def METHOD_NAME(self, t, x_im1, v_im1_2, dt):
    """
    Step forward the positions and velocities by the given timestep.
    Parameters
    ----------
    dt : numeric
        The timestep to move forward.
    """
    x_i = x_im1 + v_im1_2 * dt
    F_i = self.F(t, np.vstack((x_i, v_im1_2)), *self._func_args)
    a_i = F_i[self.ndim:]
    v_i = v_im1_2 + a_i * dt / 2
    v_ip1_2 = v_i + a_i * dt / 2
    return x_i, v_i, v_ip1_2