(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/share/maxima/5.27.0/share/stringproc/stringproc.mac (%i3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%o3) check_sign(x0, xf) := block([ret], if xf > x0 then ret : 1.0 else ret : - 1.0, ret) (%i4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%o4) est_size_answer() := block([min_size], min_size : glob_large_float, if omniabs(array_y ) < min_size then (min_size : omniabs(array_y ), 1 1 omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), if min_size < 1.0 then (min_size : 1.0, omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")), min_size) (%i5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%o5) test_suggested_h() := block([max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms], max_value3 : 0.0, no_terms : glob_max_terms, hn_div_ho : 0.5, hn_div_ho_2 : 0.25, hn_div_ho_3 : 0.125, omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""), omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""), omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""), value3 : omniabs(array_y hn_div_ho_3 + array_y hn_div_ho_2 no_terms no_terms - 1 + array_y hn_div_ho + array_y ), no_terms - 2 no_terms - 3 if value3 > max_value3 then (max_value3 : value3, omniout_float(ALWAYS, "value3", 32, value3, 32, "")), omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""), max_value3) (%i6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%o6) reached_interval() := block([ret], if glob_check_sign array_x >= glob_check_sign glob_next_display 1 then ret : true else ret : false, return(ret)) (%i7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%o7) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if reached_interval() then (if iter >= 0 then (ind_var : array_x , 1 omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y(ind_var), omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y , term_no abserr : omniabs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "), if omniabs(analytic_val_y) # 0.0 abserr 100.0 then (relerr : -----------------------, omniabs(analytic_val_y) if relerr > 1.0E-34 then glob_good_digits : 2 - floor(log10(relerr)) else glob_good_digits : 16) else (relerr : - 1.0, glob_good_digits : - 1), if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")))) (%i8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%o8) adjust_for_pole(h_param) := block([hnew, sz2, tmp], block(hnew : h_param, glob_normmax : glob_small_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), 1, 1 if tmp < glob_normmax then glob_normmax : tmp), if glob_look_poles and (omniabs(array_pole ) > glob_small_float) 1 array_pole 1 and (array_pole # glob_large_float) then (sz2 : -----------, 1 10.0 if sz2 < hnew then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2), return(hnew)) 1 (%i9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o9) prog_report(x_start, x_end) := block([clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec], clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), glob_total_exp_sec : total_clock_sec + glob_optimal_expect_sec, percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec)), omniout_str_noeol(INFO, "Expected Total Time "), omniout_timestr(convfloat(glob_total_exp_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%o10) check_for_pole() := block([cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, h_new, ratio, term], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (rad_c : glob_large_float, ord_no : glob_large_float) elseif ((omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float)) 1, m - 5 or ((omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float) or (omniabs(array_y_higher ) <= glob_small_float)) 1, m 1, m - 1 1, m - 2 1, m - 3 1, m - 4 1, m - 5 then (rad_c : glob_large_float, ord_no : glob_large_float) array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (rad_c : glob_large_float, ord_no : glob_large_float) else (if omniabs(nr1 dr2 - nr2 dr1) > dr1 dr2 - ds2 dr1 + ds1 dr2 glob_small_float then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if (not found) and ((array_real_pole # glob_large_float) 1, 1 and (array_real_pole # glob_large_float) and (array_real_pole > 0.0) 1, 2 1, 1 and (array_real_pole > 0.0) and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 1, 2 1, 1 1, 2 1, 1 1, 2 0.0))) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used"))), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then (if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used"))), if not found then (array_poles : glob_large_float, 1, 1 array_poles : glob_large_float, array_type_pole : 3, 1, 2 1 if reached_interval() then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, array_pole : glob_large_float, 1 2 if array_pole > array_poles then (array_pole : array_poles , 1 1, 1 1 1, 1 array_pole : array_poles ), if array_pole glob_ratio_of_radius < 2 1, 2 1 omniabs(glob_h) then (h_new : array_pole glob_ratio_of_radius, term : 1, 1 ratio : 1.0, while term <= glob_max_terms do (array_y : term array_y ratio, array_y_higher : array_y_higher ratio, term 1, term 1, term ratio h_new array_x : array_x ratio, ratio : ---------------, term : 1 + term), term term omniabs(glob_h) glob_h : h_new), if reached_interval() then display_pole()) (%i11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%o11) get_norms() := block([iii], if not glob_initial_pass then (iii : 1, while iii <= glob_max_terms do (array_norms : 0.0, iii iii : 1 + iii), iii : 1, while iii <= glob_max_terms do (if omniabs(array_y ) > array_norms iii iii then array_norms : omniabs(array_y ), iii : 1 + iii))) iii iii (%i12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4_g : sinh(array_tmp3 ), array_tmp4 : cosh(array_tmp3 ), 1 1 1 1 array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4_g : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp4 : att(1, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 3 3 2.0 array_tmp4_g : att(2, array_tmp4, array_tmp3, 1), 3 array_tmp4 : att(2, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 4 4 2.0 array_tmp4_g : att(3, array_tmp4, array_tmp3, 1), 4 array_tmp4 : att(3, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 5 5 2.0 array_tmp4_g : att(4, array_tmp4, array_tmp3, 1), 5 array_tmp4 : att(4, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4_g : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp4 : att(kkk - 1, array_tmp4_g, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) (%o12) atomall() := block([kkk, order_d, adj2, adj3, temporary, term, temp, temp2], array_tmp1 : array_const_0D1 array_x , 1 1 1 array_tmp2 : array_const_0D2 + array_tmp1 , array_tmp3 : sqrt(array_tmp2 ), 1 1 1 1 1 array_tmp4_g : sinh(array_tmp3 ), array_tmp4 : cosh(array_tmp3 ), 1 1 1 1 array_tmp5 : array_tmp4 + array_const_0D0 , 1 1 1 if not array_y_set_initial then (if 1 <= glob_max_terms 1, 2 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(0, 1), 1 array_y : temporary, array_y_higher : temporary, 2 1, 2 temporary 1.