(%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) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "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, " "))) (%o3) display_alot(iter) := block([abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no], if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "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, " "))) (%i4) 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 (%o4) 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 (%i5) 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, "%")) (%o5) 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, "%")) (%i6) 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 - 3 + 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 - 3 + 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) 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 glob_display_flag 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 glob_display_flag 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 display_pole()) (%o6) 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 - 3 + 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 - 3 + 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) 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 glob_display_flag 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 glob_display_flag 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 display_pole()) (%i7) 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 (%o7) 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 (%i8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2], array_tmp1 : array_y_higher , if not array_y_set_initial 1 2, 1 1, 4 then (if 1 <= glob_max_terms then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(0, 3), array_y : temporary, 1 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 3 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 2 glob_h array_y_higher : temporary)), kkk : 2, array_tmp1 : array_y_higher , 4, 1 2 2, 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 5 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(1, 4), 2 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y_higher : temporary, glob_h 2, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, glob_h 3, 3 temporary 4.0 temporary : -------------, array_y_higher : temporary)), kkk : 3, glob_h 4, 2 array_tmp1 : array_y_higher , if not array_y_set_initial 3 2, 3 1, 6 then (if 3 <= glob_max_terms then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(2, 5), array_y : temporary, 3 6 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 5 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 4 glob_h array_y_higher : temporary)), kkk : 4, array_tmp1 : array_y_higher , 4, 3 4 2, 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 7 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(3, 6), 4 array_y : temporary, array_y_higher : temporary, 7 1, 7 temporary 2.0 temporary : -------------, array_y_higher : temporary, glob_h 2, 6 temporary 3.0 temporary : -------------, array_y_higher : temporary, glob_h 3, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary)), kkk : 5, glob_h 4, 4 array_tmp1 : array_y_higher , if not array_y_set_initial 5 2, 5 1, 8 then (if 5 <= glob_max_terms then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(4, 7), array_y : temporary, 5 8 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 8 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 7 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 6 glob_h array_y_higher : temporary)), kkk : 6, 4, 5 while kkk <= glob_max_terms do (array_tmp1 : array_y_higher , kkk 2, kkk order_d : 3, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp3 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)) (%o8) atomall() := block([kkk, order_d, adj2, temporary, term, temp, temp2], array_tmp1 : array_y_higher , if not array_y_set_initial 1 2, 1 1, 4 then (if 1 <= glob_max_terms then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(0, 3), array_y : temporary, 1 4 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 4 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 3 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 2 glob_h array_y_higher : temporary)), kkk : 2, array_tmp1 : array_y_higher , 4, 1 2 2, 2 if not array_y_set_initial then (if 2 <= glob_max_terms 1, 5 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(1, 4), 2 array_y : temporary, array_y_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y_higher : temporary, glob_h 2, 4 temporary 3.0 temporary : -------------, array_y_higher : temporary, glob_h 3, 3 temporary 4.0 temporary : -------------, array_y_higher : temporary)), kkk : 3, glob_h 4, 2 array_tmp1 : array_y_higher , if not array_y_set_initial 3 2, 3 1, 6 then (if 3 <= glob_max_terms then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(2, 5), array_y : temporary, 3 6 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 6 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 5 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 4 glob_h array_y_higher : temporary)), kkk : 4, array_tmp1 : array_y_higher , 4, 3 4 2, 4 if not array_y_set_initial then (if 4 <= glob_max_terms 1, 7 then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(3, 6), 4 array_y : temporary, array_y_higher : temporary, 7 1, 7 temporary 2.0 temporary : -------------, array_y_higher : temporary, glob_h 2, 6 temporary 3.0 temporary : -------------, array_y_higher : temporary, glob_h 3, 5 temporary 4.0 temporary : -------------, array_y_higher : temporary)), kkk : 5, glob_h 4, 4 array_tmp1 : array_y_higher , if not array_y_set_initial 5 2, 5 1, 8 then (if 5 <= glob_max_terms then (temporary : array_tmp3 expt(glob_h, 3) factorial_3(4, 7), array_y : temporary, 5 8 temporary 2.0 array_y_higher : temporary, temporary : -------------, 1, 8 glob_h temporary 3.0 array_y_higher : temporary, temporary : -------------, 2, 7 glob_h temporary 4.0 array_y_higher : temporary, temporary : -------------, 3, 6 glob_h array_y_higher : temporary)), kkk : 6, 4, 5 while kkk <= glob_max_terms do (array_tmp1 : array_y_higher , kkk 2, kkk order_d : 3, if 1 + order_d + kkk <= glob_max_terms then (if not array_y_set_initial 1, order_d + kkk array_tmp3 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) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) 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)) (%o13) 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)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) 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 (%o16) 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 (%i17) 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 (%o17) 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 (%i18) 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)) (%o18) 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)) (%i19) 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, "")) (%o19) 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, "")) (%i20) 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~%")) (%o20) 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~%")) (%i21) 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) (%o21) 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) (%i22) 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) (%o22) 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) (%i23) 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 (%o23) 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 (%i24) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o24) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i25) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o25) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i26) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o26) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i27) log_revs(file, revs) := printf(file, revs) (%o27) log_revs(file, revs) := printf(file, revs) (%i28) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o28) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i29) 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, "")) (%o29) 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, "")) (%i30) logstart(file) := printf(file, "") (%o30) logstart(file) := printf(file, "") (%i31) logend(file) := printf(file, "~%") (%o31) logend(file) := printf(file, "~%") (%i32) 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()) (%o32) 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()) (%i33) 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 (%o33) 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 (%i34) 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 (%o34) 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 (%i35) factorial_2(nnn) := block([ret], ret : nnn!) (%o35) factorial_2(nnn) := block([ret], ret : nnn!) (%i36) 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 (%o36) 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 (%i37) 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) (%o37) 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) (%i38) convfp(mmm) := mmm (%o38) convfp(mmm) := mmm (%i39) convfloat(mmm) := mmm (%o39) convfloat(mmm) := mmm (%i40) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%o40) elapsed_time_seconds() := block([t], t : elapsed_real_time(), t) (%i41) arcsin(x) := asin(x) (%o41) arcsin(x) := asin(x) (%i42) arccos(x) := acos(x) (%o42) arccos(x) := acos(x) (%i43) arctan(x) := atan(x) (%o43) arctan(x) := atan(x) (%i44) omniabs(x) := abs(x) (%o44) omniabs(x) := abs(x) y (%i45) expt(x, y) := x y (%o45) expt(x, y) := x (%i46) exact_soln_y(x) := 2.0 - cos(x) (%o46) exact_soln_y(x) := 2.0 - cos(x) (%i47) exact_soln_yp(x) := sin(x) (%o47) exact_soln_yp(x) := sin(x) (%i48) exact_soln_ypp(x) := cos(x) (%o48) exact_soln_ypp(x) := cos(x) (%i49) exact_soln_yppp(x) := - sin(x) (%o49) exact_soln_yppp(x) := - sin(x) (%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(ALWAYS, 1, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(hours_in_day, 24, fixnum), define_variable(min_in_hour, 60, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(centuries_in_millinium, 10, fixnum), define_variable(years_in_century, 100, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(djd_debug, true, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_almost_1, 0.999, float), define_variable(glob_html_log, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_start, 0, fixnum), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_disp_incr, 0.1, float), define_variable(sec_in_minute, 