  In this paper, we develop a new type of Runge--Kutta (RK) discontinuous
Galerkin (DG) method for solving hyperbolic conservation laws. Compared with
the original RKDG method, the new method features improved compactness and
allows simple boundary treatment. The key idea is to hybridize two different
spatial operators in an explicit RK scheme, utilizing local projected
derivatives for inner RK stages and the usual DG spatial discretization for the
final stage only. Limiters are applied only at the final stage for the control
of spurious oscillations. We also explore the connections between our method
and Lax--Wendroff DG schemes and ADER-DG schemes. Numerical examples are given
to confirm that the new RKDG method is as accurate as the original RKDG method,
while being more compact, for problems including two-dimensional Euler
equations for compressible gas dynamics.