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 2, glob_h 2, 1 array_tmp1 : array_const_0D1 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp2 2 ----------- array_tmp3 1 array_tmp3 : -----------, array_tmp4_g : att(1, array_tmp4, array_tmp3, 1), 2 2.0 2 array_tmp4 : att(1, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 2 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 3, glob_h 2, 2 - ats(3, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 3 3 2.0 array_tmp4_g : att(2, array_tmp4, array_tmp3, 1), 3 array_tmp4 : att(2, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 3 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 4, glob_h 2, 3 - ats(4, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 4 4 2.0 array_tmp4_g : att(3, array_tmp4, array_tmp3, 1), 4 array_tmp4 : att(3, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 4 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 5, glob_h 2, 4 - ats(5, array_tmp3, array_tmp3, 2) ----------------------------------- array_tmp3 1 array_tmp3 : 0.0, array_tmp3 : -----------------------------------, 5 5 2.0 array_tmp4_g : att(4, array_tmp4, array_tmp3, 1), 5 array_tmp4 : att(4, array_tmp4_g, array_tmp3, 1), array_tmp5 : array_tmp4 , 5 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp5 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 5.0 temporary : -------------, array_y_higher : temporary, 0)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : 0.0, kkk - ats(kkk, array_tmp3, array_tmp3, 2) ------------------------------------- array_tmp3 1 array_tmp3 : -------------------------------------, kkk 2.0 array_tmp4_g : att(kkk - 1, array_tmp4, array_tmp3, 1), kkk array_tmp4 : att(kkk - 1, array_tmp4_g, array_tmp3, 1), kkk array_tmp5 : array_tmp4 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk then (temporary : array_tmp5 expt(glob_h, order_d) kkk factorial_3(kkk - 1, - 1 + order_d + kkk), array_y : temporary, order_d + kkk array_y_higher : temporary, term : - 1 + order_d + kkk, 1, order_d + kkk adj2 : - 1 + order_d + kkk, adj3 : 2, while term >= 1 do (if adj3 <= 1 + order_d then (if adj2 > 0 temporary convfp(adj2) then temporary : ---------------------- else temporary : temporary, glob_h array_y_higher : temporary), term : term - 1, adj2 : adj2 - 1, adj3, term adj3 : 1 + adj3))), kkk : 1 + kkk)) log(x) (%i13) log10(x) := --------- log(10.0) log(x) (%o13) log10(x) := --------- log(10.0) (%i14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o14) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o15) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o16) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o17) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o18) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o19) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%o20) dump_series(iolevel, dump_label, series_name, arr_series, numb) := block([i], if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i))) i (%i21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%o21) dump_series_2(iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) := (array_series2, numb, subnum) := block([i, sub, ts_term], if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub))) sub, i (%i22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o22) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%o23) logitem_time(fd, secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), printf(fd, "~%"), secs if secs >= 0 then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(fd, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(fd, "= ~d Seconds~%", sec_int)) else printf(fd, " Unknown~%"), printf(fd, "~%")) (%i24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o24) omniout_timestr(secs_in) := block([days, days_int, hours, hours_int, minutes, minutes_int, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= 0 secs then (years_int : trunc(----------------), glob_sec_in_year sec_temp : mod(trunc(secs), trunc(glob_sec_in_year)), sec_temp days_int : trunc(---------------), sec_temp : glob_sec_in_day sec_temp mod(sec_temp, trunc(glob_sec_in_day)), hours_int : trunc(----------------), glob_sec_in_hour sec_temp : mod(sec_temp, trunc(glob_sec_in_hour)), sec_temp minutes_int : trunc(------------------), glob_sec_in_minute sec_int : mod(sec_temp, trunc(glob_sec_in_minute)), if years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o25) ats(mmm_ats, arr_a, arr_b, jjj_ats) := block([iii_ats, lll_ats, ma_ats, ret_ats], ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : arr_a arr_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o26) att(mmm_att, arr_aa, arr_bb, jjj_att) := block([al_att, iii_att, lll_att, ma_att, ret_att], ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : arr_aa arr_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o27) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o28) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o29) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o30) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o31) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error > + 1.0E-34 then (good_digits : 1 - floor(log10(rel_error)), printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i32) log_revs(file, revs) := printf(file, revs) (%o32) log_revs(file, revs) := printf(file, revs) (%i33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o33) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o34) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i35) logstart(file) := printf(file, "") (%o35) logstart(file) := printf(file, "") (%i36) logend(file) := printf(file, "~%") (%o36) logend(file) := printf(file, "~%") (%i37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o37) chk_data() := block([errflag], errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o38) comp_expect_sec(t_end2, t_start2, t2, clock_sec2) := block([ms2, rrr, sec_left, sub1, sub2], ms2 : clock_sec2, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if sub2 > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o39) comp_percent(t_end2, t_start2, t2) := block([rrr, sub1, sub2], sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if sub2 > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i40) factorial_2(nnn) := nnn! (%o40) factorial_2(nnn) := nnn! (%i41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%o41) factorial_1(nnn) := block([ret], if nnn <= glob_max_terms then (if array_fact_1 = 0 nnn then (ret : factorial_2(nnn), array_fact_1 : ret) nnn else ret : array_fact_1 ) else ret : factorial_2(nnn), ret) nnn (%i42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%o42) factorial_3(mmm, nnn) := block([ret], if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) factorial_1(mmm) then (if array_fact_2 = 0 then (ret : ----------------, mmm, nnn factorial_1(nnn) array_fact_2 : ret) else ret : array_fact_2 ) mmm, nnn mmm, nnn factorial_2(mmm) else ret : ----------------, ret) factorial_2(nnn) (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i46) Si(x) := 0.0 (%o46) Si(x) := 0.0 (%i47) Ci(x) := 0.0 (%o47) Ci(x) := 0.0 (%i48) ln(x) := log(x) (%o48) ln(x) := log(x) (%i49) arcsin(x) := asin(x) (%o49) arcsin(x) := asin(x) (%i50) arccos(x) := acos(x) (%o50) arccos(x) := acos(x) (%i51) arctan(x) := atan(x) (%o51) arctan(x) := atan(x) (%i52) omniabs(x) := abs(x) (%o52) omniabs(x) := abs(x) (%i53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%o53) expt(x, y) := (if (x = 0.0) and (y < 0.0) y then print("expt error x = ", x, "y = ", y), x ) (%i54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%o54) estimated_needed_step_error(x_start, x_end, estimated_h, estimated_answer) := block([desired_abs_gbl_error, range, estimated_steps, step_error], omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""), desired_abs_gbl_error : expt(10.0, - glob_desired_digits_correct) omniabs(estimated_answer), omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""), range : x_end - x_start, omniout_float(ALWAYS, "range", 32, range, 32, range ""), estimated_steps : -----------, omniout_float(ALWAYS, "estimated_steps", estimated_h desired_abs_gbl_error 32, estimated_steps, 32, ""), step_error : omniabs(---------------------), estimated_steps omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""), step_error) (%i55) exact_soln_y(x) := block(20.0 sqrt(0.2 + 0.1 x) sinh(sqrt(0.2 + 0.1 x)) - 20.0 cosh(sqrt(0.2 + 0.1 x))) (%o55) exact_soln_y(x) := block(20.0 sqrt(0.2 + 0.1 x) sinh(sqrt(0.2 + 0.1 x)) - 20.0 cosh(sqrt(0.2 + 0.1 x))) (%i56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/cosh_sqrtpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), 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, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (20.\ 0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 *\ x + 0.2))) "), 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_g, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_g : 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_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_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 : - 1.0, 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_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-12T21:10:38-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "cosh_sqrt"), logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "cosh_sqrt diffeq.max"), logitem_str(html_log_file, "cosh_sqrt maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%o56) main() := block([d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it], define_variable(glob_max_terms, 30, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_check_sign, 1.0, float), define_variable(glob_desired_digits_correct, 8.0, float), define_variable(glob_max_value3, 0.0, float), define_variable(glob_ratio_of_radius, 0.01, float), define_variable(glob_percent_done, 0.0, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_total_exp_sec, 0.1, float), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_html_log, true, boolean), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_djd_debug, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_djd_debug2, true, boolean), define_variable(glob_sec_in_minute, 60, fixnum), define_variable(glob_min_in_hour, 60, fixnum), define_variable(glob_hours_in_day, 24, fixnum), define_variable(glob_days_in_year, 365, fixnum), define_variable(glob_sec_in_hour, 3600, fixnum), define_variable(glob_sec_in_day, 86400, fixnum), define_variable(glob_sec_in_year, 31536000, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_clock_sec, 0.0, float), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(glob_initial_pass, true, boolean), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_optimal_done, false, boolean), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_h, 0.1, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_neg_h, false, boolean), define_variable(glob_display_interval, 0.0, float), define_variable(glob_next_display, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_warned2, false, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_normmax, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_max_minutes, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/cosh_sqrtpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits:32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start:-1.0,"), 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, "glob_subiter_method:3,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := (block("), omniout_str(ALWAYS, " (20.