Extrapolation methods for hyperbolic systems with relaxation

A splitting scheme is used for numerical solution of hyperbolic systems with a stiff relaxation. High-order flux in the convection step guarantees a good spatial accuracy. The relaxation term is treated implicity. Extrapolation is used to combine the steps, obtaining high accuracy in time. A third-order scheme both in space and in time is presented and applied to the Broadwell model of gas dynamics.