60, fixnum), define_variable(djd_debug2, true, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_h, 0.1, float), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_not_yet_finished, true, boolean), define_variable(days_in_year, 365, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/diff2postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"), omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "glob_max_minutes : 1,"), 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, " (2.0 - cos(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_yp (x) := ("), omniout_str(ALWAYS, " ( sin(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_ypp (x) := ("), omniout_str(ALWAYS, " ( cos(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_yppp (x) := ("), omniout_str(ALWAYS, " ( -sin(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_norms, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_m1, 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_y_init, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y_higher_work2, 1 + 4, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 4, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 4, 1 + max_terms), term : 1, while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 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_m1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), ord : 1, term while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 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 <= 4 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 4 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 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 <= 4 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term), term array_const_3 : 3, 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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 array_y_init : exact_soln_yp(x_start), 1 + 1 array_y_init : exact_soln_ypp(x_start), glob_h : 0.001, 1 + 2 glob_look_poles : true, glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 1, 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), chk_data(), array_y_set_initial : true, array_y_set_initial : true, 1, 1 1, 2 array_y_set_initial : true, array_y_set_initial : false, 1, 3 1, 4 array_y_set_initial : false, array_y_set_initial : false, 1, 5 1, 6 array_y_set_initial : false, array_y_set_initial : false, 1, 7 1, 8 array_y_set_initial : false, array_y_set_initial : false, 1, 9 1, 10 array_y_set_initial : false, array_y_set_initial : false, 1, 11 1, 12 array_y_set_initial : false, array_y_set_initial : false, 1, 13 1, 14 array_y_set_initial : false, array_y_set_initial : false, 1, 15 1, 16 array_y_set_initial : false, array_y_set_initial : false, 1, 17 1, 18 array_y_set_initial : false, array_y_set_initial : false, 1, 19 1, 20 array_y_set_initial : false, array_y_set_initial : false, 1, 21 1, 22 array_y_set_initial : false, array_y_set_initial : false, 1, 23 1, 24 array_y_set_initial : false, array_y_set_initial : false, 1, 25 1, 26 array_y_set_initial : false, array_y_set_initial : false, 1, 27 1, 28 array_y_set_initial : false, array_y_set_initial : false, 1, 29 1, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 3, 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 (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (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(), array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 3, ord : 4, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 4, iii array_y_higher 4, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, calc_term : 3, factorial_1(calc_term - 1) 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 : 3, 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 : 2, calc_term : 2, factorial_1(calc_term - 1) 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 : 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 : 2, calc_term : 1, factorial_1(calc_term - 1) 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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 , 3 ) = m1 * diff ( y , x , 1 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-08-21T17:31:46-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "diff2"), logitem_str(html_log_file, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_good_digits), logitem_integer(html_log_file, glob_max_terms), 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, " 123 "), logitem_str(html_log_file, "diff2 diffeq.max"), logitem_str(html_log_file, "diff2 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(ALWAYS, 1, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(INFO, 2, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_warned2, false, boolean), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(hours_in_day, 24, fixnum), define_variable(min_in_hour, 60, fixnum), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_iter, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(centuries_in_millinium, 10, fixnum), define_variable(years_in_century, 100, fixnum), define_variable(glob_dump, false, boolean), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_dump_analytic, false, boolean), define_variable(djd_debug, true, boolean), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_almost_1, 