(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr # 0.0 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 array_tmp4 : array_const_0D3 array_x , 1 1 1 array_tmp5 : array_const_0D1 + array_tmp4 , array_tmp6 : sin(array_tmp5 ), 1 1 1 1 1 array_tmp6_g : cos(array_tmp5 ), array_tmp7 : array_tmp6 + array_tmp3 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_tmp2 , array_tmp4 : array_const_0D3 array_x , 2 2 2 1 2 array_tmp6_g array_tmp5 1 2 array_tmp5 : array_tmp4 , array_tmp6 : -------------------------, 2 2 2 1 - array_tmp6 array_tmp5 1 2 array_tmp6_g : -------------------------, 2 1 array_tmp7 : array_tmp6 + array_tmp3 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp6_g array_tmp5 2 2 array_tmp6 : -------------------------, 3 2 - array_tmp6 array_tmp5 2 2 array_tmp6_g : -------------------------, array_tmp7 : + (array_tmp6 ), 3 2 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp6_g array_tmp5 3 2 array_tmp6 : -------------------------, 4 3 - array_tmp6 array_tmp5 3 2 array_tmp6_g : -------------------------, array_tmp7 : + (array_tmp6 ), 4 3 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp6_g array_tmp5 4 2 array_tmp6 : -------------------------, 5 4 - array_tmp6 array_tmp5 4 2 array_tmp6_g : -------------------------, array_tmp7 : + (array_tmp6 ), 5 4 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp6 : kkk array_tmp6_g array_tmp5 kkk - 1 2 -------------------------------, array_tmp6_g : kkk - 1 kkk - array_tmp6 array_tmp5 kkk - 1 2 -------------------------------, array_tmp7 : array_tmp6 , order_d : 1, kkk - 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp7 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , 1 1 1 array_tmp3 : array_tmp2 + array_const_0D0 , 1 1 1 array_tmp4 : array_const_0D3 array_x , 1 1 1 array_tmp5 : array_const_0D1 + array_tmp4 , array_tmp6 : sin(array_tmp5 ), 1 1 1 1 1 array_tmp6_g : cos(array_tmp5 ), array_tmp7 : array_tmp6 + array_tmp3 , 1 1 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(0, 1), 1 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 2 1, 2 glob_h array_y_higher : temporary, 0)), kkk : 2, 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3 : array_tmp2 , array_tmp4 : array_const_0D3 array_x , 2 2 2 1 2 array_tmp6_g array_tmp5 1 2 array_tmp5 : array_tmp4 , array_tmp6 : -------------------------, 2 2 2 1 - array_tmp6 array_tmp5 1 2 array_tmp6_g : -------------------------, 2 1 array_tmp7 : array_tmp6 + array_tmp3 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(1, 2), 2 temporary array_y : temporary, array_y_higher : temporary, temporary : ---------, 3 1, 3 glob_h array_y_higher : temporary, 0)), kkk : 3, 2, 2 array_tmp6_g array_tmp5 2 2 array_tmp6 : -------------------------, 3 2 - array_tmp6 array_tmp5 2 2 array_tmp6_g : -------------------------, array_tmp7 : + (array_tmp6 ), 3 2 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 array_tmp6_g array_tmp5 3 2 array_tmp6 : -------------------------, 4 3 - array_tmp6 array_tmp5 3 2 array_tmp6_g : -------------------------, array_tmp7 : + (array_tmp6 ), 4 3 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 array_tmp6_g array_tmp5 4 2 array_tmp6 : -------------------------, 5 4 - array_tmp6 array_tmp5 4 2 array_tmp6_g : -------------------------, array_tmp7 : + (array_tmp6 ), 5 4 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp7 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp6 : kkk array_tmp6_g array_tmp5 kkk - 1 2 -------------------------------, array_tmp6_g : kkk - 1 kkk - array_tmp6 array_tmp5 kkk - 1 2 -------------------------------, array_tmp7 : array_tmp6 , order_d : 1, kkk - 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp7 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : - 2 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d temporary convfp(adj2) then (if adj2 > 1 then temporary : ---------------------- glob_h temporary else temporary : ---------, array_y_higher : temporary), glob_h adj3, term term : term - 1, adj2 : adj2 - 1, adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) omniabs(x) := abs(x) (%o49) omniabs(x) := abs(x) y (%i50) expt(x, y) := x y (%o50) expt(x, y) := x (%i51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o51) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) - cos(0.1 + 0.3 x) (%i52) exact_soln_y(x) := block(------------------ + 0.2 x + 0.05 x x) 0.3 - cos(0.1 + 0.3 x) (%o52) exact_soln_y(x) := block(------------------ + 0.2 x + 0.05 x x) 0.3 (%i53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/add_lin_fullpostode.ode#################"), omniout_str(ALWAYS, "\ diff ( y , x , 1 ) = (0.1 * x + 0.2) + sin(0.3 * x + 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:-5.0,"), 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, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3) "), 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_g, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6_g : 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_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\ = (0.1 * x + 0.2) + sin(0.3 * x + 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, "2012-12-14T19:23:02-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "add_lin_full"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) + sin(0.3 * x + 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, " 151 "), logitem_str(html_log_file, "add_lin_full diffeq.max"), logitem_str(html_log_file, "add_lin_full maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o53) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "######\ ########temp/add_lin_fullpostode.ode#################"), omniout_str(ALWAYS, "\ diff ( y , x , 1 ) = (0.1 * x + 0.2) + sin(0.3 * x + 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:-5.0,"), 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, "glob_display_interval:0.1,"), omniout_str(ALWAYS, "glob_max_minutes:10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_desired_digits_correct:10,"), omniout_str(ALWAYS, "glob_display_interval:0.001,"), omniout_str(ALWAYS, "glob_look_poles:true,"), omniout_str(ALWAYS, "glob_max_iter:10000000,"), omniout_str(ALWAYS, "glob_max_minutes:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3) "), 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_g, 1 + max_terms), array(array_tmp6, 1 + max_terms), array(array_tmp7, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp6 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp7 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_tmp1, 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp6_g : 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_tmp7, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp7 : 0.0, term : 1 + term), term array(array_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 0.0, term : 1 + term), term array(array_const_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_0D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_0D1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D1 : 0.0, term : 1 + term), term array_const_0D1 : 0.1, array(array_const_0D2, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D2 : 0.0, term : 1 + term), term array_const_0D2 : 0.2, array(array_const_0D3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_0D3 : 0.0, term : 1 + term), term array_const_0D3 : 0.3, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), iiif, jjjf x_start : - 5.0, x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 glob_h : 0.05, glob_look_poles : true, glob_max_iter : 1000000, glob_display_interval : 0.1, glob_max_minutes : 10, glob_desired_digits_correct : 10, glob_display_interval : 0.001, glob_look_poles : true, glob_max_iter : 10000000, glob_max_minutes : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 )\ = (0.1 * x + 0.2) + sin(0.3 * x + 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, "2012-12-14T19:23:02-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "add_lin_full"), logitem_str(html_log_file, "diff ( y , x , 1 ) = (0.1 * x + 0.2) + sin(0.3 * x + 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, " 151 "), logitem_str(html_log_file, "add_lin_full diffeq.max"), logitem_str(html_log_file, "add_lin_full maxima results"), logitem_str(html_log_file, "Languages compared"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i54) main() "##############ECHO OF PROBLEM#################" "##############temp/add_lin_fullpostode.ode#################" "diff ( y , x , 1 ) = (0.1 * x + 0.2) + sin(0.3 * x + 0.1) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-5.0," "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," "glob_display_interval:0.1," "glob_max_minutes:10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_desired_digits_correct:10," "glob_display_interval:0.001," "glob_look_poles:true," "glob_max_iter:10000000," "glob_max_minutes:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (0.05 * x * x + 0.2 * x - cos(0.3 * x + 0.1) / 0.3) " "));" "/* 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 = 10. "" estimated_steps = 10000. "" step_error = 1.00000000000000E-14 "" est_needed_step_err = 1.00000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 2.414010176299410700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-116 "" max_value3 = 2.414010176299410700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-116 "" value3 = 2.414010176299410700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-116 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -5. " " y[1] (analytic) = -0.3165571430008035 " " y[1] (numeric) = -0.3165571430008035 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.999 " " y[1] (analytic) = -0.3178425172209396 " " y[1] (numeric) = -0.317842517220939 " " absolute error = 6.1062266354383610000000000000000E-16 " " relative error = 1.92114846334223540000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.998000000000000 " " y[1] (analytic) = -0.31912774036224445 " " y[1] (numeric) = -0.3191277403622438 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 2.08735791510622080000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.996999999999999 " " y[1] (analytic) = -0.3204128123360356 " " y[1] (numeric) = -0.32041281233603436 " " absolute error = 1.2212453270876722000000000000000E-15 " " relative error = 3.8114746978559680000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.995999999999999 " " y[1] (analytic) = -0.3216977330536337 " " y[1] (numeric) = -0.3216977330536317 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 6.212047021146110000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.994999999999998 " " y[1] (analytic) = -0.3229825024263635 " " y[1] (numeric) = -0.32298250242636145 " " absolute error = 2.0539125955565396000000000000000E-15 " " relative error = 6.3592070162525580000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.993999999999998 " " y[1] (analytic) = -0.3242671203655565 " " y[1] (numeric) = -0.3242671203655539 " " absolute error = 2.609024107869118000000000000000E-15 " " relative error = 8.0459101278226520000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.992999999999998 " " y[1] (analytic) = -0.3255515867825466 " " y[1] (numeric) = -0.32555158678254387 " " absolute error = 2.7200464103316335000000000000000E-15 " " relative error = 8.3551932190350490000000000000E-13 "%" Correct digits = 15 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.991999999999997 " " y[1] (analytic) = -0.32683590158867426 " " y[1] (numeric) = -0.32683590158867093 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 1.0190646308088713000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.990999999999997 " " y[1] (analytic) = -0.3281200646952833 " " y[1] (numeric) = -0.3281200646952792 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.2519274598241686000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.989999999999997 " " y[1] (analytic) = -0.3294040760137217 " " y[1] (numeric) = -0.3294040760137176 " " absolute error = 4.107825191113079000000000000000E-15 " " relative error = 1.2470474685146164000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.988999999999996 " " y[1] (analytic) = -0.33068793545534436 " " y[1] (numeric) = -0.3306879354553395 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.4772178796375685000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.987999999999996 " " y[1] (analytic) = -0.33197164293150794 " " y[1] (numeric) = -0.33197164293150305 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 1.4715055976508673000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.986999999999996 " " y[1] (analytic) = -0.33325519835357664 " " y[1] (numeric) = -0.33325519835357115 " " absolute error = 5.495603971894525000000000000000E-15 " " relative error = 1.6490677411920837000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.985999999999995 " " y[1] (analytic) = -0.3345386016329177 " " y[1] (numeric) = -0.3345386016329113 " " absolute error = 6.38378239159465000000000000000E-15 " " relative error = 1.9082349123344045000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.984999999999995 " " y[1] (analytic) = -0.3358218526809019 " " y[1] (numeric) = -0.3358218526808957 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 1.851353295882299000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.983999999999995 " " y[1] (analytic) = -0.33710495140890817 " " y[1] (numeric) = -0.3371049514089013 " " absolute error = 6.8833827526759700000000000000000E-15 " " relative error = 2.0419109016071468000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.982999999999994 " " y[1] (analytic) = -0.33838789772831657 " " y[1] (numeric) = -0.33838789772830963 " " absolute error = 6.938893903907228000000000000000E-15 " " relative error = 2.0505738977338656000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.981999999999994 " " y[1] (analytic) = -0.33967069155051466 " " y[1] (numeric) = -0.33967069155050705 " " absolute error = 7.605027718682322000000000000000E-15 " " relative error = 2.238941394668821000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.980999999999994 " " y[1] (analytic) = -0.340953332786893 " " y[1] (numeric) = -0.3409533327868846 " " absolute error = 8.382183835919932000000000000000E-15 " " relative error = 2.4584548763331993000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.979999999999993 " " y[1] (analytic) = -0.34223582134884656 " " y[1] (numeric) = -0.3422358213488381 " " absolute error = 8.43769498715119000000000000000E-15 " " relative error = 2.465462251699978800000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.978999999999993 " " y[1] (analytic) = -0.3435181571477772 " " y[1] (numeric) = -0.3435181571477681 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 2.6501739755229090000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.977999999999993 " " y[1] (analytic) = -0.344800340095089 " " y[1] (numeric) = -0.34480034009507987 " " absolute error = 9.103828801926284000000000000000E-15 " " relative error = 2.6403189739939440000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.976999999999992 " " y[1] (analytic) = -0.34608237010219334 " " y[1] (numeric) = -0.3460823701021834 " " absolute error = 9.936496070395151000000000000000E-15 " " relative error = 2.8711361597127993000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.975999999999992 " " y[1] (analytic) = -0.3473642470805042 " " y[1] (numeric) = -0.3473642470804935 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 3.068289591107919000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.974999999999992 " " y[1] (analytic) = -0.34864597094144034 " " y[1] (numeric) = -0.3486459709414298 " " absolute error = 1.054711873393898700000000000000E-14 " " relative error = 3.025165816618748000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.973999999999991 " " y[1] (analytic) = -0.3499275415964278 " " y[1] (numeric) = -0.3499275415964166 " " absolute error = 1.121325254871408100000000000000E-14 " " relative error = 3.204449840546232000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.972999999999991 " " y[1] (analytic) = -0.3512089589568943 " " y[1] (numeric) = -0.35120895895688303 " " absolute error = 1.126876369994533900000000000000E-14 " " relative error = 3.2085638513932135000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.971999999999990 " " y[1] (analytic) = -0.3524902229342751 " " y[1] (numeric) = -0.3524902229342631 " " absolute error = 1.204591981718294800000000000000E-14 " " relative error = 3.4173770032279777000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.97099999999999 " " y[1] (analytic) = -0.3537713334400082 " " y[1] (numeric) = -0.35377133343999545 " " absolute error = 1.2767564783189300000000000000E-14 " " relative error = 3.6089879468298963000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96999999999999 " " y[1] (analytic) = -0.35505229038553643 " " y[1] (numeric) = -0.3550522903855237 " " absolute error = 1.271205363195804200000000000000E-14 " " relative error = 3.5803328062338524000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.96899999999999 " " y[1] (analytic) = -0.3563330936823096 " " y[1] (numeric) = -0.35633309368229626 " " absolute error = 1.332267629550187800000000000000E-14 " " relative error = 3.7388265450808145000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.967999999999990 " " y[1] (analytic) = -0.35761374324177975 " " y[1] (numeric) = -0.35761374324176626 " " absolute error = 1.348920974919565200000000000000E-14 " " relative error = 3.77200541201676000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.966999999999989 " " y[1] (analytic) = -0.35889423897540584 " " y[1] (numeric) = -0.3588942389753918 " " absolute error = 1.40443212615082300000000000000E-14 " " relative error = 3.913220034292792000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.965999999999989 " " y[1] (analytic) = -0.3601745807946506 " " y[1] (numeric) = -0.3601745807946357 " " absolute error = 1.487698852997709800000000000000E-14 " " relative error = 4.13049374477068960000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.964999999999988 " " y[1] (analytic) = -0.3614547686109806 " " y[1] (numeric) = -0.36145476861096576 " " absolute error = 1.48214773787458400000000000000E-14 " " relative error = 4.100506803576745000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.963999999999988 " " y[1] (analytic) = -0.3627348023358702 " " y[1] (numeric) = -0.36273480233585453 " " absolute error = 1.565414464721470700000000000000E-14 " " relative error = 4.315589391039443000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.962999999999988 " " y[1] (analytic) = -0.3640146818807951 " " y[1] (numeric) = -0.3640146818807795 " " absolute error = 1.55986334959834500000000000000E-14 " " relative error = 4.285166031048049400000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.961999999999987 " " y[1] (analytic) = -0.36529440715723926 " " y[1] (numeric) = -0.36529440715722306 " " absolute error = 1.620925615952728500000000000000E-14 " " relative error = 4.437312984250013000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.960999999999987 " " y[1] (analytic) = -0.36657397807668934 " " y[1] (numeric) = -0.36657397807667236 " " absolute error = 1.698641227676489500000000000000E-14 " " relative error = 4.633829265756349600000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.959999999999987 " " y[1] (analytic) = -0.3678533945506365 " " y[1] (numeric) = -0.36785339455061955 " " absolute error = 1.693090112553363700000000000000E-14 " " relative error = 4.602621961995523300000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.958999999999986 " " y[1] (analytic) = -0.36913265649057936 " " y[1] (numeric) = -0.3691326564905616 " " absolute error = 1.776356839400250500000000000000E-14 " " relative error = 4.812245159473136000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.957999999999986 " " y[1] (analytic) = -0.3704117638080181 " " y[1] (numeric) = -0.3704117638080005 " " absolute error = 1.75970349403087300000000000000E-14 " " relative error = 4.750668488333744000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.956999999999986 " " y[1] (analytic) = -0.3716907164144614 " " y[1] (numeric) = -0.37169071641444307 " " absolute error = 1.831867990631508300000000000000E-14 " " relative error = 4.928473888997663700000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.955999999999985 " " y[1] (analytic) = -0.3729695142214202 " " y[1] (numeric) = -0.37296951422140107 " " absolute error = 1.91513471747839500000000000000E-14 " " relative error = 5.134829106545797000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.954999999999985 " " y[1] (analytic) = -0.37424815714041015 " " y[1] (numeric) = -0.37424815714039117 " " absolute error = 1.898481372109017700000000000000E-14 " " relative error = 5.0727874964438290000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.953999999999985 " " y[1] (analytic) = -0.37552664508295475 " " y[1] (numeric) = -0.37552664508293504 " " absolute error = 1.97064586870965290000000000000E-14 " " relative error = 5.247685868666743000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.952999999999984 " " y[1] (analytic) = -0.3768049779605791 " " y[1] (numeric) = -0.3768049779605593 " " absolute error = 1.981748098955904400000000000000E-14 " " relative error = 5.259346916492257000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.951999999999984 " " y[1] (analytic) = -0.378083155684816 " " y[1] (numeric) = -0.37808315568479545 " " absolute error = 2.053912595556539600000000000000E-14 " " relative error = 5.432436131242928000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.950999999999984 " " y[1] (analytic) = -0.3793611781672014 " " y[1] (numeric) = -0.37936117816718 " " absolute error = 2.137179322403426300000000000000E-14 " " relative error = 5.633626858522345000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.949999999999983 " " y[1] (analytic) = -0.3806390453192756 " " y[1] (numeric) = -0.38063904531925447 " " absolute error = 2.114974861910923200000000000000E-14 " " relative error = 5.556379167925106000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.948999999999983 " " y[1] (analytic) = -0.3819167570525872 " " y[1] (numeric) = -0.3819167570525652 " " absolute error = 2.1982415887578100000000000000E-14 " " relative error = 5.755813402173207000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.947999999999983 " " y[1] (analytic) = -0.3831943132786858 " " y[1] (numeric) = -0.38319431327866377 " " absolute error = 2.203792703880935700000000000000E-14 " " relative error = 5.75111014833402000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.946999999999982 " " y[1] (analytic) = -0.38447171390912915 " " y[1] (numeric) = -0.38447171390910656 " " absolute error = 2.259303855112193600000000000000E-14 " " relative error = 5.876385110729331000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.945999999999982 " " y[1] (analytic) = -0.38574895885547833 " " y[1] (numeric) = -0.385748958855455 " " absolute error = 2.331468351712828700000000000000E-14 " " relative error = 6.044004262850955000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.944999999999982 " " y[1] (analytic) = -0.38702604802929896 " " y[1] (numeric) = -0.3870260480292756 " " absolute error = 2.337019466835954500000000000000E-14 " " relative error = 6.038403561558304000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.943999999999981 " " y[1] (analytic) = -0.3883029813421637 " " y[1] (numeric) = -0.38830298134213975 " " absolute error = 2.392530618067212300000000000000E-14 " " relative error = 6.16150463176322900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.942999999999981 " " y[1] (analytic) = -0.3895797587056481 " " y[1] (numeric) = -0.389579758705624 " " absolute error = 2.409183963436589700000000000000E-14 " " relative error = 6.184058359297048000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.941999999999980 " " y[1] (analytic) = -0.3908563800313347 " " y[1] (numeric) = -0.3908563800313099 " " absolute error = 2.48134846003722500000000000000E-14 " " relative error = 6.348491637358706000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.94099999999998 " " y[1] (analytic) = -0.3921328452308095 " " y[1] (numeric) = -0.392132845230784 " " absolute error = 2.547961841514734000000000000000E-14 " " relative error = 6.497700645338708000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93999999999998 " " y[1] (analytic) = -0.39340915421566347 " " y[1] (numeric) = -0.393409154215638 " " absolute error = 2.547961841514734000000000000000E-14 " " relative error = 6.47662062311331900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.93899999999998 " " y[1] (analytic) = -0.3946853068974947 " " y[1] (numeric) = -0.3946853068974685 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 6.638520087589308000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.937999999999980 " " y[1] (analytic) = -0.39596130318790335 " " y[1] (numeric) = -0.3959613031878773 " " absolute error = 2.60347299274599200000000000000E-14 " " relative error = 6.575069260014317000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.936999999999979 " " y[1] (analytic) = -0.397237142998498 " " y[1] (numeric) = -0.39723714299847124 " " absolute error = 2.675637489346627000000000000000E-14 " " relative error = 6.7356175939387030000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.935999999999979 " " y[1] (analytic) = -0.3985128262408898 " " y[1] (numeric) = -0.3985128262408622 " " absolute error = 2.75890421619351400000000000000E-14 " " relative error = 6.922999799574415000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.934999999999978 " " y[1] (analytic) = -0.39978835282669467 " " y[1] (numeric) = -0.39978835282666725 " " absolute error = 2.742250870824136700000000000000E-14 " " relative error = 6.859256532700647000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.933999999999978 " " y[1] (analytic) = -0.40106372266753687 " " y[1] (numeric) = -0.40106372266750845 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 7.086581962927692000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.932999999999978 " " y[1] (analytic) = -0.4023389356750414 " " y[1] (numeric) = -0.40233893567501305 " " absolute error = 2.83661982791727500000000000000E-14 " " relative error = 7.050323934366467000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.931999999999977 " " y[1] (analytic) = -0.40361399176084234 " " y[1] (numeric) = -0.40361399176081336 " " absolute error = 2.897682094271658600000000000000E-14 " " relative error = 7.179340046240649000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.930999999999977 " " y[1] (analytic) = -0.40488889083657664 " " y[1] (numeric) = -0.4048888908365469 " " absolute error = 2.975397705995419500000000000000E-14 " " relative error = 7.348677065077504000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.929999999999977 " " y[1] (analytic) = -0.4061636328138858 " " y[1] (numeric) = -0.40616363281385615 " " absolute error = 2.96429547574916800000000000000E-14 " " relative error = 7.298278910922291000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.928999999999976 " " y[1] (analytic) = -0.40743821760441934 " " y[1] (numeric) = -0.40743821760438886 " " absolute error = 3.04756220259605470000000000000E-14 " " relative error = 7.479814290653815000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.927999999999976 " " y[1] (analytic) = -0.4087126451198283 " " y[1] (numeric) = -0.40871264511979793 " " absolute error = 3.03645997234980300000000000000E-14 " " relative error = 7.429327202390715000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.926999999999976 " " y[1] (analytic) = -0.40998691527177245 " " y[1] (numeric) = -0.40998691527174136 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 7.582252879679808000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.925999999999975 " " y[1] (analytic) = -0.4112610279719142 " " y[1] (numeric) = -0.41126102797188235 " " absolute error = 3.18634008067419900000000000000E-14 " " relative error = 7.747731644759202000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.924999999999975 " " y[1] (analytic) = -0.41253498313192116 " " y[1] (numeric) = -0.41253498313188924 " " absolute error = 3.19189119579732500000000000000E-14 " " relative error = 7.737261871865583000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.923999999999975 " " y[1] (analytic) = -0.41380878066346816 " " y[1] (numeric) = -0.4138087806634356 " " absolute error = 3.252953462151708700000000000000E-14 " " relative error = 7.861006373369316000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.922999999999974 " " y[1] (analytic) = -0.41508242047823285 " " y[1] (numeric) = -0.41508242047820015 " " absolute error = 3.26960680752108600000000000000E-14 " " relative error = 7.877006219039686000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.921999999999974 " " y[1] (analytic) = -0.4163559024879001 " " y[1] (numeric) = -0.4163559024878668 " " absolute error = 3.330669073875469600000000000000E-14 " " relative error = 7.999572130413748000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.920999999999974 " " y[1] (analytic) = -0.4176292266041587 " " y[1] (numeric) = -0.41762922660412466 " " absolute error = 3.40283357047610500000000000000E-14 " " relative error = 8.14797756887214000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.919999999999973 " " y[1] (analytic) = -0.4189023927387019 " " y[1] (numeric) = -0.41890239273866803 " " absolute error = 3.386180225106727400000000000000E-14 " " relative error = 8.08345878133697000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.918999999999973 " " y[1] (analytic) = -0.42017540080323124 " " y[1] (numeric) = -0.4201754008031965 " " absolute error = 3.4749980670767400000000000000E-14 " " relative error = 8.270351049665772000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.917999999999973 " " y[1] (analytic) = -0.4214482507094496 " " y[1] (numeric) = -0.42144825070941483 " " absolute error = 3.4749980670767400000000000000E-14 " " relative error = 8.24537309438837000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.916999999999972 " " y[1] (analytic) = -0.42272094236906843 " " y[1] (numeric) = -0.422720942369033 " " absolute error = 3.541611448554249400000000000000E-14 " " relative error = 8.378131040080209000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.915999999999972 " " y[1] (analytic) = -0.4239934756938025 " " y[1] (numeric) = -0.42399347569376633 " " absolute error = 3.619327060278010300000000000000E-14 " " relative error = 8.53628007920527000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.914999999999972 " " y[1] (analytic) = -0.42526585059537136 " " y[1] (numeric) = -0.4252658505953353 " " absolute error = 3.60822483003175900000000000000E-14 " " relative error = 8.484633376934101000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.913999999999971 " " y[1] (analytic) = -0.42653806698550245 " " y[1] (numeric) = -0.42653806698546565 " " absolute error = 