function unew = convdiff(u, a, d, dx, dt)
    n = size(u, 2);
    unew = zeros(size(u));

    amu = (a * (dt / dx));
    nm1 = ((amu/2) * (1 + amu)) + ((d*dt)/(dx^2));
    np0 = 1 - (amu^2) - ((2*d*dt)/(dx^2));
    np1 = ((d*dt)/(dx^2)) + (amu - 1)*(amu/2);

    %unew(1) = (((amu/2) * (1 + amu) + (d*dt/(dx^2))) * u(n - 1)) + (((1 - (amu)^2) - ((2*d*dt)/(dx^2))) * u(1)) - (((amu/2) * (1 - amu) - (d*dt/(dx^2))) * u(2));
    unew(1) = (nm1 * u(n-1)) + (np0 * u(1)) - (np1 * u(2));
    unew(end) = unew(1);

    for i = 2:(n-1)
        unew(i) = ((nm1 * u(i-1)) + (np0 * u(i)) + (np1 * u(i + 1)));
    end

end