(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac (%i3) reached_interval() := block([ret], if (((array_x >= glob_next_display) and (not glob_neg_h)) 1 or ((array_x <= glob_next_display) and glob_neg_h)) 1 or (glob_next_display = 0.0) then ret : true else ret : false, return(ret)) (%o3) reached_interval() := block([ret], if (((array_x >= glob_next_display) and (not glob_neg_h)) 1 or ((array_x <= glob_next_display) and glob_neg_h)) 1 or (glob_next_display = 0.0) then ret : true else ret : false, return(ret)) (%i4) 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) relerr if relerr # 0.0 then glob_good_digits : - floor(log10(------)) 100.0 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, " ")))) (%o4) 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) relerr if relerr # 0.0 then glob_good_digits : - floor(log10(------)) 100.0 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, " ")))) (%i5) 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 (%o5) 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 (%i6) 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)), 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, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o6) 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)), 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, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i7) 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], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 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 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 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 omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if reached_interval() then display_pole()) (%o7) 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], n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((omniabs(array_y_higher ) < glob_small_float) 1, m or (omniabs(array_y_higher ) < glob_small_float) 1, m - 1 or (omniabs(array_y_higher ) < glob_small_float)) do m : 1, m - 2 array_y_higher 1, m m - 1, if m > 10 then (rm0 : ----------------------, array_y_higher 1, m - 1 array_y_higher 1, m - 1 rm1 : ----------------------, hdrc : convfloat(m - 1) rm0 array_y_higher 1, m - 2 - convfloat(m - 2) rm1, if omniabs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 1, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if omniabs(array_y_higher ) > 1, n glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (omniabs(array_y_higher ) >= glob_large_float) 1, m or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 1 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 2 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 3 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 4 or (omniabs(array_y_higher ) >= glob_large_float) 1, m - 5 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y_higher array_y_higher 1, m 1, m - 1 else (rm0 : ----------------------, rm1 : ----------------------, array_y_higher array_y_higher 1, m - 1 1, m - 2 array_y_higher array_y_higher 1, m - 2 1, m - 3 rm2 : ----------------------, rm3 : ----------------------, array_y_higher array_y_higher 1, m - 3 1, m - 4 array_y_higher 1, m - 4 rm4 : ----------------------, nr1 : convfloat(m - 3) rm2 array_y_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (omniabs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (omniabs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if omniabs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if omniabs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) omniabs(glob_h) else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, array_complex_pole : ord_no), 1, 1 1, 2 found : false, if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 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 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 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 omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if reached_interval() 1 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if reached_interval() then display_pole()) (%i8) 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 (%o8) 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 (%i9) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2], array_tmp1 : array_const_2D0 array_x , 1 1 1 array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sinh(array_tmp2 ), 1 1 1 1 1 array_tmp3_g : cosh(array_tmp2 ), array_tmp4 : 1 1 1 array_tmp3 + array_const_0D0 , if not array_y_set_initial 1 1 1, 2 then (if 1 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary, 1 2 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 2 glob_h array_y_higher : temporary)), kkk : 2, 2, 1 array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_g array_tmp2 1 2 array_tmp3 : -------------------------, 2 1 array_tmp3 array_tmp2 1 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 2 1 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp3_g array_tmp2 2 2 array_tmp3 : -------------------------, 3 2 array_tmp3 array_tmp2 2 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 3 2 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp3_g array_tmp2 3 2 array_tmp3 : -------------------------, 4 3 array_tmp3 array_tmp2 3 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 4 3 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp3_g array_tmp2 4 2 array_tmp3 : -------------------------, 5 4 array_tmp3 array_tmp2 4 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 5 4 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk array_tmp3_g array_tmp2 kkk - 1 2 -------------------------------, array_tmp3_g : kkk - 1 kkk - array_tmp3 array_tmp2 kkk - 1 2 -------------------------------, array_tmp4 : array_tmp3 , order_d : 1, kkk - 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) (%o9) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2], array_tmp1 : array_const_2D0 array_x , 1 1 1 array_tmp2 : array_const_3D0 + array_tmp1 , array_tmp3 : sinh(array_tmp2 ), 1 1 1 1 1 array_tmp3_g : cosh(array_tmp2 ), array_tmp4 : 1 1 1 array_tmp3 + array_const_0D0 , if not array_y_set_initial 1 1 1, 2 then (if 1 <= glob_max_terms then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(0, 1), array_y : temporary, 1 2 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 2 glob_h array_y_higher : temporary)), kkk : 2, 2, 1 array_tmp1 : array_const_2D0 array_x , array_tmp2 : array_tmp1 , 2 1 2 2 2 array_tmp3_g array_tmp2 1 2 array_tmp3 : -------------------------, 2 1 array_tmp3 array_tmp2 1 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 2 1 2 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 3 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(1, 2), 2 array_y : temporary, array_y_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp3_g array_tmp2 2 2 array_tmp3 : -------------------------, 3 2 array_tmp3 array_tmp2 2 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 3 2 3 3 if not array_y_set_initial then (if 3 <= glob_max_terms 1, 4 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(2, 3), 3 array_y : temporary, array_y_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp3_g array_tmp2 3 2 array_tmp3 : -------------------------, 4 3 array_tmp3 array_tmp2 3 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 4 3 4 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 5 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(3, 4), 4 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp3_g array_tmp2 4 2 array_tmp3 : -------------------------, 5 4 array_tmp3 array_tmp2 4 2 array_tmp3_g : -----------------------, array_tmp4 : array_tmp3 , 5 4 5 5 if not array_y_set_initial then (if 5 <= glob_max_terms 1, 6 then (temporary : array_tmp4 expt(glob_h, 1) factorial_3(4, 5), 5 array_y : temporary, array_y_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp3 : kkk array_tmp3_g array_tmp2 kkk - 1 2 -------------------------------, array_tmp3_g : kkk - 1 kkk - array_tmp3 array_tmp2 kkk - 1 2 -------------------------------, array_tmp4 : array_tmp3 , order_d : 1, kkk - 1 kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp4 expt(glob_h, order_d) kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y : temporary, array_y_higher : temporary, order_d + kkk 1, order_d + kkk term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) temporary convfp(adj2) and (term >= 1) do (temporary : ----------------------, glob_h array_y_higher : temporary, adj2 : 1 + adj2, term : term - 1))), adj2, term kkk : 1 + kkk)) log(x) (%i10) log10(x) := --------- log(10.0) log(x) (%o10) log10(x) := --------- log(10.0) (%i11) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o11) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i12) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o12) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i13) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o13) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i14) 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)) (%o14) 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)) (%i15) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o15) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i16) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o16) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i17) dump_series(iolevel, dump_label, series_name, array_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 (%o17) dump_series(iolevel, dump_label, series_name, array_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 (%i18) dump_series_2(iolevel, dump_label, series_name, 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 (%o18) dump_series_2(iolevel, dump_label, series_name, 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 (%i19) 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)) (%o19) 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)) (%i20) logitem_time(fd, secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_minute min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, "")) (%o20) logitem_time(fd, secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_minute min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_minute, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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, "")) (%i21) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%")) (%o21) omniout_timestr(secs_in) := block([cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int], secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_minute) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_minute), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif 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~%")) (%i22) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_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 : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o23) att(mmm_att, array_aa, array_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 : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i24) 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 (%o24) 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 (%i25) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o25) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i26) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o26) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i27) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o27) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i28) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 rel_error then (good_digits : - floor(log10(---------)), 100.0 printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%o28) logitem_good_digits(file, rel_error) := block([good_digits], printf(file, ""), if rel_error # - 1.0 then (if rel_error # 0.0 rel_error then (good_digits : - floor(log10(---------)), 100.0 printf(file, "~d", good_digits)) else (good_digits : 16, printf(file, "~d", good_digits))) else printf(file, "Unknown"), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) 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, "")) (%o31) 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, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) not_reached_end(x, x_end) := block([ret], if (glob_neg_h and (x > x_end)) or ((not glob_neg_h) and (x < x_end)) then ret : true else ret : false, ret) (%o34) not_reached_end(x, x_end) := block([ret], if (glob_neg_h and (x > x_end)) or ((not glob_neg_h) and (x < x_end)) then ret : true else ret : false, ret) (%i35) 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()) (%o35) 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()) (%i36) 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 (%o36) 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 (%i37) 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 (%o37) 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 (%i38) factorial_2(nnn) := block([ret], ret : nnn!) (%o38) factorial_2(nnn) := block([ret], ret : nnn!) (%i39) 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 (%o39) 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 (%i40) 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) (%o40) 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) (%i41) convfp(mmm) := mmm (%o41) convfp(mmm) := mmm (%i42) convfloat(mmm) := mmm (%o42) convfloat(mmm) := mmm (%i43) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o43) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i44) arcsin(x) := asin(x) (%o44) arcsin(x) := asin(x) (%i45) arccos(x) := acos(x) (%o45) arccos(x) := acos(x) (%i46) arctan(x) := atan(x) (%o46) arctan(x) := atan(x) (%i47) omniabs(x) := abs(x) (%o47) omniabs(x) := abs(x) y (%i48) expt(x, y) := x y (%o48) expt(x, y) := x cosh(3.0 + 2.0 x) (%i49) exact_soln_y(x) := ----------------- 2.0 cosh(3.0 + 2.0 x) (%o49) exact_soln_y(x) := ----------------- 2.0 (%i50) 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], define_variable(DEBUGL, 3, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_log10abserr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_html_log, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(days_in_year, 365, fixnum), define_variable(djd_debug, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_percent_done, 0.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(centuries_in_millinium, 10, fixnum), define_variable(djd_debug2, true, boolean), define_variable(glob_max_hours, 0.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(sec_in_minute, 60, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_next_display, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_h, 0.1, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_display_interval, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(years_in_century, 100, fixnum), define_variable(min_in_hour, 60, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_neg_h, false, boolean), define_variable(hours_in_day, 24, fixnum), define_variable(glob_log10normmin, 0.1, 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/lin_sinhpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.0,"), omniout_str(ALWAYS, "x_end : 10.0 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.005 ,"), omniout_str(ALWAYS, "glob_display_interval : 0.1,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10000,"), omniout_str(ALWAYS, "glob_max_minutes : 10,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, " (cosh(2.0*x+3.0)/2.0) "), omniout_str(ALWAYS, ");"), 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_m1, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp3_g, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_g : 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_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 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_y_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 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_norms : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, 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, 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 <= 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 <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_tmp3_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 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_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 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_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 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_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 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_const_3D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, 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_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 10, glob_h : 0.005, glob_display_interval : 0.1, glob_look_poles : true, glob_max_iter : 10000, glob_max_minutes : 10, 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, if glob_html_log 1, 30 then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), 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 not_reached_end(array_x , x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-09-20T23:54:43-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_sinh"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"), 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_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 130 "), logitem_str(html_log_file, "lin_sinh diffeq.max"), logitem_str(html_log_file, "lin_sinh maxima results"), logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o50) 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], define_variable(DEBUGL, 3, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(ALWAYS, 1, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_start, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_log10abserr, 0.0, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_almost_1, 0.999, float), define_variable(glob_html_log, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(days_in_year, 365, fixnum), define_variable(djd_debug, true, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_percent_done, 0.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_warned, false, boolean), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(centuries_in_millinium, 10, fixnum), define_variable(djd_debug2, true, boolean), define_variable(glob_max_hours, 0.