Abstract: We consider stiff relaxation processes, emphasizing the application to hyperbolic conservation laws. We present first and second-order accurate exponential time-differencing methods for systems of monotonic relaxation ODEs. Some desirable accuracy and robustness properties of these methods are established.

Through operator splitting, we show how the methods may be applied to hyperbolic conservation laws with relaxation terms. In particular, global second-order accuracy for smooth solutions may be achieved through Strang splitting and MUSCL interpolation. An application to granular-gas flow is presented.