0.999, float), define_variable(glob_html_log, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_start, 0, fixnum), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_hmax, 1.0, float), define_variable(glob_disp_incr, 0.1, float), define_variable(sec_in_minute, 60, fixnum), define_variable(djd_debug2, true, boolean), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_max_hours, 0.0, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_h, 0.1, float), define_variable(glob_good_digits, 0, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_not_yet_finished, true, boolean), define_variable(days_in_year, 365, fixnum), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_display_flag, true, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 1, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/diff2postode.ode#################"), omniout_str(ALWAYS, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms : 30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.1,"), omniout_str(ALWAYS, "x_end : 5.0 ,"), omniout_str(ALWAYS, "array_y_init[0 + 1] : exact_soln_y(x_start),"), omniout_str(ALWAYS, "array_y_init[1 + 1] : exact_soln_yp(x_start),"), omniout_str(ALWAYS, "array_y_init[2 + 1] : exact_soln_ypp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "glob_max_minutes : 1,"), 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, " (2.0 - cos(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_yp (x) := ("), omniout_str(ALWAYS, " ( sin(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_ypp (x) := ("), omniout_str(ALWAYS, " ( cos(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_yppp (x) := ("), omniout_str(ALWAYS, " ( -sin(x)) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_norms, 1 + max_terms), array(array_y, 1 + max_terms), array(array_x, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_fact_1, 1 + max_terms), array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_m1, 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_y_init, 1 + max_terms), array(array_poles, 1 + 1, 1 + 3), array(array_fact_2, 1 + max_terms, 1 + max_terms), array(array_y_higher_work2, 1 + 4, 1 + max_terms), array(array_real_pole, 1 + 1, 1 + 3), array(array_y_higher, 1 + 4, 1 + max_terms), array(array_complex_pole, 1 + 1, 1 + 3), array(array_y_set_initial, 1 + 2, 1 + max_terms), array(array_y_higher_work, 1 + 4, 1 + max_terms), term : 1, while term <= max_terms do (array_norms : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_y : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_x : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_fact_1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 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_m1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp0 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp1 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp2 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_tmp3 : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y_init : 0.0, term : 1 + term), ord : 1, term while ord <= 1 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 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 <= 4 do (term : 1, while term <= max_terms do (array_y_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 4 do (term : 1, while term <= max_terms do (array_y_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 1 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 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 <= 4 do (term : 1, while term <= max_terms do (array_y_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), 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_m1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_m1 : 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_1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_3, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_3 : 0.0, term : 1 + term), term array_const_3 : 3, 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_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, iiif : 0, while iiif <= glob_max_terms do (jjjf : 0, 1 while jjjf <= glob_max_terms do (array_fact_1 : 0, iiif array_fact_2 : 0, jjjf : 1 + jjjf), iiif : 1 + iiif), x_start : 0.1, iiif, jjjf x_end : 5.0, array_y_init : exact_soln_y(x_start), 1 + 0 array_y_init : exact_soln_yp(x_start), 1 + 1 array_y_init : exact_soln_ypp(x_start), glob_h : 0.001, 1 + 2 glob_look_poles : true, glob_h : 1.0E-5, glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 1, 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), chk_data(), array_y_set_initial : true, array_y_set_initial : true, 1, 1 1, 2 array_y_set_initial : true, array_y_set_initial : false, 1, 3 1, 4 array_y_set_initial : false, array_y_set_initial : false, 1, 5 1, 6 array_y_set_initial : false, array_y_set_initial : false, 1, 7 1, 8 array_y_set_initial : false, array_y_set_initial : false, 1, 9 1, 10 array_y_set_initial : false, array_y_set_initial : false, 1, 11 1, 12 array_y_set_initial : false, array_y_set_initial : false, 1, 13 1, 14 array_y_set_initial : false, array_y_set_initial : false, 1, 15 1, 16 array_y_set_initial : false, array_y_set_initial : false, 1, 17 1, 18 array_y_set_initial : false, array_y_set_initial : false, 1, 19 1, 20 array_y_set_initial : false, array_y_set_initial : false, 1, 21 1, 22 