改进的欧拉法matlab程序

改进的欧拉法matlab程序如下：

function [y1, y2, y3, y4] = exam4_6(a, b, k)
    h = (b - a) / k;
    x = a:h:b;
    [m, n] = size(x);
    y1 = zeros(m, n);
    y2 = zeros(m, n);
    y3 = zeros(m, n);
    y1(1) = 1;
    y2(1) = 1;
    y3(1) = 1;

    for i = 1:n-1
        x1 = x(i);
        x2 = x(i+1);
        y1(i+1) = y1(i) + h * ((sin(x1) - y1(i)) / x1);
    end

    for i = 1:n-1
        x1 = x(i);
        x2 = x(i+1);
        yy = y2(i);
        y2(i+1) = y2(i) + h * (sin(x1)/x1 - y2(i)/x1);
    end

    for i = 1:n-1
        x1 = x(i);
        x2 = x(i+1);
        z1 = (sin(x1) - y3(i)) / x1;
        yy = y3(i);
        z2 = sin(x2) / x2 - yy / x2;        y3(i+1) = y3(i) + h * 0.5 * (z1 + z2);
    end

    for i = 1:n
        y4(i) = (exp(-x(i)) * exp(pi)) / 2 - (2^(1/2) * cos(x(i) + pi/4)) / 2;
    end
end