theory_rect

ns = 5 : 21;
n = length(ns);

y_theory = zeros(n, 1);
y_fact = zeros(n, 1);
y_runge = zeros(n, 1);
for i = 1 : n
    error = 0;
    h = 0.4 / ns(i);
    for j = 1 : ns(i)
        error = error + h^3 * exp(-(h * (j - 1))) / 24;
    end;
    y_theory(i) = error;
    y_fact(i) = abs(Rectangle(0, 0.4, ns(i)) + exp(-0.4) - 1);
    y_runge(i) = (Rectangle(0, 0.4, idivide(ns(i), 2, 'floor')) - Rectangle(0, 0.4, ns(i))) / (2^2 - 1);
end;

semilogy(ns, y_theory, ns, y_fact, '--', ns, y_runge, '-.');
legend ('теоретическая погрешность', 'фактичекая погрешность', 'Рунге');