array_y_set_initial : false, array_y_set_initial : false, 1, 23 1, 24 array_y_set_initial : false, array_y_set_initial : false, 1, 25 1, 26 array_y_set_initial : false, array_y_set_initial : false, 1, 27 1, 28 array_y_set_initial : false, array_y_set_initial : false, 1, 29 1, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 3, 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 (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (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(), array_x : glob_h + array_x , 1 1 array_x : glob_h, order_diff : 3, ord : 4, calc_term : 1, 2 iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 4, iii array_y_higher 4, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, 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 : 3, calc_term : 2, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 3, calc_term : 1, factorial_1(calc_term - 1) iii : glob_max_terms, while iii >= calc_term do (array_y_higher_work : 3, iii array_y_higher 3, iii --------------------------- expt(glob_h, calc_term - 1) -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, 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 : 2, calc_term : 3, factorial_1(calc_term - 1) 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 : 3, 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 : 2, calc_term : 2, factorial_1(calc_term - 1) 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 : 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 : 2, calc_term : 1, factorial_1(calc_term - 1) 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 : 4, 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 : 4, 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 : 3, 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 : 3, 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 , 3 ) = m1 * diff ( y , x , 1 ) ;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-08-21T17:31:46-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "diff2"), logitem_str(html_log_file, "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_good_digits), logitem_integer(html_log_file, glob_max_terms), 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, " 123 "), logitem_str(html_log_file, "diff2 diffeq.max"), logitem_str(html_log_file, "diff2 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/diff2postode.ode#################" "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms : 30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.1," "x_end : 5.0 ," "array_y_init[0 + 1] : exact_soln_y(x_start)," "array_y_init[1 + 1] : exact_soln_yp(x_start)," "array_y_init[2 + 1] : exact_soln_ypp(x_start)," "glob_h : 0.001 ," "glob_look_poles : true," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 100," "glob_max_minutes : 1," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y (x) := (" " (2.0 - cos(x)) " ");" "exact_soln_yp (x) := (" " ( sin(x)) " ");" "exact_soln_ypp (x) := (" " ( cos(x)) " ");" "exact_soln_yppp (x) := (" " ( -sin(x)) " ");" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.1 " " y[1] (analytic) = 1.0049958347219743 " " y[1] (numeric) = 1.0049958347219743 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10001 " " y[1] (analytic) = 1.004996833105891 " " y[1] (numeric) = 1.004996833105891 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10002 " " y[1] (analytic) = 1.004997831589308 " " y[1] (numeric) = 1.004997831589308 " " absolute error = 0.0 " " relative error = 0.0 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10003 " " y[1] (analytic) = 1.004998830172225 " " y[1] (numeric) = 1.0049988301722255 " " absolute error = 4.4408920985006260000000000000000E-16 " " relative error = 4.41880325148199250000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10003999999999999 " " y[1] (analytic) = 1.0049998288546425 " " y[1] (numeric) = 1.0049998288546433 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 8.83759772091052200000000000000E-14 "%" Correct digits = 16 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10004999999999999 " " y[1] (analytic) = 1.0050008276365596 " " y[1] (numeric) = 1.0050008276365616 " " absolute error = 1.9984014443252818000000000000000E-15 " " relative error = 1.98845751104989900000000000000E-13 "%" Correct digits = 15 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10005999999999998 " " y[1] (analytic) = 1.005001826517977 " " y[1] (numeric) = 1.0050018265179803 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 3.3140925578366520000000000000E-13 "%" Correct digits = 15 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10006999999999998 " " y[1] (analytic) = 1.0050028254988939 " " y[1] (numeric) = 1.0050028254988994 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 5.5234821060031860000000000000E-13 "%" Correct digits = 15 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10007999999999997 " " y[1] (analytic) = 1.005003824579311 " " y[1] (numeric) = 1.005003824579319 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 7.9538063257094630000000000000E-13 "%" Correct digits = 15 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10008999999999997 " " y[1] (analytic) = 1.005004823759227 " " y[1] (numeric) = 1.0050048237592388 " " absolute error = 1.17683640610266600000000000000E-14 " " relative error = 