3.68038932663239400000000000000E-14 " " relative error = 8.628513165643165000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.912999999999971 " " y[1] (analytic) = -0.42781012477592517 " " y[1] (numeric) = -0.4278101247758884 " " absolute error = 3.67483821150926800000000000000E-14 " " relative error = 8.589881348493199000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.911999999999970 " " y[1] (analytic) = -0.42908202387837746 " " y[1] (numeric) = -0.4290820238783399 " " absolute error = 3.75810493835615500000000000000E-14 " " relative error = 8.75847676951711100000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.91099999999997 " " y[1] (analytic) = -0.43035376420460003 " " y[1] (numeric) = -0.4303537642045616 " " absolute error = 3.841371665203041600000000000000E-14 " " relative error = 8.926078925562193000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90999999999997 " " y[1] (analytic) = -0.4316253456663388 " " y[1] (numeric) = -0.4316253456663005 " " absolute error = 3.8302694349567900000000000000E-14 " " relative error = 8.874060509684988000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.90899999999997 " " y[1] (analytic) = -0.43289676817534783 " " y[1] (numeric) = -0.43289676817530875 " " absolute error = 3.90798504668055100000000000000E-14 " " relative error = 9.027521880453483000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.907999999999970 " " y[1] (analytic) = -0.4341680316433828 " " y[1] (numeric) = -0.43416803164334383 " " absolute error = 3.896882816434299500000000000000E-14 " " relative error = 8.97551761626504000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.906999999999969 " " y[1] (analytic) = -0.43543913598220807 " " y[1] (numeric) = -0.4354391359821685 " " absolute error = 3.95794508278868300000000000000E-14 " " relative error = 9.089548356421513000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.905999999999969 " " y[1] (analytic) = -0.4367100811035911 " " y[1] (numeric) = -0.43671008110355086 " " absolute error = 4.024558464266192500000000000000E-14 " " relative error = 9.215629861568356000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.904999999999968 " " y[1] (analytic) = -0.4379808669193048 " " y[1] (numeric) = -0.43798086691926436 " " absolute error = 4.046762924758695600000000000000E-14 " " relative error = 9.239588371115502000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.903999999999968 " " y[1] (analytic) = -0.4392514933411289 " " y[1] (numeric) = -0.43925149334108776 " " absolute error = 4.11337630623620500000000000000E-14 " " relative error = 9.36451296943388900000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.902999999999968 " " y[1] (analytic) = -0.44052196028084634 " " y[1] (numeric) = -0.4405219602808052 " " absolute error = 4.11337630623620500000000000000E-14 " " relative error = 9.337505679884383000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.901999999999967 " " y[1] (analytic) = -0.4417922676502479 " " y[1] (numeric) = -0.4417922676502062 " " absolute error = 4.174438572590588600000000000000E-14 " " relative error = 9.44887196598776000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.900999999999967 " " y[1] (analytic) = -0.4430624153611279 " " y[1] (numeric) = -0.44306241536108554 " " absolute error = 4.23550083894497200000000000000E-14 " " relative error = 9.559603099018753000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.899999999999967 " " y[1] (analytic) = -0.4443324033252859 " " y[1] (numeric) = -0.44433240332524343 " " absolute error = 4.24660306919122400000000000000E-14 " " relative error = 9.557266220988119000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.898999999999966 " " y[1] (analytic) = -0.4456022314545288 " " y[1] (numeric) = -0.4456022314544855 " " absolute error = 4.329869796038110500000000000000E-14 " " relative error = 9.716894329511340000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.897999999999966 " " y[1] (analytic) = -0.44687189966066587 " " y[1] (numeric) = -0.4468718996606227 " " absolute error = 4.31876756579185900000000000000E-14 " " relative error = 9.66444202258261000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.896999999999966 " " y[1] (analytic) = -0.44814140785551515 " " y[1] (numeric) = -0.44814140785547135 " " absolute error = 4.379829832146242600000000000000E-14 " " relative error = 9.773320999514375000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.895999999999965 " " y[1] (analytic) = -0.44941075595089786 " " y[1] (numeric) = -0.4494107559508533 " " absolute error = 4.457545443870003500000000000000E-14 " " relative error = 9.918644324474134000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.894999999999965 " " y[1] (analytic) = -0.4506799438586402 " " y[1] (numeric) = -0.4506799438585956 " " absolute error = 4.457545443870003500000000000000E-14 " " relative error = 9.890711811369518000000000000E-12 "%" Correct digits = 14 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.893999999999965 " " y[1] (analytic) = -0.4519489714905762 " " y[1] (numeric) = -0.4519489714905309 " " absolute error = 4.52970994047063870000000000000E-14 " " relative error = 1.002261367147527500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.892999999999964 " " y[1] (analytic) = -0.4532178387585427 " " y[1] (numeric) = -0.45321783875849725 " " absolute error = 4.54636328584001600000000000000E-14 " " relative error = 1.003129819049807100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.891999999999964 " " y[1] (analytic) = -0.45448654557438417 " " y[1] (numeric) = -0.45448654557433804 " " absolute error = 4.612976667317525400000000000000E-14 " " relative error = 1.014986408780837300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.890999999999964 " " y[1] (analytic) = -0.455755091849949 " " y[1] (numeric) = -0.4557550918499022 " " absolute error = 4.67959004879503500000000000000E-14 " " relative error = 1.026777348729155700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.889999999999963 " " y[1] (analytic) = -0.4570234774970908 " " y[1] (numeric) = -0.45702347749704403 " " absolute error = 4.67959004879503500000000000000E-14 " " relative error = 1.023927714703633100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.888999999999963 " " y[1] (analytic) = -0.4582917024276708 " " y[1] (numeric) = -0.45829170242762335 " " absolute error = 4.74620343027254400000000000000E-14 " " relative error = 1.035629361197436700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.887999999999963 " " y[1] (analytic) = -0.4595597665535529 " " y[1] (numeric) = -0.4595597665535054 " " absolute error = 4.7517545453956700000000000000E-14 " " relative error = 1.033979667330591600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.886999999999962 " " y[1] (analytic) = -0.46082766978660916 " " y[1] (numeric) = -0.4608276697865609 " " absolute error = 4.82391904199630500000000000000E-14 " " relative error = 1.046794573821938500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.885999999999962 " " y[1] (analytic) = -0.4620954120387152 " " y[1] (numeric) = -0.4620954120386661 " " absolute error = 4.90718576884319200000000000000E-14 " " relative error = 1.061942110005640900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.884999999999962 " " y[1] (analytic) = -0.4633629932217517 " " y[1] (numeric) = -0.4633629932217027 " " absolute error = 4.896083538596940300000000000000E-14 " " relative error = 1.056641037419624200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.883999999999961 " " y[1] (analytic) = -0.46463041324760757 " " y[1] (numeric) = -0.4646304132475579 " " absolute error = 4.968248035197575500000000000000E-14 " " relative error = 1.069290320552032400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.882999999999961 " " y[1] (analytic) = -0.465897672028174 " " y[1] (numeric) = -0.4658976720281243 " " absolute error = 4.968248035197575500000000000000E-14 " " relative error = 1.066381811604573400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.881999999999960 " " y[1] (analytic) = -0.46716476947535046 " " y[1] (numeric) = -0.4671647694753002 " " absolute error = 5.023759186428833000000000000000E-14 " " relative error = 1.0753720131915699000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.88099999999996 " " y[1] (analytic) = -0.4684317055010404 " " y[1] (numeric) = -0.46843170550098934 " " absolute error = 5.1070259132757200000000000000E-14 " " relative error = 1.090239164706663400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87999999999996 " " y[1] (analytic) = -0.46969848001715186 " " y[1] (numeric) = -0.4696984800171009 " " absolute error = 5.095923683029469000000000000000E-14 " " relative error = 1.084935101949527800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.87899999999996 " " y[1] (analytic) = -0.4709650929356015 " " y[1] (numeric) = -0.4709650929355497 " " absolute error = 5.17919040987635500000000000000E-14 " " relative error = 1.099697299770907600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.877999999999960 " " y[1] (analytic) = -0.4722315441683078 " " y[1] (numeric) = -0.47223154416825613 " " absolute error = 5.16808817963010400000000000000E-14 " " relative error = 1.094397069287719600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.876999999999959 " " y[1] (analytic) = -0.47349783362719844 " " y[1] (numeric) = -0.47349783362714604 " " absolute error = 5.24025267623073900000000000000E-14 " " relative error = 1.10671101409020910000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.875999999999959 " " y[1] (analytic) = -0.47476396122420406 " " y[1] (numeric) = -0.4747639612241509 " " absolute error = 5.317968287954500000000000000E-14 " " relative error = 1.12012888978384890000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.874999999999958 " " y[1] (analytic) = -0.4760299268712608 " " y[1] (numeric) = -0.4760299268712077 " " absolute error = 5.30686605770824800000000000000E-14 " " relative error = 1.114817736899019800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.873999999999958 " " y[1] (analytic) = -0.4772957304803128 " " y[1] (numeric) = -0.4772957304802591 " " absolute error = 5.373479439185758000000000000000E-14 " " relative error = 1.1258176212425600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.872999999999958 " " y[1] (analytic) = -0.47856137196330695 " " y[1] (numeric) = -0.47856137196325316 " " absolute error = 5.379030554308883000000000000000E-14 " " relative error = 1.124000153259614400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.871999999999957 " " y[1] (analytic) = -0.47982685123219826 " " y[1] (numeric) = -0.47982685123214375 " " absolute error = 5.451195050909519000000000000000E-14 " " relative error = 1.136075448239467400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.870999999999957 " " y[1] (analytic) = -0.4810921681989455 " " y[1] (numeric) = -0.48109216819889017 " " absolute error = 5.534461777756405000000000000000E-14 " " relative error = 1.150395317902524000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.869999999999957 " " y[1] (analytic) = -0.4823573227755126 " " y[1] (numeric) = -0.48235732277545745 " " absolute error = 5.51225731726390200000000000000E-14 " " relative error = 1.142774672839223700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.868999999999956 " " y[1] (analytic) = -0.4836223148738722 " " y[1] (numeric) = -0.48362231487381613 " " absolute error = 5.606626274357040000000000000000E-14 " " relative error = 1.159298506690957500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.867999999999956 " " y[1] (analytic) = -0.48488714440599845 " " y[1] (numeric) = -0.48488714440594244 " " absolute error = 5.60107515923391500000000000000E-14 " " relative error = 1.15512964693988800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.866999999999956 " " y[1] (analytic) = -0.48615181128387475 " " y[1] (numeric) = -0.48615181128381824 " " absolute error = 5.65103519534204700000000000000E-14 " " relative error = 1.162401345460026100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.865999999999955 " " y[1] (analytic) = -0.4874163154194884 " " y[1] (numeric) = -0.487416315419431 " " absolute error = 5.73985303731205900000000000000E-14 " " relative error = 1.177607900214035900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.864999999999955 " " y[1] (analytic) = -0.4886806567248312 " " y[1] (numeric) = -0.4886806567247738 " " absolute error = 5.73985303731205900000000000000E-14 " " relative error = 1.174561128689013100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.863999999999955 " " y[1] (analytic) = -0.48994483511190345 " " y[1] (numeric) = -0.4899448351118455 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 1.182860553519184500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.862999999999954 " " y[1] (analytic) = -0.49120885049270846 " " y[1] (numeric) = -0.4912088504926505 " " absolute error = 5.79536418854331700000000000000E-14 " " relative error = 1.179816728206395400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.861999999999954 " " y[1] (analytic) = -0.4924727027792577 " " y[1] (numeric) = -0.4924727027791989 " " absolute error = 5.87863091539020400000000000000E-14 " " relative error = 1.193696804353681600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.860999999999954 " " y[1] (analytic) = -0.4937363918835661 " " y[1] (numeric) = -0.49373639188350654 " " absolute error = 5.95634652711396500000000000000E-14 " " relative error = 1.206381912500102300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.859999999999953 " " y[1] (analytic) = -0.4949999177176544 " " y[1] (numeric) = -0.4949999177175949 " " absolute error = 5.95079541199083900000000000000E-14 " " relative error = 1.202181091146189700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.858999999999953 " " y[1] (analytic) = -0.49626328019355137 " " y[1] (numeric) = -0.49626328019349114 " " absolute error = 6.02295990859147400000000000000E-14 " " relative error = 1.213662212977436900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.857999999999953 " " y[1] (analytic) = -0.4975264792232883 " " y[1] (numeric) = -0.4975264792232281 " " absolute error = 6.01740879346834800000000000000E-14 " " relative error = 1.20946503246669500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.856999999999952 " " y[1] (analytic) = -0.4987895147189054 " " y[1] (numeric) = -0.4987895147188445 " " absolute error = 6.0951244051921090000000000000E-14 " " relative error = 1.221983266554237400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.855999999999952 " " y[1] (analytic) = -0.5000523865924461 " " y[1] (numeric) = -0.5000523865923845 " " absolute error = 6.16173778666961900000000000000E-14 " " relative error = 1.232218453882027600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.854999999999952 " " y[1] (analytic) = -0.5013150947559598 " " y[1] (numeric) = -0.5013150947558982 " " absolute error = 6.16173778666961900000000000000E-14 " " relative error = 1.229114752602682400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.853999999999951 " " y[1] (analytic) = -0.5025776391215035 " " y[1] (numeric) = -0.5025776391214413 " " absolute error = 6.22835116814712800000000000000E-14 " " relative error = 1.239281393225964300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.852999999999951 " " y[1] (analytic) = -0.5038400196011377 " " y[1] (numeric) = -0.5038400196010754 " " absolute error = 6.22835116814712800000000000000E-14 " " relative error = 1.23617635079439900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.851999999999950 " " y[1] (analytic) = -0.5051022361069306 " " y[1] (numeric) = -0.5051022361068677 " " absolute error = 6.29496454962463800000000000000E-14 " " relative error = 1.246275327969838400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.85099999999995 " " y[1] (analytic) = -0.5063642885509548 " " y[1] (numeric) = -0.5063642885508912 " " absolute error = 6.36157793110214700000000000000E-14 " " relative error = 1.256324364679597400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84999999999995 " " y[1] (analytic) = -0.5076261768452884 " " y[1] (numeric) = -0.5076261768452247 " " absolute error = 6.37268016134839900000000000000E-14 " " relative error = 1.255388404308123200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.84899999999995 " " y[1] (analytic) = -0.5088879009020171 " " y[1] (numeric) = -0.5088879009019528 " " absolute error = 6.42819131257965600000000000000E-14 " " relative error = 1.263184151398671400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.847999999999950 " " y[1] (analytic) = -0.5101494606332302 " " y[1] (numeric) = -0.5101494606331658 " " absolute error = 6.43929354282590800000000000000E-14 " " relative error = 1.262236665865145400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.846999999999949 " " y[1] (analytic) = -0.5114108559510249 " " y[1] (numeric) = -0.5114108559509598 " " absolute error = 6.50590692430341700000000000000E-14 " " relative error = 1.272148772087555000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.845999999999949 " " y[1] (analytic) = -0.5126720867675026 " " y[1] (numeric) = -0.5126720867674368 " " absolute error = 6.58362253602717800000000000000E-14 " " relative error = 1.284178075217280000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.844999999999948 " " y[1] (analytic) = -0.5139331529947704 " " y[1] (numeric) = -0.5139331529947044 " " absolute error = 6.5947247662734300000000000000E-14 " " relative error = 1.283187264305662700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.843999999999948 " " y[1] (analytic) = -0.5151940545449427 " " y[1] (numeric) = -0.5151940545448763 " " absolute error = 6.63913368725843600000000000000E-14 " " relative error = 1.288666596341568300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.842999999999948 " " y[1] (analytic) = -0.5164547913301383 " " y[1] (numeric) = -0.5164547913300718 " " absolute error = 6.65023591750468800000000000000E-14 " " relative error = 1.287670485228124300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.841999999999947 " " y[1] (analytic) = -0.5177153632624832 " " y[1] (numeric) = -0.517715363262416 " " absolute error = 6.72795152922844900000000000000E-14 " " relative error = 1.299546431620449400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.840999999999947 " " y[1] (analytic) = -0.5189757702541079 " " y[1] (numeric) = -0.51897577025404 " " absolute error = 6.79456491070595800000000000000E-14 " " relative error = 1.309225844470371400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.839999999999947 " " y[1] (analytic) = -0.5202360122171487 " " y[1] (numeric) = -0.5202360122170806 " " absolute error = 6.8056671409522100000000000000E-14 " " relative error = 1.30818839548375900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.838999999999946 " " y[1] (analytic) = -0.5214960890637494 " " y[1] (numeric) = -0.5214960890636806 " " absolute error = 6.8833827526759700000000000000E-14 " " relative error = 1.31992988960546600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.837999999999946 " " y[1] (analytic) = -0.5227560007060574 " " y[1] (numeric) = -0.5227560007059886 " " absolute error = 6.8833827526759700000000000000E-14 " " relative error = 1.316748682631852800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.836999999999946 " " y[1] (analytic) = -0.5240157470562286 " " y[1] (numeric) = -0.524015747056159 " " absolute error = 6.9499961341534800000000000000E-14 " " relative error = 1.326295282765180500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.835999999999945 " " y[1] (analytic) = -0.5252753280264225 " " y[1] (numeric) = -0.5252753280263522 " " absolute error = 7.02771174587724100000000000000E-14 " " relative error = 1.337910115116568400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.834999999999945 " " y[1] (analytic) = -0.5265347435288048 " " y[1] (numeric) = -0.5265347435287344 " " absolute error = 7.03881397612349200000000000000E-14 " " relative error = 1.33681852197440500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.833999999999945 " " y[1] (analytic) = -0.5277939934755486 " " y[1] (numeric) = -0.5277939934754777 " " absolute error = 7.08322289710849900000000000000E-14 " " relative error = 1.342043104822989400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.832999999999944 " " y[1] (analytic) = -0.529053077778831 " " y[1] (numeric) = -0.5290530777787601 " " absolute error = 7.0943251273547500000000000000E-14 " " relative error = 1.340947709280789800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.831999999999944 " " y[1] (analytic) = -0.530311996350837 " " y[1] (numeric) = -0.5303119963507654 " " absolute error = 