\ 0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 *\ x + 0.2))) "), 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_g, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_tmp5, 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_g : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp5 : 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_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4_g : 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_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_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 : - 1.0, 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_subiter_method : 3, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_abserr : expt(10.0, glob_log10_abserr), glob_relerr : expt(10.0, glob_log10_relerr), if glob_h > 0.0 then (glob_neg_h : false, glob_display_interval : omniabs(glob_display_interval)) else (glob_neg_h : true, glob_display_interval : - omniabs(glob_display_interval)), chk_data(), array_y_set_initial : true, 1, 1 array_y_set_initial : false, array_y_set_initial : false, 1, 2 1, 3 array_y_set_initial : false, array_y_set_initial : false, 1, 4 1, 5 array_y_set_initial : false, array_y_set_initial : false, 1, 6 1, 7 array_y_set_initial : false, array_y_set_initial : false, 1, 8 1, 9 array_y_set_initial : false, array_y_set_initial : false, 1, 10 1, 11 array_y_set_initial : false, array_y_set_initial : false, 1, 12 1, 13 array_y_set_initial : false, array_y_set_initial : false, 1, 14 1, 15 array_y_set_initial : false, array_y_set_initial : false, 1, 16 1, 17 array_y_set_initial : false, array_y_set_initial : false, 1, 18 1, 19 array_y_set_initial : false, array_y_set_initial : false, 1, 20 1, 21 array_y_set_initial : false, array_y_set_initial : false, 1, 22 1, 23 array_y_set_initial : false, array_y_set_initial : false, 1, 24 1, 25 array_y_set_initial : false, array_y_set_initial : false, 1, 26 1, 27 array_y_set_initial : false, array_y_set_initial : false, 1, 28 1, 29 array_y_set_initial : false, omniout_str(ALWAYS, "START of Optimize"), 1, 30 glob_check_sign : check_sign(x_start, x_end), glob_h : check_sign(x_start, x_end), if glob_display_interval < glob_h then glob_h : glob_display_interval, found_h : - 1.0, best_h : 0.0, min_value : glob_large_float, est_answer : est_size_answer(), opt_iter : 1, while (opt_iter <= 20) and (found_h < 0.0) do (omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""), array_x : x_start, array_x : glob_h, 1 2 glob_next_display : x_start, order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : term_no array_y_init expt(glob_h, term_no - 1) term_no ---------------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), atomall(), est_needed_step_err : estimated_needed_step_error(x_start, x_end, glob_h, est_answer), omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""), value3 : test_suggested_h(), omniout_float(ALWAYS, "value3", 32, value3, 32, ""), if (value3 < est_needed_step_err) and (found_h < 0.0) then (best_h : glob_h, found_h : 1.0), omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""), opt_iter : 1 + opt_iter, glob_h : glob_h 0.5), if found_h > 0.0 then glob_h : best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found"), if glob_html_log then html_log_file : openw("html/entry.html"), if found_h > 0.0 then (omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, array_x : glob_h, glob_next_display : x_start, 1 2 order_diff : 1, term_no : 1, while term_no <= order_diff do (array_y : (array_y_init expt(glob_h, term_no - 1)) term_no term_no /factorial_1(term_no - 1), term_no : 1 + term_no), rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, array_y_init expt(glob_h, term_no - 1) it array_y_higher : ----------------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), glob_log10normmin : - glob_large_float, if omniabs(array_y_higher ) > glob_small_float 1, 1 then (tmp : omniabs(array_y_higher ), log10norm : log10(tmp), 1, 1 if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (glob_check_sign array_x < glob_check_sign x_end) 1 and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), display_alot(current_iter), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 2, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1)), ord, term_no omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2013-01-12T21:10:38-06:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "cosh_sqrt"), logitem_str(html_log_file, "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_good_digits(html_log_file, array_last_rel_error ), logitem_integer(html_log_file, glob_max_terms), 1 logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_total_exp_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 156 "), logitem_str(html_log_file, "cosh_sqrt diffeq.max"), logitem_str(html_log_file, "cosh_sqrt maxima results"), logitem_str(html_log_file, "Languages compared - single equations"), logend(html_log_file)), if glob_html_log then close(html_log_file))) (%i57) main() "##############ECHO OF PROBLEM#################" "##############temp/cosh_sqrtpostode.ode#################" "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits:32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start:-1.0," "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," "glob_subiter_method:3," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (block(" " (20.0 * sqrt(0.1 * x + 0.2) * sinh( sqrt(0.1 * x + 0.2)) - 20.0 * cosh( sqrt(0.1 * x + 0.2))) " "));" "/* 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 = 6. "" estimated_steps = 6000. "" step_error = 1.666666666666666900000000000000E-14 "" est_needed_step_err = 1.666666666666666900000000000000E-14 "" hn_div_ho = 0.5 "" hn_div_ho_2 = 0.25 "" hn_div_ho_3 = 0.125 "" value3 = 1.61494151324143200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-100 "" max_value3 = 1.61494151324143200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-100 "" value3 = 1.61494151324143200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000E-100 "" best_h = 1.000E-3 "" "START of Soultion" x[1] = -1. " " y[1] (analytic) = -18.9748607633924 " " y[1] (numeric) = -18.9748607633924 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " " " "TOP MAIN SOLVE