1.1709758782059392000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10009999999999997 " " y[1] (analytic) = 1.0050058230386432 " " y[1] (numeric) = 1.0050058230386592 " " absolute error = 1.598721155460225400000000000000E-14 " " relative error = 1.5907581019048023000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10010999999999996 " " y[1] (analytic) = 1.0050068224175583 " " y[1] (numeric) = 1.00500682241758 " " absolute error = 2.176037128265306800000000000000E-14 " " relative error = 2.1651963745189493000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10011999999999996 " " y[1] (analytic) = 1.005007821895973 " " y[1] (numeric) = 1.0050078218960015 " " absolute error = 2.84217094304040100000000000000E-14 " " relative error = 2.828008778756142000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10012999999999996 " " y[1] (analytic) = 1.0050088214738868 " " y[1] (numeric) = 1.0050088214739232 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 3.6233826439752614000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10013999999999995 " " y[1] (analytic) = 1.0050098211512999 " " y[1] (numeric) = 1.0050098211513454 " " absolute error = 4.55191440096314200000000000000E-14 " " relative error = 4.529223799772072500000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10014999999999995 " " y[1] (analytic) = 1.005010820928212 " " y[1] (numeric) = 1.005010820928268 " " absolute error = 5.59552404411078900000000000000E-14 " " relative error = 5.567625668888670000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10015999999999994 " " y[1] (analytic) = 1.0050118208046228 " " y[1] (numeric) = 1.005011820804691 " " absolute error = 6.81676937119846100000000000000E-14 " " relative error = 6.782775316752877000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10016999999999994 " " y[1] (analytic) = 1.0050128207805327 " " y[1] (numeric) = 1.0050128207806144 " " absolute error = 8.17124146124115200000000000000E-14 " " relative error = 8.130484798089485000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10017999999999994 " " y[1] (analytic) = 1.005013820855941 " " y[1] (numeric) = 1.0050138208560382 " " absolute error = 9.72555369571637100000000000000E-14 " " relative error = 9.677034776928143000000000000E-12 "%" Correct digits = 14 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10018999999999993 " " y[1] (analytic) = 1.0050148210308483 " " y[1] (numeric) = 1.0050148210309624 " " absolute error = 1.1413092693146609000000000000E-13 " " relative error = 1.135614366506570400000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10019999999999993 " " y[1] (analytic) = 1.0050158213052538 " " y[1] (numeric) = 1.005015821305387 " " absolute error = 1.33226762955018780000000000000E-13 " " relative error = 1.325618563715662800000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10020999999999992 " " y[1] (analytic) = 1.0050168216791577 " " y[1] (numeric) = 1.005016821679312 " " absolute error = 1.54321000422896760000000000000E-13 " " relative error = 1.535506641222790500000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10021999999999992 " " y[1] (analytic) = 1.00501782215256 " " y[1] (numeric) = 1.0050178221527375 " " absolute error = 1.77413639335100020000000000000E-13 " " relative error = 1.765278539589608700000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10022999999999992 " " y[1] (analytic) = 1.0050188227254606 " " y[1] (numeric) = 1.0050188227256633 " " absolute error = 2.02726724296553580000000000000E-13 " " relative error = 2.017143557040942400000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10023999999999991 " " y[1] (analytic) = 1.0050198233978591 " " y[1] (numeric) = 1.0050198233980896 " " absolute error = 2.3048229991218250000000000000E-13 " " relative error = 2.293310982990840200000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10024999999999991 " " y[1] (analytic) = 1.005020824169756 " " y[1] (numeric) = 1.0050208241700163 " " absolute error = 2.6023627697213670000000000000E-13 " " relative error = 2.58936203821564500000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1002599999999999 " " y[1] (analytic) = 1.0050218250411507 " " y[1] (numeric) = 1.0050218250414433 " " absolute error = 2.92654789291191260000000000000E-13 " " relative error = 2.91192471645288400000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1002699999999999 " " y[1] (analytic) = 1.005022826012043 " " y[1] (numeric) = 1.0050228260123708 " " absolute error = 3.2773783686934620000000000000E-13 " " relative error = 3.2609989384004200000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1002799999999999 " " y[1] (analytic) = 1.0050238270824332 " " y[1] (numeric) = 1.0050238270827987 " " absolute error = 3.65485419706601530000000000000E-13 " " relative error = 3.63658462474068300000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1002899999999999 " " y[1] (analytic) = 1.0050248282523209 " " y[1] (numeric) = 1.005024828252727 " " absolute error = 4.06119582407882260000000000000E-13 " " relative error = 4.04089104061339800000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10029999999999989 " " y[1] (analytic) = 1.0050258295217063 " " y[1] (numeric) = 1.0050258295221557 " " absolute error = 4.49418280368263370000000000000E-13 " " relative error = 