7.1609385088322600000000000000E-14 " " relative error = 1.35032557402205500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.830999999999944 " " y[1] (analytic) = -0.5315707491037559 " " y[1] (numeric) = -0.5315707491036836 " " absolute error = 7.22755189030976900000000000000E-14 " " relative error = 1.359659443732680300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.829999999999943 " " y[1] (analytic) = -0.5328293359497827 " " y[1] (numeric) = -0.5328293359497104 " " absolute error = 7.22755189030976900000000000000E-14 " " relative error = 1.35644781596464900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.828999999999943 " " y[1] (analytic) = -0.5340877568011203 " " y[1] (numeric) = -0.5340877568010474 " " absolute error = 7.29416527178727800000000000000E-14 " " relative error = 1.365724111609513400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.827999999999943 " " y[1] (analytic) = -0.5353460115699753 " " y[1] (numeric) = -0.5353460115699022 " " absolute error = 7.3052675020335300000000000000E-14 " " relative error = 1.364588013014206600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.826999999999942 " " y[1] (analytic) = -0.5366041001685623 " " y[1] (numeric) = -0.5366041001684886 " " absolute error = 7.3718808835110390000000000000E-14 " " relative error = 1.373802563415994500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.825999999999942 " " y[1] (analytic) = -0.5378620225091003 " " y[1] (numeric) = -0.5378620225090259 " " absolute error = 7.43849426498854900000000000000E-14 " " relative error = 1.382974434649305000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.824999999999942 " " y[1] (analytic) = -0.539119778503814 " " y[1] (numeric) = -0.5391197785037397 " " absolute error = 7.42739203474229700000000000000E-14 " " relative error = 1.377688656749912200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.823999999999941 " " y[1] (analytic) = -0.5403773680649363 " " y[1] (numeric) = -0.5403773680648615 " " absolute error = 7.48290318597355500000000000000E-14 " " relative error = 1.38475510415424100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.822999999999941 " " y[1] (analytic) = -0.5416347911047035 " " y[1] (numeric) = -0.5416347911046285 " " absolute error = 7.49400541621980700000000000000E-14 " " relative error = 1.383590112617256200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.821999999999940 " " y[1] (analytic) = -0.5428920475353602 " " y[1] (numeric) = -0.5428920475352844 " " absolute error = 7.58282325818981900000000000000E-14 " " relative error = 1.396746055245159400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.82099999999994 " " y[1] (analytic) = -0.5441491372691549 " " y[1] (numeric) = -0.5441491372690785 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 1.403720760774245800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.81999999999994 " " y[1] (analytic) = -0.5454060602183427 " " y[1] (numeric) = -0.5454060602182663 " " absolute error = 7.63833440942107700000000000000E-14 " " relative error = 1.400485797015753600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8189999999999396 " " y[1] (analytic) = -0.5466628162951861 " " y[1] (numeric) = -0.5466628162951092 " " absolute error = 7.69384556065233500000000000000E-14 " " relative error = 1.407420686264094800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.817999999999940 " " y[1] (analytic) = -0.5479194054119517 " " y[1] (numeric) = -0.5479194054118746 " " absolute error = 7.71605002114483800000000000000E-14 " " relative error = 1.408245436268778800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.816999999999939 " " y[1] (analytic) = -0.5491758274809136 " " y[1] (numeric) = -0.5491758274808359 " " absolute error = 7.77156117237609600000000000000E-14 " " relative error = 1.41513169070541300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8159999999999386 " " y[1] (analytic) = -0.5504320824143514 " " y[1] (numeric) = -0.5504320824142729 " " absolute error = 7.84927678409985700000000000000E-14 " " relative error = 1.426020945158338300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.814999999999938 " " y[1] (analytic) = -0.5516881701245493 " " y[1] (numeric) = -0.5516881701244709 " " absolute error = 7.83817455385360500000000000000E-14 " " relative error = 1.420761759688277700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.813999999999938 " " y[1] (analytic) = -0.5529440905238008 " " y[1] (numeric) = -0.5529440905237216 " " absolute error = 7.91589016557736600000000000000E-14 " " relative error = 1.431589612989387000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8129999999999376 " " y[1] (analytic) = -0.5541998435244018 " " y[1] (numeric) = -0.5541998435243227 " " absolute error = 7.90478793533111500000000000000E-14 " " relative error = 1.426342505811816000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.811999999999937 " " y[1] (analytic) = -0.5554554290386575 " " y[1] (numeric) = -0.5554554290385779 " " absolute error = 7.96029908656237200000000000000E-14 " " relative error = 1.433112122126430000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.810999999999937 " " y[1] (analytic) = -0.5567108469788773 " " y[1] (numeric) = -0.5567108469787969 " " absolute error = 8.03801469828613300000000000000E-14 " " relative error = 1.443840144647138800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8099999999999365 " " y[1] (analytic) = -0.5579660972573762 " " y[1] (numeric) = -0.5579660972572957 " " absolute error = 8.04911692853238500000000000000E-14 " " relative error = 1.442581721021577200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.808999999999936 " " y[1] (analytic) = -0.5592211797864775 " " y[1] (numeric) = -0.5592211797863963 " " absolute error = 8.11573031000989400000000000000E-14 " " relative error = 1.451255890041334400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.807999999999936 " " y[1] (analytic) = -0.5604760944785079 " " y[1] (numeric) = -0.5604760944784267 " " absolute error = 8.11573031000989400000000000000E-14 " " relative error = 1.44800650553368100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8069999999999355 " " y[1] (analytic) = -0.561730841245803 " " y[1] (numeric) = -0.5617308412457211 " " absolute error = 8.18234369148740400000000000000E-14 " " relative error = 1.45663066555873220000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.805999999999935 " " y[1] (analytic) = -0.5629854200007023 " " y[1] (numeric) = -0.5629854200006199 " " absolute error = 8.23785484271866200000000000000E-14 " " relative error = 1.463244792859535200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.804999999999935 " " y[1] (analytic) = -0.5642398306555518 " " y[1] (numeric) = -0.5642398306554693 " " absolute error = 8.24895707296491300000000000000E-14 " " relative error = 1.46195936989790500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8039999999999345 " " y[1] (analytic) = -0.565494073122705 " " y[1] (numeric) = -0.565494073122622 " " absolute error = 8.30446822419617100000000000000E-14 " " relative error = 1.468533202892509700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.802999999999934 " " y[1] (analytic) = -0.5667481473145198 " " y[1] (numeric) = -0.5667481473144366 " " absolute error = 8.32667268468867400000000000000E-14 " " relative error = 1.469201571128867500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.801999999999934 " " y[1] (analytic) = -0.5680020531433618 " " y[1] (numeric) = -0.5680020531432779 " " absolute error = 8.39328606616618300000000000000E-14 " " relative error = 1.477685867457198500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.8009999999999335 " " y[1] (analytic) = -0.5692557905216017 " " y[1] (numeric) = -0.569255790521517 " " absolute error = 8.47100167788994400000000000000E-14 " " relative error = 1.488083532734568200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.799999999999933 " " y[1] (analytic) = -0.5705093593616156 " " y[1] (numeric) = -0.5705093593615309 " " absolute error = 8.47100167788994400000000000000E-14 " " relative error = 1.484813796458793200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.798999999999933 " " y[1] (analytic) = -0.5717627595757885 " " y[1] (numeric) = -0.571762759575703 " " absolute error = 8.54871728961370500000000000000E-14 " " relative error = 1.49515111756426870000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7979999999999325 " " y[1] (analytic) = -0.5730159910765081 " " y[1] (numeric) = -0.5730159910764228 " " absolute error = 8.53761505936745400000000000000E-14 " " relative error = 1.489943595348550400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.796999999999932 " " y[1] (analytic) = -0.574269053776172 " " y[1] (numeric) = -0.5742690537760858 " " absolute error = 8.61533067109121500000000000000E-14 " " relative error = 1.50022548045034300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.795999999999932 " " y[1] (analytic) = -0.575521947587181 " " y[1] (numeric) = -0.5755219475870941 " " absolute error = 8.69304628281497600000000000000E-14 " " relative error = 1.51046303607702800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7949999999999315 " " y[1] (analytic) = -0.5767746724219424 " " y[1] (numeric) = -0.5767746724218555 " " absolute error = 8.68194405256872400000000000000E-14 " " relative error = 1.505257506560101800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.793999999999931 " " y[1] (analytic) = -0.5780272281928721 " " y[1] (numeric) = -0.5780272281927845 " " absolute error = 8.75965966429248500000000000000E-14 " " relative error = 1.515440663872952300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.792999999999930 " " y[1] (analytic) = -0.5792796148123891 " " y[1] (numeric) = -0.5792796148123015 " " absolute error = 8.75965966429248500000000000000E-14 " " relative error = 1.512164322773462400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7919999999999305 " " y[1] (analytic) = -0.5805318321929215 " " y[1] (numeric) = -0.5805318321928332 " " absolute error = 8.82627304576999400000000000000E-14 " " relative error = 1.520377101877311300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.79099999999993 " " y[1] (analytic) = -0.5817838802469016 " " y[1] (numeric) = -0.5817838802468125 " " absolute error = 8.91509088774000700000000000000E-14 " " relative error = 