Loop" x[1] = -1. " " y[1] (analytic) = -18.9748607633924 " " y[1] (numeric) = -18.9748607633924 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.999 " " y[1] (analytic) = -18.973810319915465 " " y[1] (numeric) = -18.973810319915465 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.998 " " y[1] (analytic) = -18.97275982560018 " " y[1] (numeric) = -18.97275982560018 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.997 " " y[1] (analytic) = -18.971709280445697 " " y[1] (numeric) = -18.9717092804457 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.87263763442881400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.996 " " y[1] (analytic) = -18.970658684451184 " " y[1] (numeric) = -18.970658684451188 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.872741341191485300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.995 " " y[1] (analytic) = -18.969608037615796 " " y[1] (numeric) = -18.969608037615796 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.994 " " y[1] (analytic) = -18.968557339938688 " " y[1] (numeric) = -18.968557339938688 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.993 " " y[1] (analytic) = -18.967506591419017 " " y[1] (numeric) = -18.967506591419017 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.992 " " y[1] (analytic) = -18.966455792055946 " " y[1] (numeric) = -18.966455792055946 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.991 " " y[1] (analytic) = -18.965404941848632 " " y[1] (numeric) = -18.965404941848632 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.99 " " y[1] (analytic) = -18.96435404079623 " " y[1] (numeric) = -18.96435404079623 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.989 " " y[1] (analytic) = -18.963303088897902 " " y[1] (numeric) = -18.963303088897902 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.988 " " y[1] (analytic) = -18.962252086152805 " " y[1] (numeric) = -18.962252086152805 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.987 " " y[1] (analytic) = -18.961201032560098 " " y[1] (numeric) = -18.961201032560098 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.986 " " y[1] (analytic) = -18.960149928118938 " " y[1] (numeric) = -18.960149928118938 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.985 " " y[1] (analytic) = -18.959098772828483 " " y[1] (numeric) = -18.959098772828483 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.984 " " y[1] (analytic) = -18.958047566687892 " " y[1] (numeric) = -18.958047566687892 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.983 " " y[1] (analytic) = -18.956996309696322 " " y[1] (numeric) = -18.956996309696322 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.982 " " y[1] (analytic) = -18.95594500185293 " " y[1] (numeric) = -18.955945001852932 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.874194970735157700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.981 " " y[1] (analytic) = -18.95489364315688 " " y[1] (numeric) = -18.95489364315688 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.98 " " y[1] (analytic) = -18.953842233607325 " " y[1] (numeric) = -18.953842233607325 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.979 " " y[1] (analytic) = -18.95279077320342 " " y[1] (numeric) = -18.952790773203425 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.874506884666050400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.978 " " y[1] (analytic) = -18.951739261944336 " " y[1] (numeric) = -18.951739261944336 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.977 " " y[1] (analytic) = -18.950687699829217 " " y[1] (numeric) = -18.95068769982922 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.87471491012567200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.976 " " y[1] (analytic) = -18.949636086857232 " " y[1] (numeric) = -18.949636086857232 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.975 " " y[1] (analytic) = -18.948584423027526 " " y[1] (numeric) = -18.94858442302753 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.87492300189085220000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.974 " " y[1] (analytic) = -18.94753270833927 " " y[1] (numeric) = -18.947532708339274 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.875027072647229300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.973 " " y[1] (analytic) = -18.946480942791617 " " y[1] (numeric) = -18.94648094279162 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.875131159991041700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.972 " " y[1] (analytic) = -18.945429126383726 " " y[1] (numeric) = -18.94542912638373 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.875235263925973400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.971 " " y[1] (analytic) = -18.94437725911475 " " y[1] (numeric) = -18.944377259114756 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75067876891142070000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.97 " " y[1] (analytic) = -18.943325340983854 " " y[1] (numeric) = -18.94332534098386 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75088704316787600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.969 " " y[1] (analytic) = -18.942273371990197 " " y[1] (numeric) = -18.9422733719902 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.875547675314343500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.968 " " y[1] (analytic) = -18.941221352132928 " " y[1] (numeric) = -18.941221352132935 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75130369130123500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.967 " " y[1] (analytic) = -18.940169281411208 " " y[1] (numeric) = -18.94016928141122 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.62726809778934500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.966 " " y[1] (analytic) = -18.93911715982421 " " y[1] (numeric) = -18.939117159824214 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.875860236155525400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.965 " " y[1] (analytic) = -18.938064987371067 " " y[1] (numeric) = -18.938064987371074 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75192891266308800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.964 " " y[1] (analytic) = -18.937012764050955 " " y[1] (numeric) = -18.937012764050962 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75213738625638840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.963 " " y[1] (analytic) = -18.935960489863024 " " y[1] (numeric) = -18.93596048986303 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75234589309834330000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.962 " " y[1] (analytic) = -18.93490816480644 " " y[1] (numeric) = -18.934908164806444 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.876277216598171000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.961 " " y[1] (analytic) = -18.933855788880347 " " y[1] (numeric) = -18.933855788880354 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75276300655777900000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.96 " " y[1] (analytic) = -18.93280336208392 " " y[1] (numeric) = -18.932803362083924 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.87648580659502300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.959 " " y[1] (analytic) = -18.931750884416303 " " y[1] (numeric) = -18.93175088441631 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75318025310054300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.958 " " y[1] (analytic) = -18.930698355876665 " " y[1] (numeric) = -18.930698355876668 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.87669446314833400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.957 " " y[1] (analytic) = -18.929645776464152 " " y[1] (numeric) = -18.92964577646416 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75359763278582450000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.956 " " y[1] (analytic) = -18.92859314617793 " " y[1] (numeric) = -18.92859314617794 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75380637257541400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.955 " " y[1] (analytic) = -18.927540465017156 " " y[1] (numeric) = -18.927540465017163 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.754015145672843000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.954 " " y[1] (analytic) = -18.92648773298099 " " y[1] (numeric) = -18.926487732980995 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.877111976042760100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.953 " " y[1] (analytic) = -18.92543495006859 " " y[1] (numeric) = -18.92543495006859 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.952 " " y[1] (analytic) = -18.9243821162791 " " y[1] (numeric) = -18.924382116279105 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.877320832443132300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.951 " " y[1] (analytic) = -18.923329231611692 " " y[1] (numeric) = -18.9233292316117 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7548505712891600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.95 " " y[1] (analytic) = -18.922276296065526 " " y[1] (numeric) = -18.92227629606553 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.877529755518478300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.949 " " y[1] (analytic) = -18.92122330963975 " " y[1] (numeric) = -18.921223309639757 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.755268484137078700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.948 " " y[1] (analytic) = -18.920170272333536 " " y[1] (numeric) = -18.920170272333536 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.947 " " y[1] (analytic) = -18.919117184146025 " " y[1] (numeric) = -18.919117184146025 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.946 " " y[1] (analytic) = -18.91806404507638 " " y[1] (numeric) = -18.91806404507638 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.945 " " y[1] (analytic) = -18.917010855123763 " " y[1] (numeric) = -18.917010855123767 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.878052355104628800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.944 " " y[1] (analytic) = -18.91595761428733 " " y[1] (numeric) = -18.915957614287336 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.756313850182362300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.943 " " y[1] (analytic) = -18.91490432256624 " " y[1] (numeric) = -18.914904322566247 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.756523023552353300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.942 " " y[1] (analytic) = -18.91385097995965 " " y[1] (numeric) = -18.91385097995966 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75673223032666600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.941 " " y[1] (analytic) = -18.912797586466716 " " y[1] (numeric) = -18.912797586466727 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.63541220576910600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.94 " " y[1] (analytic) = -18.911744142086597 " " y[1] (numeric) = -18.91174414208661 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.51430148823601400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.939 " " y[1] (analytic) = -18.91069064681846 " " y[1] (numeric) = -18.910690646818466 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.757360051149914400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.938 " " y[1] (analytic) = -18.90963710066145 " " y[1] (numeric) = -18.909637100661453 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.878784695807953500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9369999999999999 " " y[1] (analytic) = -18.908583503614718 " " y[1] (numeric) = -18.90858350361473 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.636668148285146000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9359999999999999 " " y[1] (analytic) = -18.907529855677446 " " y[1] (numeric) = -18.90752985567745 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.878994086439965400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9349999999999999 " " y[1] (analytic) = -18.906476156848772 " " y[1] (numeric) = -18.906476156848775 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.879098806846430400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9339999999999999 " " y[1] (analytic) = -18.90542240712786 " " y[1] (numeric) = -18.905422407127865 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75840708796967300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9329999999999999 " " y[1] (analytic) = -18.904368606513867 " " y[1] (numeric) = -18.904368606513874 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75861659571782250000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9319999999999999 " " y[1] (analytic) = -18.90331475500595 " " y[1] (numeric) = -18.903314755005958 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75882613694476600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9309999999999999 " " y[1] (analytic) = -18.902260852603273 " " y[1] (numeric) = -18.90226085260328 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75903571165796370000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9299999999999999 " " y[1] (analytic) = -18.901206899304988 " " y[1] (numeric) = -18.901206899304995 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75924531986487840000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9289999999999999 " " y[1] (analytic) = -18.900152895110253 " " y[1] (numeric) = -18.90015289511026 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.759454961572972000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9279999999999999 " " y[1] (analytic) = -18.899098840018226 " " y[1] (numeric) = -18.899098840018233 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.75966463678971300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9269999999999999 " " y[1] (analytic) = -18.898044734028062 " " y[1] (numeric) = -18.898044734028073 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.639811518283856000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9259999999999999 " " y[1] (analytic) = -18.89699057713893 " " y[1] (numeric) = -18.896990577138936 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.76008408777901200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9249999999999999 " " y[1] (analytic) = -18.89593636934997 " " y[1] (numeric) = -18.895936369349982 " " absolute error = 1.421085471520200400000000000000E-14 " " relative error = 7.5205877271330300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9239999999999999 " " y[1] (analytic) = -18.894882110660355 " " y[1] (numeric) = -18.894882110660365 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.640755509338826000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9229999999999999 " " y[1] (analytic) = -18.893827801069236 " " y[1] (numeric) = -18.893827801069246 " " absolute error = 1.065814103640150300000000000000E-14 " " relative error = 5.641070273646900000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9219999999999999 " " y[1] (analytic) = -18.892773440575773 " " y[1] (numeric) = -18.89277344057578 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7609233921901397000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9209999999999999 " " y[1] (analytic) = -18.89171902917912 " " y[1] (numeric) = -18.89171902917913 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.76113330217665500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9199999999999999 " " y[1] (analytic) = -18.89066456687844 " " y[1] (numeric) = -18.890664566878446 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.76134324573162870000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9189999999999999 " " y[1] (analytic) = -18.889610053672882 " " y[1] (numeric) = -18.88961005367289 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.76155322286254800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9179999999999999 " " y[1] (analytic) = -18.888555489561615 " " y[1] (numeric) = -18.888555489561618 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.880881616788450400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9169999999999999 " " y[1] (analytic) = -18.887500874543782 " " y[1] (numeric) = -18.88750087454379 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.761973277882180000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9159999999999999 " " y[1] (analytic) = -18.88644620861856 " " y[1] (numeric) = -18.886446208618562 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.881091677892938200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9149999999999999 " " y[1] (analytic) = -18.88539149178509 " " y[1] (numeric) = -18.885391491785093 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.881196733647744200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9139999999999999 " " y[1] (analytic) = -18.884336724042537 " " y[1] (numeric) = -18.88433672404254 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.88130180620925600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9129999999999999 " " y[1] (analytic) = -18.883281905390056 " " y[1] (numeric) = -18.88328190539006 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.88140689558122400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9119999999999999 " " y[1] (analytic) = -18.88222703582681 " " y[1] (numeric) = -18.882227035826812 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.881512001767399700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9109999999999999 " " y[1] (analytic) = -18.881172115351944 " " y[1] (numeric) = -18.88117211535195 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7632342495430700000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9099999999999999 " " y[1] (analytic) = -18.880117143964632 " " y[1] (numeric) = -18.880117143964636 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.881722264597383300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9089999999999999 " " y[1] (analytic) = -18.87906212166402 " " y[1] (numeric) = -18.879062121664024 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.881827421248699600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9079999999999999 " " y[1] (analytic) = -18.878007048449266 " " y[1] (numeric) = -18.878007048449273 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.7638651894584800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9069999999999999 " " y[1] (analytic) = -18.876951924319535 " " y[1] (numeric) = -18.876951924319542 