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(sec_in_minute, 60, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_next_display, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_h, 0.1, float), define_variable(glob_disp_incr, 0.1, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_display_interval, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(years_in_century, 100, fixnum), define_variable(min_in_hour, 60, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_neg_h, false, boolean), define_variable(hours_in_day, 24, fixnum), define_variable(glob_log10normmin, 0.1, 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/lin_sinhpostode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.0,"), omniout_str(ALWAYS, "x_end : 10.0 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.005 ,"), omniout_str(ALWAYS, "glob_display_interval : 0.1,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10000,"), omniout_str(ALWAYS, "glob_max_minutes : 10,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y (x) := ("), omniout_str(ALWAYS, " (cosh(2.0*x+3.0)/2.0) "), omniout_str(ALWAYS, ");"), 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_m1, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_tmp3_g, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_y_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y_higher, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 2, 1 + max_terms), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_y_higher_work2, 1 + 2, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), term : 1, while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_last_rel_error : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_fact_1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_x : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3_g : 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_tmp0 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_tmp3 : 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_y_init : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_pole : 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_norms : 0.0, term : 1 + term), ord : 1, term while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= max_terms do (term : 1, while term <= max_terms do (array_fact_2 : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, term : 1 + term), ord, 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, 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 <= 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 <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_tmp3_g, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3_g : 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_y, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y : 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_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 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_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 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_const_3D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_3D0 : 0.0, term : 1 + term), term array_const_3D0 : 3.0, 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_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.0, iiif, jjjf x_end : 10.0, array_y_init : exact_soln_y(x_start), glob_h : 1.0E-5, 1 + 0 glob_look_poles : true, glob_max_iter : 10, glob_h : 0.005, glob_display_interval : 0.1, glob_look_poles : true, glob_max_iter : 10000, glob_max_minutes : 10, 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, if glob_html_log 1, 30 then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, glob_next_display : x_start, order_diff : 1, term_no : 1, 2 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), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), 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 not_reached_end(array_x , x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (if reached_interval () then (omniout_str(INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop")), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, atomall(), if glob_look_poles then check_for_pole(), if reached_interval() then glob_next_display : glob_display_interval + glob_next_display, array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 1, ord : 2, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 2, iii array_y_higher 2, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, ord : 1, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 1, iii array_y_higher 1, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y_higher_work + temp_sum, ord, iii iii : iii - 1), array_y_higher_work2 : ord, calc_term temp_sum expt(glob_h, calc_term - 1) ------------------------------------, term_no : glob_max_terms, factorial_1(calc_term - 1) while term_no >= 1 do (array_y : array_y_higher_work2 , term_no 1, term_no ord : 1, while ord <= order_diff do (array_y_higher : ord, term_no array_y_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-09-20T23:54:43-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "lin_sinh"), logitem_str(html_log_file, "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;"), 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_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 130 "), logitem_str(html_log_file, "lin_sinh diffeq.max"), logitem_str(html_log_file, "lin_sinh maxima results"), logitem_str(html_log_file, "c c++ Maple and Maxima"), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i51) main() "##############ECHO OF PROBLEM#################" "##############temp/lin_sinhpostode.ode#################" "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.0," "x_end : 10.0 ," "array_y_init[0 + 1] : exact_soln_y(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 10," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.005 ," "glob_display_interval : 0.1," "glob_look_poles : true," "glob_max_iter : 10000," "glob_max_minutes : 10," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (" " (cosh(2.0*x+3.0)/2.0) " ");" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.0 " " y[1] (analytic) = 5.033830997888883 " " y[1] (numeric) = 