1.532371588562501400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.78999999999993 " " y[1] (analytic) = -0.5830357588867675 " " y[1] (numeric) = -0.5830357588866786 " " absolute error = 8.89288642724750400000000000000E-14 " " relative error = 1.525272899937962200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7889999999999295 " " y[1] (analytic) = -0.5842874680249668 " " y[1] (numeric) = -0.5842874680248769 " " absolute error = 8.99280649946376800000000000000E-14 " " relative error = 1.539106517184363800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.787999999999930 " " y[1] (analytic) = -0.5855390075739488 " " y[1] (numeric) = -0.5855390075738591 " " absolute error = 8.97060203897126500000000000000E-14 " " relative error = 1.532024668371620200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.786999999999929 " " y[1] (analytic) = -0.5867903774461736 " " y[1] (numeric) = -0.5867903774460832 " " absolute error = 9.03721542044877400000000000000E-14 " " relative error = 1.540109682742328300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7859999999999285 " " y[1] (analytic) = -0.5880415775541044 " " y[1] (numeric) = -0.5880415775540133 " " absolute error = 9.10382880192628400000000000000E-14 " " relative error = 1.548160733768635700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.784999999999928 " " y[1] (analytic) = -0.5892926078102111 " " y[1] (numeric) = -0.5892926078101199 " " absolute error = 9.11493103217253500000000000000E-14 " " relative error = 1.546758081022477400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.783999999999928 " " y[1] (analytic) = -0.5905434681269719 " " y[1] (numeric) = -0.59054346812688 " " absolute error = 9.19264664389629600000000000000E-14 " " relative error = 1.55664182910237500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7829999999999275 " " y[1] (analytic) = -0.5917941584168681 " " y[1] (numeric) = -0.5917941584167763 " " absolute error = 9.18154441365004500000000000000E-14 " " relative error = 1.551476012911644200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.781999999999927 " " y[1] (analytic) = -0.593044678592391 " " y[1] (numeric) = -0.5930446785922985 " " absolute error = 9.24815779512755400000000000000E-14 " " relative error = 1.559436941088204200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.780999999999927 " " y[1] (analytic) = -0.5942950285660353 " " y[1] (numeric) = -0.5942950285659421 " " absolute error = 9.32587340685131500000000000000E-14 " " relative error = 1.56923294972760590000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7799999999999265 " " y[1] (analytic) = -0.5955452082503023 " " y[1] (numeric) = -0.5955452082502091 " " absolute error = 9.32587340685131500000000000000E-14 " " relative error = 1.565938786452586700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.778999999999926 " " y[1] (analytic) = -0.5967952175577018 " " y[1] (numeric) = -0.5967952175576079 " " absolute error = 9.39248678832882400000000000000E-14 " " relative error = 1.5738207197380402000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.777999999999926 " " y[1] (analytic) = -0.5980450564007471 " " y[1] (numeric) = -0.5980450564006532 " " absolute error = 9.39248678832882400000000000000E-14 " " relative error = 1.570531632659289700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7769999999999255 " " y[1] (analytic) = -0.5992947246919605 " " y[1] (numeric) = -0.599294724691866 " " absolute error = 9.45910016980633400000000000000E-14 " " relative error = 1.578372006305969500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.775999999999925 " " y[1] (analytic) = -0.6005442223438687 " " y[1] (numeric) = -0.6005442223437735 " " absolute error = 9.52571355128384300000000000000E-14 " " relative error = 1.586180200702932700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.774999999999925 " " y[1] (analytic) = -0.601793549269005 " " y[1] (numeric) = -0.6017935492689095 " " absolute error = 9.54791801177634600000000000000E-14 " " relative error = 1.586576995279219000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7739999999999245 " " y[1] (analytic) = -0.6030427053799102 " " y[1] (numeric) = -0.6030427053798142 " " absolute error = 9.60342916300760400000000000000E-14 " " relative error = 1.592495701769172400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.772999999999924 " " y[1] (analytic) = -0.6042916905891298 " " y[1] (numeric) = -0.6042916905890339 " " absolute error = 9.59232693276135300000000000000E-14 " " relative error = 1.587367008705630200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.771999999999924 " " y[1] (analytic) = -0.6055405048092183 " " y[1] (numeric) = -0.6055405048091215 " " absolute error = 9.68114477473136500000000000000E-14 " " relative error = 1.598760891772468600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7709999999999235 " " y[1] (analytic) = -0.6067891479527336 " " y[1] (numeric) = -0.6067891479526362 " " absolute error = 9.74775815620887400000000000000E-14 " " relative error = 1.606448992882810200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.769999999999923 " " y[1] (analytic) = -0.6080376199322409 " " y[1] (numeric) = -0.6080376199321436 " " absolute error = 9.73665592596262300000000000000E-14 " " relative error = 1.601324590252765000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.768999999999923 " " y[1] (analytic) = -0.6092859206603138 " " y[1] (numeric) = -0.6092859206602157 " " absolute error = 9.81437153768638400000000000000E-14 " " relative error = 1.610799003372678200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7679999999999225 " " y[1] (analytic) = -0.6105340500495291 " " y[1] (numeric) = -0.6105340500494311 " " absolute error = 9.80326930744013200000000000000E-14 " " relative error = 1.60568756265843800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.766999999999922 " " y[1] (analytic) = -0.6117820080124733 " " y[1] (numeric) = -0.6117820080123744 " " absolute error = 9.89208714941014500000000000000E-14 " " relative error = 1.616930053491939200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.765999999999922 " " y[1] (analytic) = -0.6130297944617367 " " y[1] (numeric) = -0.6130297944616371 " " absolute error = 9.95870053088765400000000000000E-14 " " relative error = 1.624505141651682900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7649999999999215 " " y[1] (analytic) = -0.6142774093099163 " " y[1] (numeric) = -0.6142774093098168 " " absolute error = 9.94759830064140300000000000000E-14 " " relative error = 1.619398361371714200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.763999999999921 " " y[1] (analytic) = -0.615524852469618 " " y[1] (numeric) = -0.6155248524695177 " " absolute error = 1.00253139123651640000000000000E-13 " " relative error = 1.6287423443816200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.762999999999920 " " y[1] (analytic) = -0.6167721238534507 " " y[1] (numeric) = -0.6167721238533505 " " absolute error = 1.00253139123651640000000000000E-13 " " relative error = 1.625448609727901000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7619999999999205 " " y[1] (analytic) = -0.618019223374033 " " y[1] (numeric) = -0.6180192233739321 " " absolute error = 1.00919272938426730000000000000E-13 " " relative error = 1.632947149887425400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.76099999999992 " " y[1] (analytic) = -0.6192661509439877 " " y[1] (numeric) = -0.6192661509438862 " " absolute error = 1.01585406753201820000000000000E-13 " " relative error = 1.640415943909554500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.75999999999992 " " y[1] (analytic) = -0.620512906475944 " " y[1] (numeric) = -0.6205129064758427 " " absolute error = 1.01363362148276790000000000000E-13 " " relative error = 1.633541560383425200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7589999999999195 " " y[1] (analytic) = -0.6217594898825402 " " y[1] (numeric) = -0.6217594898824381 " " absolute error = 1.02029495963051890000000000000E-13 " " relative error = 1.640980115676671200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.757999999999920 " " y[1] (analytic) = -0.6230059010764178 " " y[1] (numeric) = -0.6230059010763155 " " absolute error = 1.02362562870439430000000000000E-13 " " relative error = 1.643043231108715400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.756999999999919 " " y[1] (analytic) = -0.6242521399702273 " " y[1] (numeric) = -0.6242521399701243 " " absolute error = 1.03028696685214530000000000000E-13 " " relative error = 1.65043401677611080000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7559999999999185 " " y[1] (analytic) = -0.6254982064766241 " " y[1] (numeric) = -0.6254982064765205 " " absolute error = 1.0358380819752710000000000000E-13 " " relative error = 1.65602086664653300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.754999999999918 " " y[1] (analytic) = -0.6267441005082705 " " y[1] (numeric) = -0.6267441005081668 " " absolute error = 1.03694830499989620000000000000E-13 " " relative error = 1.65450030428521400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.753999999999918 " " y[1] (analytic) = -0.6279898219778365 " " y[1] (numeric) = -0.627989821977732 " " absolute error = 1.04471986617227230000000000000E-13 " " relative error = 1.663593627810648300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7529999999999175 " " y[1] (analytic) = -0.6292353707979962 " " y[1] (numeric) = -0.6292353707978918 " " absolute error = 1.04360964314764710000000000000E-13 " " relative error = 1.658536203748593500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.751999999999917 " " y[1] (analytic) = -0.6304807468814335 " " y[1] (numeric) = -0.6304807468813284 " " absolute error = 1.05138120432002320000000000000E-13 " " relative error = 1.667586535386691400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.750999999999917 " " y[1] (analytic) = -0.6317259501408361 " " y[1] (numeric) = -0.6317259501407302 " " absolute error = 1.05915276549239930000000000000E-13 " " relative error = 1.676601642304346400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7499999999999165 " " y[1] (analytic) = -0.6329709804888984 " " y[1] (numeric) = -0.6329709804887925 " " absolute error = 1.05915276549239930000000000000E-13 " " relative error = 1.673303829307188400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.748999999999916 " " y[1] (analytic) = -0.6342158378383238 " " y[1] (numeric) = -0.6342158378382172 " " absolute error = 1.06581410364015030000000000000E-13 " " relative error = 1.680522686524032700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.747999999999916 " " y[1] (analytic) = -0.6354605221018189 " " y[1] (numeric) = -0.6354605221017126 " " absolute error = 1.06359365759090000000000000E-13 " " relative error = 1.673736794967228300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7469999999999155 " " y[1] (analytic) = -0.6367050331921005 " " y[1] (numeric) = -0.6367050331919935 " " absolute error = 1.07025499573865090000000000000E-13 " " relative error = 1.68092749380817900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.745999999999915 " " y[1] (analytic) = -0.6379493710218892 " " y[1] (numeric) = -0.6379493710217814 " " absolute error = 1.0780265569110270000000000000E-13 " " relative error = 1.689830895489726800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.744999999999915 " " y[1] (analytic) = -0.6391935355039123 " " y[1] (numeric) = -0.6391935355038045 " " absolute error = 1.0780265569110270000000000000E-13 " " relative error = 1.686541707686636500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7439999999999145 " " y[1] (analytic) = -0.640437526550906 " " y[1] (numeric) = -0.6404375265507974 " " absolute error = 1.08579811808340310000000000000E-13 " " relative error = 1.695400523968354500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.742999999999914 " " y[1] (analytic) = -0.6416813440756101 " " y[1] (numeric) = -0.6416813440755016 " " absolute error = 1.0846878950587780000000000000E-13 " " relative error = 1.690384027949810300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.741999999999914 " " y[1] (analytic) = -0.6429249879907739 " " y[1] (numeric) = -0.6429249879906648 " " absolute error = 1.09134923320652890000000000000E-13 " " relative error = 1.697475216536753800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7409999999999135 " " y[1] (analytic) = -0.6441684582091515 " " y[1] (numeric) = -0.6441684582090416 " " absolute error = 1.0991207943789050000000000000E-13 " " relative error = 1.7062629819450700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.739999999999913 " " y[1] (analytic) = -0.6454117546435032 " " y[1] (numeric) = -0.6454117546433932 " " absolute error = 1.10023101740353010000000000000E-13 " " relative error = 1.70469628030132330000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.738999999999913 " " y[1] (analytic) = -0.6466548772065981 " " y[1] (numeric) = -0.6466548772064874 " " absolute error = 1.10689235555128110000000000000E-13 " " relative error = 1.711720416202231500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7379999999999125 " " y[1] (analytic) = -0.6478978258112094 " " y[1] (numeric) = -0.6478978258110988 " " absolute error = 1.10578213252665590000000000000E-13 " " relative error = 1.706723017849529300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.736999999999912 " " y[1] (analytic) = -0.6491406003701198 " " y[1] (numeric) = -0.6491406003700084 " " absolute error = 1.1135536936990320000000000000E-13 " " relative error = 1.71542758697286600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.735999999999912 " " y[1] (analytic) = -0.6503832007961162 " " y[1] (numeric) = -0.6503832007960041 " " absolute error = 1.12132525487140810000000000000E-13 " " relative error = 1.724099351734215700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7349999999999115 " " y[1] (analytic) = -0.6516256270019922 " " y[1] (numeric) = -0.6516256270018802 " " absolute error = 1.1202150318467830000000000000E-13 " " relative error = 1.71910831223855200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.733999999999911 " " y[1] (analytic) = -0.6528678789005508 " " y[1] (numeric) = -0.652867878900438 " " absolute error = 1.1279865930191590000000000000E-13 " " relative error = 1.727740986306023600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.732999999999910 " " y[1] (analytic) = -0.6541099564045978 " " y[1] (numeric) = -0.6541099564044852 " " absolute error = 1.12576614696990870000000000000E-13 " " relative error = 1.72106560364534420000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7319999999999105 " " y[1] (analytic) = -0.6553518594269497 " " y[1] (numeric) = -0.6553518594268364 " " absolute error = 1.13353770814228480000000000000E-13 " " relative error = 1.729662763348941400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.73099999999991 " " y[1] (analytic) = -0.6565935878804268 " " y[1] (numeric) = -0.6565935878803127 " " absolute error = 1.14019904629003580000000000000E-13 " " relative error = 1.736536980159604000000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.72999999999991 " " y[1] (analytic) = -0.6578351416778564 " " y[1] (numeric) = -0.6578351416777423 " " absolute error = 1.1413092693146609000000000000E-13 " " relative error = 1.73494724894700600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7289999999999095 " " y[1] (analytic) = -0.6590765207320745 " " y[1] (numeric) = -0.6590765207319597 " " absolute error = 1.14797060746241190000000000000E-13 " " relative error = 1.741786532142420300000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.727999999999910 " " y[1] (analytic) = -0.660317724955921 " " y[1] (numeric) = -0.6603177249558062 " " absolute error = 1.14797060746241190000000000000E-13 " " relative error = 1.738512482818848600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.726999999999909 " " y[1] (analytic) = -0.6615587542622456 " " y[1] (numeric) = -0.6615587542621301 " " absolute error = 1.1557421686347880000000000000E-13 " " relative error = 1.74699852611525620000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7259999999999085 " " y[1] (analytic) = -0.6627996085639022 " " y[1] (numeric) = -0.6627996085637862 " " absolute error = 1.16018306073328860000000000000E-13 " " relative error = 1.7504281018618500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.724999999999908 " " y[1] (analytic) = -0.6640402877737521 " " y[1] (numeric) = -0.664040287773636 " " absolute error = 1.16129328375791370000000000000E-13 " " relative error = 1.748829559199249500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.723999999999908 " " y[1] (analytic) = -0.6652807918046647 " " y[1] (numeric) = -0.665280791804548 " " absolute error = 1.16684439888103950000000000000E-13 " " relative error = 1.75391265350652220000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7229999999999075 " " y[1] (analytic) = -0.6665211205695142 " " y[1] (numeric) = -0.6665211205693973 " " absolute error = 1.16906484493028980000000000000E-13 " " relative error = 1.753980194853200200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.721999999999907 " " y[1] (analytic) = -0.6677612739811833 " " y[1] (numeric) = -0.6677612739810658 " " absolute error = 1.17572618307804080000000000000E-13 " " relative error = 1.760698364654149400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.720999999999907 " " y[1] (analytic) = -0.6690012519525605 " " y[1] (numeric) = -0.6690012519524422 " " absolute error = 1.18349774425041690000000000000E-13 " " relative error = 1.769051613575066400000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7199999999999065 " " y[1] (analytic) = -0.6702410543965402 " " y[1] (numeric) = -0.670241054396422 " " absolute error = 1.18238752122579170000000000000E-13 " " relative error = 1.764122793537869500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.718999999999906 " " y[1] (analytic) = -0.6714806812260266 " " y[1] (numeric) = -0.6714806812259075 " " absolute error = 1.19015908239816780000000000000E-13 " " relative error = 1.772439797113908600000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.717999999999906 " " y[1] (analytic) = -0.6727201323539266 " " y[1] (numeric) = -0.6727201323538078 " " absolute error = 1.18793863634891750000000000000E-13 " " relative error = 1.76587347280983100000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7169999999999055 " " y[1] (analytic) = -0.6739594076931583 " " y[1] (numeric) = -0.6739594076930386 " " absolute error = 1.19682042054591880000000000000E-13 " " relative error = 1.77580490291309900000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.715999999999905 " " y[1] (analytic) = -0.6751985071566432 " " y[1] (numeric) = -0.675198507156523 " " absolute error = 1.20237153566904450000000000000E-13 " " relative error = 1.78076746752951500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.714999999999905 " " y[1] (analytic) = -0.6764374306573103 " " y[1] (numeric) = -0.6764374306571902 " " absolute error = 1.20126131264441940000000000000E-13 " " relative error = 1.775864637586842500000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7139999999999045 " " y[1] (analytic) = -0.6776761781080977 " " y[1] (numeric) = -0.6776761781079768 " " absolute error = 1.20903287381679550000000000000E-13 " " relative error = 1.784086430767144200000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.712999999999904 " " y[1] (analytic) = -0.6789147494219467 " " y[1] (numeric) = -0.6789147494218258 " " absolute error = 1.20903287381679550000000000000E-13 " " relative error = 1.78083165058088800000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.711999999999904 " " y[1] (analytic) = -0.680153144511809 " " y[1] (numeric) = -0.6801531445116875 " " absolute error = 1.21458398893992130000000000000E-13 " " relative error = 1.785750751489517700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = -4.7109999999999035 " " y[1] (analytic) = -0.6813913632906411 " " y[1] (numeric) = -0.6813913632905187 " " absolute error = 1.22346577313692250000000000000E-13 " " relative error = 1.795540476516231700000000000E-11 "%" Correct digits = 13 h = 1.000E-3 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = (0.1 * x + 0.2) + sin(0.3 * x + 0.1) ;" Iterations = 289 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 2 Minutes 59 Seconds "Expected Time Remaining "= 0 Years 0 Days 1 Hours 40 Minutes 59 Seconds "Optimized Time Remaining "= 0 Years 0 Days 1 Hours 40 Minutes 7 Seconds "Expected Total Time "= 0 Years 0 Days 1 Hours 43 Minutes 8 Seconds "Time to Timeout " Unknown Percent Done = 2.9000000000009685 "%" (%o54) true (%o54) diffeq.max