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.764075570085520500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9059999999999999 " " y[1] (analytic) = -18.87589674927398 " " y[1] (numeric) = -18.875896749273984 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.882142992193018800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9049999999999999 " " y[1] (analytic) = -18.874841523311755 " " y[1] (numeric) = -18.874841523311762 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.76449643236755100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9039999999999999 " " y[1] (analytic) = -18.873786246432026 " " y[1] (numeric) = -18.87378624643203 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.882353457018789400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9029999999999999 " " y[1] (analytic) = -18.87273091863394 " " y[1] (numeric) = -18.872730918633945 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.882458714701823500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9019999999999999 " " y[1] (analytic) = -18.871675539916662 " " y[1] (numeric) = -18.871675539916666 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.882563989236639000000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.9009999999999999 " " y[1] (analytic) = -18.870620110279347 " " y[1] (numeric) = -18.87062011027935 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.882669280626999600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8999999999999999 " " y[1] (analytic) = -18.869564629721157 " " y[1] (numeric) = -18.869564629721157 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8989999999999999 " " y[1] (analytic) = -18.86850909824124 " " y[1] (numeric) = -18.868509098241244 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.882879913989417600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8979999999999999 " " y[1] (analytic) = -18.867453515838758 " " y[1] (numeric) = -18.867453515838765 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.765970511938016600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8969999999999999 " " y[1] (analytic) = -18.866397882512874 " " y[1] (numeric) = -18.866397882512878 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.8830906148192100000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8959999999999999 " " y[1] (analytic) = -18.86534219826274 " " y[1] (numeric) = -18.865342198262745 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.883195990543792600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8949999999999999 " " y[1] (analytic) = -18.864286463087513 " " y[1] (numeric) = -18.86428646308752 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 3.76660276629305300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8939999999999999 " " y[1] (analytic) = -18.863230676986355 " " y[1] (numeric) = -18.86323067698636 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.88340679263118320000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8929999999999999 " " y[1] (analytic) = -18.862174839958417 " " y[1] (numeric) = -18.86217483995842 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.883512219001535500000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8919999999999999 " " y[1] (analytic) = -18.86111895200286 " " y[1] (numeric) = -18.86111895200286 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8909999999999999 " " y[1] (analytic) = -18.86006301311884 " " y[1] (numeric) = -18.860063013118843 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.883723122414423800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8899999999999999 " " y[1] (analytic) = -18.859007023305516 " " y[1] (numeric) = -18.85900702330552 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.883828599464511300000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8889999999999999 " " y[1] (analytic) = -18.857950982562045 " " y[1] (numeric) = -18.85795098256205 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.883934093415396400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8879999999999999 " " y[1] (analytic) = -18.856894890887585 " " y[1] (numeric) = -18.856894890887588 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.88403960427085800000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8869999999999999 " " y[1] (analytic) = -18.85583874828129 " " y[1] (numeric) = -18.855838748281293 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.88414513203467600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8859999999999999 " " y[1] (analytic) = -18.85478255474232 " " y[1] (numeric) = -18.854782554742325 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.884250676710630400000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8849999999999999 " " y[1] (analytic) = -18.853726310269835 " " y[1] (numeric) = -18.85372631026984 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.884356238302503600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8839999999999999 " " y[1] (analytic) = -18.852670014862987 " " y[1] (numeric) = -18.85267001486299 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.884461816814078600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8829999999999999 " " y[1] (analytic) = -18.851613668520937 " " y[1] (numeric) = -18.85161366852094 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.884567412249139600000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" " " "TOP MAIN SOLVE Loop" x[1] = -0.8819999999999999 " " y[1] (analytic) = -18.85055727124284 " " y[1] (numeric) = -18.850557271242845 " " absolute error = 3.552713678800501000000000000000E-15 " " relative error = 1.884673024611471200000000000000E-14 "%" Correct digits = 16 h = 1.000E-3 " " "NO POLE" "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 1 ) = cosh(sqrt(0.1 * x + 0.2));" Iterations = 119 "Total Elapsed Time "= 0 Years 0 Days 0 Hours 3 Minutes 1 Seconds "Elapsed Time(since restart) "= 0 Years 0 Days 0 Hours 3 Minutes 0 Seconds "Expected Time Remaining "= 0 Years 0 Days 2 Hours 28 Minutes 4 Seconds "Optimized Time Remaining "= 0 Years 0 Days 2 Hours 27 Minutes 11 Seconds "Expected Total Time "= 0 Years 0 Days 2 Hours 30 Minutes 13 Seconds "Time to Timeout " Unknown Percent Done = 2.0000000000000018 "%" (%o57) true (%o57) diffeq.max