def METHOD_NAME(self, t, w, dt):
    """
    Step forward the positions and velocities by the given timestep.
    Parameters
    ----------
    dt : numeric
        The timestep to move forward.
    """
    w_i = w.copy()
    for cj, dj in zip(self._cs, self._ds):
        F_i = self.F(t, w_i, *self._func_args)
        a_i = F_i[self.ndim:]
        w_i[self.ndim:] += dj * a_i * dt
        w_i[: self.ndim] += cj * w_i[self.ndim:] * dt
    return w_i