5.033830997888883 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10000000000000002 " " y[1] (analytic) = 6.14332310027193 " " y[1] (numeric) = 6.143323100277304 " " absolute error = 5.374367617605458000000000000E-12 " " relative error = 8.74830695030115700000000000E-11 "%" Correct digits = 13 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.2000000000000001 " " y[1] (analytic) = 7.499368329339338 " " y[1] (numeric) = 7.499368329351276 " " absolute error = 1.193800613918938300000000000E-11 " " relative error = 1.5918682234189010000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.30000000000000016 " " y[1] (analytic) = 9.156389541531325 " " y[1] (numeric) = 9.156389541551276 " " absolute error = 1.995026366330421300000000000E-11 " " relative error = 2.17883518092085300000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.40000000000000024 " " y[1] (analytic) = 11.180888816289254 " " y[1] (numeric) = 11.180888816318989 " " absolute error = 2.97344371347207900000000000E-11 " " relative error = 2.65939833793903570000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.5000000000000003 " " y[1] (analytic) = 13.654116418008256 " " y[1] (numeric) = 13.654116418049934 " " absolute error = 4.167866052284807700000000000E-11 " " relative error = 3.05246119535633740000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.6000000000000004 " " y[1] (analytic) = 16.675331654436423 " " y[1] (numeric) = 16.675331654492695 " " absolute error = 5.627143195852113000000000000E-11 " " relative error = 3.37453150106014730000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.7000000000000005 " " y[1] (analytic) = 20.365786501217823 " " y[1] (numeric) = 20.365786501291915 " " absolute error = 7.40918437713844500000000000E-11 " " relative error = 3.6380546249443370000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.8000000000000006 " " y[1] (analytic) = 24.873591869419645 " " y[1] (numeric) = 24.873591869515497 " " absolute error = 9.58522150540375200000000000E-11 " " relative error = 3.85357352316619660000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.9000000000000007 " " y[1] (analytic) = 30.379661816446024 " " y[1] (numeric) = 30.379661816568454 " " absolute error = 1.22430066085144060000000000E-10 " " relative error = 4.03000095342952670000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.0000000000000007 " " y[1] (analytic) = 37.10497426239399 " " y[1] (numeric) = 37.10497426254888 " " absolute error = 1.54891210968344240000000000E-10 " " relative error = 4.17440556279611740000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.1049999999999984 " " y[1] (analytic) = 45.77487996685133 " " y[1] (numeric) = 45.77487996704825 " " absolute error = 1.96919813788554170000000000E-10 " " relative error = 4.3019187364588840000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.2049999999999963 " " y[1] (analytic) = 55.90901483018895 " " y[1] (numeric) = 55.90901483043502 " " absolute error = 2.4606805482108030000000000E-10 " " relative error = 4.4012232297145040000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.3049999999999942 " " y[1] (analytic) = 68.28697476852786 " " y[1] (numeric) = 68.28697476883394 " " absolute error = 3.06087599710735960000000000E-10 " " relative error = 4.48237164918024460000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.404999999999992 " " y[1] (analytic) = 83.40553077615874 " " y[1] (numeric) = 83.40553077653817 " " absolute error = 3.7942982089589350000000000E-10 " " relative error = 4.54921654913024700000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.50499999999999 " " y[1] (analytic) = 101.87144359051845 " " y[1] (numeric) = 101.87144359098743 " " absolute error = 4.6897241645638130000000000E-10 " " relative error = 4.6035709314325480000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.6049999999999878 " " y[1] (analytic) = 124.4258151310648 " " y[1] (numeric) = 124.4258151316431 " " absolute error = 5.7831073263514550000000000E-10 " " relative error = 4.64783559606162100000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.7049999999999856 " " y[1] (analytic) = 151.9738315214897 " " y[1] (numeric) = 151.97383152220164 " " absolute error = 7.11935399522190000000000E-10 " " relative error = 4.684592027420980700000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.8049999999999835 " " y[1] (analytic) = 185.62109138718702 " " y[1] (numeric) = 185.62109138806213 " " absolute error = 8.7510443336213940000000000E-10 " " relative error = 4.7144665879415560000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 1.9049999999999814 " " y[1] (analytic) = 226.71797741010968 " " y[1] (numeric) = 226.71797741118402 " " absolute error = 1.0743406164692715000000000E-9 " " relative error = 4.738665317774509700000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.0049999999999795 " " y[1] (analytic) = 276.9138519273116 " " y[1] (numeric) = 276.91385192862936 " " absolute error = 1.3177441360312514000000000E-9 " " relative error = 4.758679014645869600000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.1049999999999773 " " y[1] (analytic) = 338.2232516328377 " " y[1] (numeric) = 338.2232516344526 " " absolute error = 1.6149215298355557000000000E-9 " " relative error = 4.7747206084715110000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.204999999999975 " " y[1] (analytic) = 413.1067380087739 " " y[1] (numeric) = 413.1067380107519 " " absolute error = 1.9779804460995365000000000E-9 " " relative error = 4.7880614478322225000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.304999999999973 " " y[1] (analytic) = 504.5696482971407 " " y[1] (numeric) = 504.56964829956223 " " absolute error = 2.4215296434704214000000000E-9 " " relative error = 4.7991979930675190000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.404999999999971 " " y[1] (analytic) = 616.2827102358702 " " y[1] (numeric) = 616.2827102388333 " " absolute error = 2.9630200515384786000000000E-9 " " relative error = 4.8078909278575090000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.504999999999969 " " y[1] (analytic) = 752.7293612517285 " " y[1] (numeric) = 752.7293612553528 " " absolute error = 