359543250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3260000000000002 " " y[1] (analytic) = -0.28726676930190864 " " y[1] (numeric) = -0.287266769301908 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3188683341058760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3270000000000002 " " y[1] (analytic) = -0.2881479557108102 " " y[1] (numeric) = -0.28814795571080953 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.31177699363460440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3280000000000002 " " y[1] (analytic) = -0.28902914211971176 " " y[1] (numeric) = -0.2890291421197111 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.3047288930442553000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3290000000000002 " " y[1] (analytic) = -0.2899103285286133 " " y[1] (numeric) = -0.28991032852861265 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.29772363805019920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3300000000000002 " " y[1] (analytic) = -0.29079151493751487 " " y[1] (numeric) = -0.2907915149375142 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.2907608391470170000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3310000000000002 " " y[1] (analytic) = -0.29167270134641643 " " y[1] (numeric) = -0.29167270134641576 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.2838401115363008000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3320000000000002 " " y[1] (analytic) = -0.292553887755318 " " y[1] (numeric) = -0.2925538877553173 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.276961075055770300000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3330000000000002 " " y[1] (analytic) = -0.29343507416421954 " " y[1] (numeric) = -0.2934350741642189 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.27012335410965660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3340000000000002 " " y[1] (analytic) = -0.2943162605731211 " " y[1] (numeric) = -0.29431626057312044 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.26332657760034640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3350000000000002 " " y[1] (analytic) = -0.29519744698202266 " " y[1] (numeric) = -0.295197446982022 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.2565703788612410000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3360000000000002 " " y[1] (analytic) = -0.2960786333909242 " " y[1] (numeric) = -0.29607863339092355 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.24985439559082070000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3370000000000002 " " y[1] (analytic) = -0.2969598197998258 " " y[1] (numeric) = -0.2969598197998251 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.24317826978788050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3380000000000002 " " y[1] (analytic) = -0.2978410062087274 " " y[1] (numeric) = -0.29784100620872667 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.42292011832857560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3390000000000002 " " y[1] (analytic) = -0.29872219261762895 " " y[1] (numeric) = -0.2987221926176282 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.41577286134235570000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3400000000000002 " " y[1] (analytic) = -0.2996033790265305 " " y[1] (numeric) = -0.2996033790265298 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.40866764704428970000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3410000000000002 " " y[1] (analytic) = -0.30048456543543206 " " y[1] (numeric) = -0.30048456543543134 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.40160410555735640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3420000000000002 " " y[1] (analytic) = -0.3013657518443336 " " y[1] (numeric) = -0.3013657518443329 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.39458187133058050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3430000000000002 " " y[1] (analytic) = -0.3022469382532352 " " y[1] (numeric) = -0.30224693825323445 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.38760058307597250000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3440000000000002 " " y[1] (analytic) = -0.30312812466213673 " " y[1] (numeric) = -0.303128124662136 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.38065988370656540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3450000000000002 " " y[1] (analytic) = -0.3040093110710383 " " y[1] (numeric) = -0.30400931107103757 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3737594202755322000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3460000000000002 " " y[1] (analytic) = -0.30489049747993985 " " y[1] (numeric) = -0.3048904974799391 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3668988439163540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3470000000000002 " " y[1] (analytic) = -0.3057716838888414 " " y[1] (numeric) = -0.3057716838888407 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.36007780978403050000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3480000000000002 " " y[1] (analytic) = -0.30665287029774296 " " y[1] (numeric) = -0.30665287029774224 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3532959769972950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3490000000000002 " " y[1] (analytic) = -0.3075340567066445 " " y[1] (numeric) = -0.3075340567066438 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.34655300858182980000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3500000000000002 " " y[1] (analytic) = -0.3084152431155461 " " y[1] (numeric) = -0.30841524311554536 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3398485714144530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3510000000000002 " " y[1] (analytic) = -0.30929642952444764 " " y[1] (numeric) = -0.3092964295244469 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3331823361682580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3520000000000002 " " y[1] (analytic) = -0.3101776159333492 " " y[1] (numeric) = -0.31017761593334847 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3265539772586890000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3530000000000002 " " y[1] (analytic) = -0.31105880234225075 " " y[1] (numeric) = -0.31105880234225003 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.3199631727905343000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3540000000000002 " " y[1] (analytic) = -0.3119399887511523 " " y[1] (numeric) = -0.3119399887511516 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.31340960450581530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3550000000000002 " " y[1] (analytic) = -0.31282117516005387 " " y[1] (numeric) = -0.31282117516005314 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.30689295773255950000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3560000000000002 " " y[1] (analytic) = -0.3137023615689554 " " y[1] (numeric) = -0.3137023615689547 " " absolute error = 7.2164496600635180000000000000000E-16 " " relative error = 2.30041292133443460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3570000000000002 " " y[1] (analytic) = -0.31458354797785704 " " y[1] (numeric) = -0.31458354797785626 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.47042835594286140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3580000000000002 " " y[1] (analytic) = -0.3154647343867586 " " y[1] (numeric) = -0.3154647343867578 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.46352771807709920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3590000000000002 " " y[1] (analytic) = -0.31634592079566015 " " y[1] (numeric) = -0.3163459207956594 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.45666552387632740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3600000000000002 " " y[1] (analytic) = -0.3172271072045617 " " y[1] (numeric) = -0.31722710720456093 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.4498414529766710000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3610000000000002 " " y[1] (analytic) = -0.31810829361346327 " " y[1] (numeric) = -0.3181082936134625 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.4430551885639930000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3620000000000002 " " y[1] (analytic) = -0.3189894800223648 " " y[1] (numeric) = -0.31898948002236405 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.4363064173248660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3630000000000002 " " y[1] (analytic) = -0.3198706664312664 " " y[1] (numeric) = -0.3198706664312656 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.42959482939835130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3640000000000002 " " y[1] (analytic) = -0.32075185284016794 " " y[1] (numeric) = -0.32075185284016716 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.42292011832857560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3650000000000002 " " y[1] (analytic) = -0.3216330392490695 " " y[1] (numeric) = -0.3216330392490687 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.41628198101808630000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3660000000000002 " " y[1] (analytic) = -0.32251422565797105 " " y[1] (numeric) = -0.3225142256579703 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.40968011768197130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3670000000000002 " " y[1] (analytic) = -0.3233954120668726 " " y[1] (numeric) = -0.32339541206687183 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.4031142318027290000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3680000000000002 " " y[1] (analytic) = -0.32427659847577417 " " y[1] (numeric) = -0.3242765984757734 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.3965840300858740000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3690000000000002 " " y[1] (analytic) = -0.3251577848846757 " " y[1] (numeric) = -0.32515778488467495 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.39008922241626450000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3700000000000002 " " y[1] (analytic) = -0.3260389712935773 " " y[1] (numeric) = -0.3260389712935765 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.3836295218151393000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3710000000000002 " " y[1] (analytic) = -0.32692015770247884 " " y[1] (numeric) = -0.32692015770247806 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.37720464439784760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3720000000000002 " " y[1] (analytic) = -0.3278013441113804 " " y[1] (numeric) = -0.3278013441113796 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.37081430933226230000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3730000000000002 " " y[1] (analytic) = -0.32868253052028196 " " y[1] (numeric) = -0.3286825305202812 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.36445823879785940000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3740000000000002 " " y[1] (analytic) = -0.3295637169291835 " " y[1] (numeric) = -0.32956371692918274 " " absolute error = 7.7715611723760960000000000000000E-16 " " relative error = 2.35813615794545880000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3750000000000002 " " y[1] (analytic) = -0.3304449033380851 " " y[1] (numeric) = -0.3304449033380843 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.51983692306171850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3760000000000002 " " y[1] (analytic) = -0.3313260897469867 " " y[1] (numeric) = -0.33132608974698585 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.5131352291174053000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3770000000000002 " " y[1] (analytic) = -0.33220727615588824 " " y[1] (numeric) = -0.3322072761558874 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.50646908792611260000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3780000000000002 " " y[1] (analytic) = -0.3330884625647898 " " y[1] (numeric) = -0.33308846256478897 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.49983821732313370000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3790000000000002 " " y[1] (analytic) = -0.33396964897369136 " " y[1] (numeric) = -0.3339696489736905 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.4932423381217530000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3800000000000002 " " y[1] (analytic) = -0.3348508353825929 " " y[1] (numeric) = -0.3348508353825921 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.4866811740740640000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.3810000000000002 " " y[1] (analytic) = -0.3357320217914945 " " y[1] (numeric) = -0.33573202179149364 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.48015445183240040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38200000000000023 " " y[1] (analytic) = -0.33661320820039603 " " y[1] (numeric) = -0.3366132082003952 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.4736619009113730000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38300000000000023 " " y[1] (analytic) = -0.3374943946092976 " " y[1] (numeric) = -0.33749439460929676 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.46720325365050760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38400000000000023 " " y[1] (analytic) = -0.33837558101819915 " " y[1] (numeric) = -0.3383755810181983 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.460778245177459900000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38500000000000023 " " y[1] (analytic) = -0.3392567674271007 " " y[1] (numeric) = -0.33925676742709987 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.4543866133718040000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38600000000000023 " " y[1] (analytic) = -0.34013795383600226 " " y[1] (numeric) = -0.3401379538360014 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.448028098829390000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38700000000000023 " " y[1] (analytic) = -0.3410191402449038 " " y[1] (numeric) = -0.341019140244903 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.4417024448272470000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38800000000000023 " " y[1] (analytic) = -0.3419003266538054 " " y[1] (numeric) = -0.34190032665380454 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.4354093972890323000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.38900000000000023 " " y[1] (analytic) = -0.34278151306270693 " " y[1] (numeric) = -0.3427815130627061 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.42914870475101440000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39000000000000024 " " y[1] (analytic) = -0.3436626994716085 " " y[1] (numeric) = -0.34366269947160766 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.42292011832857560000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39100000000000024 " " y[1] (analytic) = -0.34454388588051005 " " y[1] (numeric) = -0.3445438858805092 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.41672339168323420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39200000000000024 " " y[1] (analytic) = -0.3454250722894116 " " y[1] (numeric) = -0.3454250722894108 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.41055828099016460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39300000000000024 " " y[1] (analytic) = -0.34630625869831316 " " y[1] (numeric) = -0.34630625869831233 " " absolute error = 8.3266726846886740000000000000000E-16 " " relative error = 2.404424544906220200000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39400000000000024 " " y[1] (analytic) = -0.3471874451072148 " " y[1] (numeric) = -0.3471874451072139 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.55821007417433350000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39500000000000024 " " y[1] (analytic) = -0.34806863151611633 " " y[1] (numeric) = -0.34806863151611545 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5517335929738920000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39600000000000024 " " y[1] (analytic) = -0.3489498179250179 " " y[1] (numeric) = -0.348949817925017 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5452898212744635000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39700000000000024 " " y[1] (analytic) = -0.34983100433391945 " " y[1] (numeric) = -0.34983100433391856 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5388785119009760000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39800000000000024 " " y[1] (analytic) = -0.350712190742821 " " y[1] (numeric) = -0.3507121907428201 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.53249942016253100000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.39900000000000024 " " y[1] (analytic) = -0.35159337715172256 " " y[1] (numeric) = -0.3515933771517217 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.52615230382127130000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40000000000000024 " " y[1] (analytic) = -0.3524745635606241 " " y[1] (numeric) = -0.35247456356062323 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.51983692306171850000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40100000000000025 " " y[1] (analytic) = -0.3533557499695257 " " y[1] (numeric) = -0.3533557499695248 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5135530404605670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40200000000000025 " " y[1] (analytic) = -0.35423693637842724 " " y[1] (numeric) = -0.35423693637842635 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5073004209569340000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40300000000000025 " " y[1] (analytic) = -0.3551181227873288 " " y[1] (numeric) = -0.3551181227873279 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.5010788318230460000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40400000000000025 " " y[1] (analytic) = -0.35599930919623035 " " y[1] (numeric) = -0.35599930919622946 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.4948880426353650000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40500000000000025 " " y[1] (analytic) = -0.3568804956051319 " " y[1] (numeric) = -0.356880495605131 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.4887278252461420000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40600000000000025 " " y[1] (analytic) = -0.35776168201403347 " " y[1] (numeric) = -0.3577616820140326 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.48259795375538770000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40700000000000025 " " y[1] (analytic) = -0.358642868422935 " " y[1] (numeric) = -0.35864286842293414 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.47649820448326150000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40800000000000025 " " y[1] (analytic) = -0.3595240548318366 " " y[1] (numeric) = -0.3595240548318357 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.47042835594286140000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.40900000000000025 " " y[1] (analytic) = -0.36040524124073814 " " y[1] (numeric) = -0.36040524124073725 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.46438818881341670000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41000000000000025 " " y[1] (analytic) = -0.3612864276496397 " " y[1] (numeric) = -0.3612864276496388 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.4583774859138720000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41100000000000025 " " y[1] (analytic) = -0.36216761405854125 " " y[1] (numeric) = -0.36216761405854037 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 2.4523960321768554000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41200000000000025 " " y[1] (analytic) = -0.36304880046744287 " " y[1] (numeric) = -0.3630488004674419 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.59934634053696660000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41300000000000026 " " y[1] (analytic) = -0.3639299868763444 " " y[1] (numeric) = -0.3639299868763435 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.5930525237317925000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41400000000000026 " " y[1] (analytic) = -0.364811173285246 " " y[1] (numeric) = -0.36481117328524504 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.5867891118387210000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41500000000000026 " " y[1] (analytic) = -0.36569235969414754 " " y[1] (numeric) = -0.3656923596941466 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.5805558850632060000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = 0.41600000000000026 " " y[1] (analytic) = -0.3665735461030491 " " y[1] (numeric) = -0.36657354610304815 " " absolute error = 9.436895709313831000000000000000E-16 " " relative error = 2.5743526257241110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = ln(0.1) + exp(0.1) + sqrt(0.1);" Iterations = 317 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 0 Hours 43 Minutes 22 Seconds "Optimized Time Remaining "= 0 Years 0 Days 0 Hours 43 Minutes 14 Seconds "Expected Total Time "= 0 Years 0 Days 0 Hours 46 Minutes 14 Seconds "Time to Timeout " Unknown Percent Done = 6.489795918367353 "%" (%o57) true (%o57) diffeq.max