def forward_diff_x(sigma, x, y, dt):
    """

    Update equation for coordinate :math:`x`: 
        
        :math:`x[n+1] = \\sigma(y[n]-x[n])t_{\\delta} + x[n]`

    INPUT::
        
        sigma : float
            Prandtl number
        x : float
            Current value of coordinate x (x[n]).
        y : float
            Current value of coordinate y (y[n]).
        dt : float
            Time step (s).

    OUTPUT::
        
        float
            x at the next time step (x[n+1]).

    """

    return sigma * (y - x) * dt + x