3.624336386565119000000000E-9 " " relative error = 4.8149262844458973000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.6049999999999667 " " y[1] (analytic) = 919.3856845466685 " " y[1] (numeric) = 919.385684551101 " " absolute error = 4.432536115928087400000000E-9 " " relative error = 4.821193314657369300000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.7049999999999645 " " y[1] (analytic) = 1122.9401835445565 " " y[1] (numeric) = 1122.9401835499757 " " absolute error = 5.419224180513993000000000E-9 " " relative error = 4.8259241764848354000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.8049999999999624 " " y[1] (analytic) = 1371.5622150185 " " y[1] (numeric) = 1371.5622150251247 " " absolute error = 6.624759407714009000000000E-9 " " relative error = 4.8300830506800260000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 2.9049999999999603 " " y[1] (analytic) = 1675.2298540627105 " " y[1] (numeric) = 1675.2298540708077 " " absolute error = 8.09723132988438000000000E-9 " " relative error = 4.8335046741479980000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.004999999999958 " " y[1] (analytic) = 2046.130349281431 " " y[1] (numeric) = 2046.130349291327 " " absolute error = 9.895984476315789000000000E-9 " " relative error = 4.8364389296073457000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.104999999999956 " " y[1] (analytic) = 2499.149239867758 " " y[1] (numeric) = 2499.1492398798514 " " absolute error = 1.209355104947462700000000E-8 " " relative error = 4.839067173961390500000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.204999999999954 " " y[1] (analytic) = 3052.467764558131 " " y[1] (numeric) = 3052.4677645729075 " " absolute error = 1.477656041970476500000000E-8 " " relative error = 4.8408571554051410000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.3049999999999518 " " y[1] (analytic) = 3728.2925385814883 " " y[1] (numeric) = 3728.292538599542 " " absolute error = 1.805346983019262600000000E-8 " " relative error = 4.8422889683065135000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.4049999999999496 " " y[1] (analytic) = 4553.746783101117 " " y[1] (numeric) = 4553.746783123170 " " absolute error = 2.205342752858996400000000E-8 " " relative error = 4.8429191562495060000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.5049999999999475 " " y[1] (analytic) = 5561.958875316023 " " y[1] (numeric) = 5561.958875342965 " " absolute error = 2.694196155061945300000000E-8 " " relative error = 4.8439699312031764000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.6049999999999454 " " y[1] (analytic) = 6793.391906559554 " " y[1] (numeric) = 6793.391906592466 " " absolute error = 3.291188477305695400000000E-8 " " relative error = 4.8446910211786753000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.7049999999999432 " " y[1] (analytic) = 8297.467608230148 " " y[1] (numeric) = 8297.467608270352 " " absolute error = 4.02033037971705200000000E-8 " " relative error = 4.8452498636202440000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.804999999999941 " " y[1] (analytic) = 10134.549819403834 " " y[1] (numeric) = 10134.549819452946 " " absolute error = 4.911271389573812500000000E-8 " " relative error = 4.8460676370356220000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 3.904999999999939 " " y[1] (analytic) = 12378.367099648152 " " y[1] (numeric) = 12378.367099708143 " " absolute error = 5.99902705289423500000000E-8 " " relative error = 4.8463799825945975000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.004999999999937 " " y[1] (analytic) = 15118.971714996147 " " y[1] (numeric) = 15118.971715069421 " " absolute error = 7.32743501430377400000000E-8 " " relative error = 4.846516781981849400000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.104999999999935 " " y[1] (analytic) = 18466.35375157721 " " y[1] (numeric) = 18466.353751666717 " " absolute error = 8.95051925908774100000000E-8 " " relative error = 4.8469337149589030000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.204999999999933 " " y[1] (analytic) = 22554.855403974852 " " y[1] (numeric) = 22554.855404084192 " " absolute error = 1.09339453047141430000000E-7 " " relative error = 4.8477124365812820000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.30499999999993 " " y[1] (analytic) = 27548.562599202767 " " y[1] (numeric) = 27548.562599336317 " " absolute error = 1.33550202008336780000000E-7 " " relative error = 4.8478101725787180000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.404999999999928 " " y[1] (analytic) = 33647.89034110066 " " y[1] (numeric) = 33647.89034126379 " " absolute error = 1.6312696970999240000000E-7 " " relative error = 4.8480593599276550000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.504999999999926 " " y[1] (analytic) = 41097.62606814316 " " y[1] (numeric) = 41097.62606834241 " " absolute error = 1.99252099264413120000000E-7 " " relative error = 4.8482629856536520000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.604999999999924 " " y[1] (analytic) = 50196.753832852766 " " y[1] (numeric) = 50196.753833096125 " " absolute error = 2.43358954321593050000000E-7 " " relative error = 4.8481014356414320000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.704999999999922 " " y[1] (analytic) = 61310.45358163182 " " y[1] (numeric) = 61310.45358192904 " " absolute error = 2.97222868539392950000000E-7 " " relative error = 4.8478334635651570000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.80499999999992 " " y[1] (analytic) = 74884.75710824537 " " y[1] (numeric) = 74884.75710860838 " " absolute error = 3.6301207728683950000000E-7 " " relative error = 4.8476097313383576000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 4.904999999999918 " " y[1] (analytic) = 91464.44887582879 " " y[1] (numeric) = 91464.44887627217 " " absolute error = 4.4338230509310960000000E-7 " " relative error = 4.847591720527840700000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.0049999999999155 " " y[1] (analytic) = 111714.9301302615 " " y[1] (numeric) = 111714.93013080304 " " absolute error = 5.415349733084440000000E-7 " " relative error = 