4.47170875779523400000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10030999999999989 " " y[1] (analytic) = 1.0050268308905888 " " y[1] (numeric) = 1.0050268308910848 " " absolute error = 4.9604764740251994000000000000E-13 " " relative error = 4.93566571713269700000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10031999999999988 " " y[1] (analytic) = 1.005027832358969 " " y[1] (numeric) = 1.0050278323595143 " " absolute error = 5.4534154969587690000000000000E-13 " " relative error = 5.426133805825742000000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10032999999999988 " " y[1] (analytic) = 1.005028833926846 " " y[1] (numeric) = 1.0050288339274442 " " absolute error = 5.9818816566803430000000000000E-13 " " relative error = 5.95195028714544400000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10033999999999987 " " y[1] (analytic) = 1.0050298355942204 " " y[1] (numeric) = 1.0050298355948746 " " absolute error = 6.5414340610914220000000000000E-13 " " relative error = 6.50869638832544900000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10034999999999987 " " y[1] (analytic) = 1.0050308373610917 " " y[1] (numeric) = 1.0050308373618053 " " absolute error = 7.1365136022905060000000000000E-13 " " relative error = 7.10079067924805500000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10035999999999987 " " y[1] (analytic) = 1.00503183922746 " " y[1] (numeric) = 1.0050318392282365 " " absolute error = 7.7648998342283450000000000000E-13 " " relative error = 7.7260237249767200000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10036999999999986 " " y[1] (analytic) = 1.0050328411933251 " " y[1] (numeric) = 1.0050328411941682 " " absolute error = 8.4310336490034390000000000000E-13 " " relative error = 8.38881407993877700000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10037999999999986 " " y[1] (analytic) = 1.005033843258687 " " y[1] (numeric) = 1.0050338432596004 " " absolute error = 9.1349150466157880000000000000E-13 " " relative error = 9.08916163160939500000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10038999999999985 " " y[1] (analytic) = 1.0050348454235452 " " y[1] (numeric) = 1.005034845424533 " " absolute error = 9.8787644731146430000000000000E-13 " " relative error = 9.82927558989410100000000000E-11 "%" Correct digits = 13 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10039999999999985 " " y[1] (analytic) = 1.0050358476879002 " " y[1] (numeric) = 1.005035847688966 " " absolute error = 1.0658141036401503000000000000E-12 " " relative error = 1.06047371951166850000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10040999999999985 " " y[1] (analytic) = 1.0050368500517517 " " y[1] (numeric) = 1.0050368500528994 " " absolute error = 1.1477485628574868000000000000E-12 " " relative error = 1.14199649773875120000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10041999999999984 " " y[1] (analytic) = 1.0050378525150991 " " y[1] (numeric) = 1.0050378525163333 " " absolute error = 1.234123914173324000000000000E-12 " " relative error = 1.22793774491671030000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10042999999999984 " " y[1] (analytic) = 1.005038855077943 " " y[1] (numeric) = 1.0050388550792675 " " absolute error = 1.3244960683778118000000000000E-12 " " relative error = 1.31785558507098140000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10043999999999983 " " y[1] (analytic) = 1.0050398577402833 " " y[1] (numeric) = 1.0050398577417021 " " absolute error = 1.41886502547095000000000000E-12 " " relative error = 1.41175000627448280000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10044999999999983 " " y[1] (analytic) = 1.005040860502119 " " y[1] (numeric) = 1.0050408605036372 " " absolute error = 1.518118963872439000000000000E-12 " " relative error = 1.51050472028966650000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10045999999999983 " " y[1] (analytic) = 1.005041863363451 " " y[1] (numeric) = 1.0050418633650726 " " absolute error = 1.6215917497675036000000000000E-12 " " relative error = 1.61345692043187160000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10046999999999982 " " y[1] (analytic) = 1.0050428663242787 " " y[1] (numeric) = 1.0050428663260085 " " absolute error = 1.7297274723659940000000000000E-12 " " relative error = 1.7210484550694720000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10047999999999982 " " y[1] (analytic) = 1.0050438693846022 " " y[1] (numeric) = 1.0050438693864447 " " absolute error = 1.8425261316679098000000000000E-12 " " relative error = 1.8332793102813570000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10048999999999982 " " y[1] (analytic) = 1.0050448725444212 " " y[1] (numeric) = 1.0050448725463814 " " absolute error = 1.9602097722781764000000000000E-12 " " relative error = 1.95037040218474260000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10049999999999981 " " y[1] (analytic) = 1.0050458758037357 " " y[1] (numeric) = 1.0050458758058185 " " absolute error = 2.0827783941967937000000000000E-12 " " relative error = 2.0723217161915070000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10050999999999981 " " y[1] (analytic) = 1.005046879162546 " " y[1] (numeric) = 1.005046879164756 " " absolute error = 2.2100099528188366000000000000E-12 " " relative error = 2.19891230811076640000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1005199999999998 " " y[1] (analytic) = 1.005047882620851 " " y[1] (numeric) = 1.0050478826231939 " " absolute error = 2.3427926265640053000000000000E-12 " " relative error = 2.33102588152788670000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1005299999999998 " " y[1] (analytic) = 1.0050488861786517 " " y[1] (numeric) = 1.0050488861811322 " " absolute error = 2.4804602816175247000000000000E-12 " " relative error = 2.467999632384660000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.1005399999999998 " " y[1] (analytic) = 1.0050498898359472 " " y[1] (numeric) = 1.005049889838571 " " absolute error = 2.62367905179417000000000000E-12 " " relative error = 2.6104963328959013000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10054999999999979 " " y[1] (analytic) = 1.0050508935927378 " " y[1] (numeric) = 1.00505089359551 " " absolute error = 2.772226892489016000000000000E-12 " " relative error = 2.7582950377559340000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10055999999999979 " " y[1] (analytic) = 1.0050518974490235 " " y[1] (numeric) = 1.0050518974519496 " " absolute error = 2.9261038037020626000000000000E-12 " " relative error = 2.91139573103534800000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10056999999999978 " " y[1] (analytic) = 1.0050529014048037 " " y[1] (numeric) = 1.0050529014078895 " " absolute error = 3.08575387464316000000000000E-12 " " relative error = 3.07024025335390360000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10057999999999978 " " y[1] (analytic) = 1.0050539054600787 " " y[1] (numeric) = 1.0050539054633298 " " absolute error = 3.2511771053123084000000000000E-12 " " relative error = 3.23482858745176740000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10058999999999978 " " y[1] (analytic) = 1.0050549096148487 " " y[1] (numeric) = 1.0050549096182706 " " absolute error = 3.4219294064996575000000000000E-12 " " relative error = 3.4047188603963830000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10059999999999977 " " y[1] (analytic) = 1.0050559138691126 " " y[1] (numeric) = 1.0050559138727118 " " absolute error = 3.5991210012298325000000000000E-12 " " relative error = 3.5810156943154330000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10060999999999977 " " y[1] (analytic) = 1.0050569182228712 " " y[1] (numeric) = 1.0050569182266533 " " absolute error = 3.782085755688058000000000000E-12 " " relative error = 3.76305628777273000000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10061999999999977 " " y[1] (analytic) = 1.0050579226761243 " " y[1] (numeric) = 1.0050579226800953 " " absolute error = 3.97104571447926000000000000E-12 " " relative error = 3.9510615506673770000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10062999999999976 " " y[1] (analytic) = 1.0050589272288712 " " y[1] (numeric) = 1.005058927233038 " " absolute error = 4.1666670114182125000000000000E-12 " " relative error = 4.14569424591497870000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10063999999999976 " " y[1] (analytic) = 1.0050599318811124 " " y[1] (numeric) = 1.005059931885481 " " absolute error = 4.368505557295066000000000000E-12 " " relative error = 4.34651250012403460000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10064999999999975 " " y[1] (analytic) = 1.0050609366328476 " " y[1] (numeric) = 1.0050609366374244 " " absolute error = 4.576783396714745300000000000E-12 " " relative error = 4.5537372211956350000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10065999999999975 " " y[1] (analytic) = 1.005061941484077 " " y[1] (numeric) = 1.0050619414888682 " " absolute error = 4.7912784850723256000000000000E-12 " " relative error = 4.767147463565790700000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10066999999999975 " " y[1] (analytic) = 1.0050629464347998 " " y[1] (numeric) = 1.0050629464398124 " " absolute error = 5.012656956182582000000000000E-12 " " relative error = 4.9874059868226994000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10067999999999974 " " y[1] (analytic) = 1.0050639514850164 " " y[1] (numeric) = 1.005063951490257 " " absolute error = 5.240696765440589000000000000E-12 " " relative error = 5.2142918445112670000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10068999999999974 " " y[1] (analytic) = 1.0050649566347265 " " y[1] (numeric) = 1.0050649566402021 " " absolute error = 5.475619957451272000000000000E-12 " " relative error = 5.4480259423086140000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " " " "TOP MAIN SOLVE Loop" "NO POLE" x[1] = 0.10069999999999973 " " y[1] (analytic) = 1.0050659618839304 " " y[1] (numeric) = 1.0050659618896476 " " absolute error = 5.717204487609706000000000000E-12 " " relative error = 5.6883873341936490000000000E-10 "%" Correct digits = 12 h = 1.00000E-5 " " "Finished!" "Maximum Time Reached before Solution Completed!" "diff ( y , x , 3 ) = m1 * diff ( y , x , 1 ) ;" Iterations = 70 "Total Elapsed Time "= 1 Minutes 1 Seconds "Elapsed Time(since restart) "= 1 Minutes 0 Seconds "Expected Time Remaining "= 4 Days 21 Hours 48 Minutes 27 Seconds "Optimized Time Remaining "= 4 Days 19 Hours 39 Minutes 3 Seconds "Time to Timeout " Unknown Percent Done = 1.448979591836172800E-2 "%" (%o51) true (%o51) diffeq.max