4.8474717987739420000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.104999999999913 " " y[1] (analytic) = 136448.9237885462 " " y[1] (numeric) = 136448.92378920768 " " absolute error = 6.6147185862064360000000E-7 " " relative error = 4.8477616404341983000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.204999999999911 " " y[1] (analytic) = 166659.091863132 " " y[1] (numeric) = 166659.09186393992 " " absolute error = 8.0792233347892760000000E-7 " " relative error = 4.847754325593170400000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.304999999999910 " " y[1] (analytic) = 203557.87447394666 " " y[1] (numeric) = 203557.8744749335 " " absolute error = 9.8682357929646970000000E-7 " " relative error = 4.8478772037029350000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.404999999999907 " " y[1] (analytic) = 248626.14932757537 " " y[1] (numeric) = 248626.14932878068 " " absolute error = 1.2053060345351696000000E-6 " " relative error = 4.8478651091005254000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.504999999999905 " " y[1] (analytic) = 303672.6645393403 " " y[1] (numeric) = 303672.6645408124 " " absolute error = 1.4720717445015907000000E-6 " " relative error = 4.8475609312239770000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.604999999999903 " " y[1] (analytic) = 370906.6300461138 " " y[1] (numeric) = 370906.63004791184 " " absolute error = 1.7980346456170082000000E-6 " " relative error = 4.8476745896762846000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.704999999999900 " " y[1] (analytic) = 453026.38095814735 " " y[1] (numeric) = 453026.38096034364 " " absolute error = 2.196291461586952200000E-6 " " relative error = 4.8480431910870453000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.8049999999998985 " " y[1] (analytic) = 553327.6712215431 " " y[1] (numeric) = 553327.6712242257 " " absolute error = 2.682558260858059000000E-6 " " relative error = 4.8480464657333355000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 5.904999999999896 " " y[1] (analytic) = 675835.943796288 " " y[1] (numeric) = 675835.9437995644 " " absolute error = 3.2763928174972534000000E-6 " " relative error = 4.8479114607210530000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.004999999999894 " " y[1] (analytic) = 825467.885816527 " " y[1] (numeric) = 825467.885820529 " " absolute error = 4.002009518444538000000E-6 " " relative error = 4.8481710642030310000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.104999999999892 " " y[1] (analytic) = 1008228.7525089153 " " y[1] (numeric) = 1008228.7525138034 " " absolute error = 4.888162948191166000000E-6 " " relative error = 4.8482677527567760000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.20499999999989 " " y[1] (analytic) = 1231453.379170746 " " y[1] (numeric) = 1231453.379176717 " " absolute error = 5.970941856503487000000E-6 " " relative error = 4.848695011519060000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.304999999999888 " " y[1] (analytic) = 1504100.553864784 " " y[1] (numeric) = 1504100.5538720763 " " absolute error = 7.292255759239197000000E-6 " " relative error = 4.8482501655236787000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.404999999999886 " " y[1] (analytic) = 1837112.5650406617 " " y[1] (numeric) = 1837112.5650495682 " " absolute error = 8.906470611691475000000E-6 " " relative error = 4.8480810491295850000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.5049999999998835 " " y[1] (analytic) = 2243854.3539913455 " " y[1] (numeric) = 2243854.3540022243 " " absolute error = 1.087877899408340500000E-5 " " relative error = 4.8482554024651114000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.604999999999881 " " y[1] (analytic) = 2740649.8968747123 " " y[1] (numeric) = 2740649.896888 " " absolute error = 1.32876448333263400000E-5 " " relative error = 4.848355438788020000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.704999999999880 " " y[1] (analytic) = 3347437.343194135 " " y[1] (numeric) = 3347437.343210365 " " absolute error = 1.623015850782394400000E-5 " " relative error = 4.8485324275964120000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.804999999999877 " " y[1] (analytic) = 4088569.2037456427 " " y[1] (numeric) = 4088569.203765466 " " absolute error = 1.98232010006904600000E-5 " " relative error = 4.8484445322656927000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 6.904999999999875 " " y[1] (analytic) = 4993789.70238363 " " y[1] (numeric) = 4993789.702407842 " " absolute error = 2.421159297227859500000E-5 " " relative error = 4.8483405219731110000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.004999999999873 " " y[1] (analytic) = 6099428.516163188 " " y[1] (numeric) = 6099428.516192760 " " absolute error = 2.957135438919067400000E-5 " " relative error = 4.8482172240937044000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.104999999999870 " " y[1] (analytic) = 7449858.812842474 " " y[1] (numeric) = 7449858.812878595 " " absolute error = 3.61204147338867200000E-5 " " relative error = 4.8484697014150620000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.204999999999869 " " y[1] (analytic) = 9099278.101909604 " " y[1] (numeric) = 9099278.10195372 " " absolute error = 4.41167503595352200000E-5 " " relative error = 4.8483791643071916000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.3049999999998665 " " y[1] (analytic) = 11113883.370938776 " " y[1] (numeric) = 11113883.370992657 " " absolute error = 5.388073623180389000000E-5 " " relative error = 4.8480566543188996000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.404999999999864 " " y[1] (analytic) = 13574527.803135006 " " y[1] (numeric) = 13574527.803200817 " " absolute error = 6.58109784126281700000E-5 " " relative error = 4.8481228494319550000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.504999999999862 " " y[1] (analytic) = 16579965.699470935 " " y[1] (numeric) = 16579965.699551318 " " absolute error = 8.03824514150619500000E-5 " " relative error = 4.8481675337619640000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.60499999999986 " " y[1] (analytic) = 20250815.83553472 " " y[1] (numeric) = 20250815.835632905 " " absolute error = 9.81837511062622100000E-5 " " relative error = 4.8483849689638775000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.704999999999858 " " y[1] (analytic) = 24734402.316515647 " " y[1] (numeric) = 24734402.316635564 " " absolute error = 1.19917094707489010000E-4 " " relative error = 4.8481905150955684000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.804999999999856 " " y[1] (analytic) = 30210667.210835375 " " y[1] (numeric) = 30210667.210981846 " " absolute error = 1.46470963954925540000E-4 " " relative error = 4.8483194009827160000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 7.904999999999854 " " y[1] (analytic) = 36899392.25717317 " " y[1] (numeric) = 36899392.25735208 " " absolute error = 1.78903341293334960000E-4 " " relative error = 4.8484088856112934000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.004999999999852 " " y[1] (analytic) = 45069019.47734514 " " y[1] (numeric) = 45069019.477563664 " " absolute error = 2.18525528907775880000E-4 " " relative error = 4.8486861139196114000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.104999999999867 " " y[1] (analytic) = 55047424.697205484 " " y[1] (numeric) = 55047424.69747059 " " absolute error = 2.65106558799743650000E-4 " " relative error = 4.8159666007627410000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.204999999999883 " " y[1] (analytic) = 67235076.35478313 " " y[1] (numeric) = 67235076.35510515 " " absolute error = 3.22014093399047850000E-4 " " relative error = 4.789376481107240300000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.304999999999898 " " y[1] (analytic) = 82121107.70484431 " " y[1] (numeric) = 82121107.70523578 " " absolute error = 3.9146840572357180000E-4 " " relative error = 4.7669645072320320000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.404999999999914 " " y[1] (analytic) = 100302947.45386834 " " y[1] (numeric) = 100302947.45434473 " " absolute error = 4.76390123367309570000E-4 " " relative error = 4.749512705859540400000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.50499999999993 " " y[1] (analytic) = 122510296.67175321 " " y[1] (numeric) = 122510296.67233333 " " absolute error = 5.8011710643768310000E-4 " " relative error = 4.735251829419810400000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.604999999999945 " " y[1] (analytic) = 149634414.25790474 " " y[1] (numeric) = 149634414.25861153 " " absolute error = 7.067918777465820000E-4 " " relative error = 4.7234580444066820000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.704999999999961 " " y[1] (analytic) = 182763886.290292 " " y[1] (numeric) = 182763886.29115358 " " absolute error = 8.6158514022827150000E-4 " " relative error = 4.7141979617339586000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.804999999999977 " " y[1] (analytic) = 223228314.80704126 " " y[1] (numeric) = 223228314.80809182 " " absolute error = 1.0505616664886475000E-3 " " relative error = 4.7062204783329290000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 8.899999999999991 " " y[1] (analytic) = 269938749.8661289 " " y[1] (numeric) = 269938749.86739755 " " absolute error = 1.268625259399414000E-3 " " relative error = 4.6996782048837560000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.000000000000007 " " y[1] (analytic) = 329703933.62080836 " " y[1] (numeric) = 329703933.62235624 " " absolute error = 1.5478730201721191000E-3 " " relative error = 4.6947362840757730000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.100000000000023 " " y[1] (analytic) = 402701293.9007255 " " y[1] (numeric) = 402701293.9026142 " " absolute error = 1.8886923789978027000E-3 " " relative error = 4.6900578855934990000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.200000000000038 " " y[1] (analytic) = 491860471.0850307 " " y[1] (numeric) = 491860471.0873358 " " absolute error = 2.305150032043457000E-3 " " relative error = 4.6865933888900635000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.300000000000054 " " y[1] (analytic) = 600759736.0132357 " " y[1] (numeric) = 600759736.0160491 " " absolute error = 2.8134584426879883000E-3 " " relative error = 4.6831674528633910000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.40000000000007 " " y[1] (analytic) = 733769598.5581645 " " y[1] (numeric) = 733769598.5615993 " " absolute error = 3.43477725982666000E-3 " " relative error = 4.6810024108056475000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.500000000000085 " " y[1] (analytic) = 896228211.5330508 " " y[1] (numeric) = 896228211.5372441 " " absolute error = 4.193305969238281000E-3 " " relative error = 4.6788372819299967000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.600000000000101 " " y[1] (analytic) = 1094655609.5074584 " " y[1] (numeric) = 1094655609.5125785 " " absolute error = 5.120038986206055000E-3 " " relative error = 4.6773057587580650000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.700000000000117 " " y[1] (analytic) = 1337015380.6879535 " " y[1] (numeric) = 1337015380.6942053 " " absolute error = 6.251811981201172000E-3 " " relative error = 4.6759461944142616000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.800000000000132 " " y[1] (analytic) = 1633034273.674887 " " y[1] (numeric) = 1633034273.6825209 " " absolute error = 7.63392448425293000E-3 " " relative error = 4.6746872416057644000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 9.900000000000148 " " y[1] (analytic) = 1994592566.0366588 " " y[1] (numeric) = 1994592566.0459812 " " absolute error = 9.322404861450195000E-3 " " relative error = 4.6738391690560716000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 10.000000000000163 " " y[1] (analytic) = 2436200861.563022 " " y[1] (numeric) = 2436200861.574407 " " absolute error = 1.138496398925781200E-2 " " relative error = 4.6732452027594423000000000E-10 "%" Correct digits = 12 h = 5.000E-3 " " "Finished!" "diff ( y , x , 1 ) = sinh (2.0 * x + 3.0) ;" Iterations = 2000 "Total Elapsed Time "= 7 Minutes 22 Seconds "Elapsed Time(since restart) "= 7 Minutes 22 Seconds "Time to Timeout "= 2 Minutes 37 Seconds Percent Done = 100.05000000000163 "%" (%o51) true (%o51) diffeq.max