ASYMPTOTIC HIGH-ORDER SCHEMES FOR 2 x 2 DISSIPATIVEHYPERBOLIC SYSTEMS

摘要

We investigate finite difference schemes which approximate 2 x 2 one-dimensionallinear dissipative hyperbolic systems. We show that it is possible to introduce some suitable mod-ifications in standard upwinding schemes, which keep into account the long-time behavior of thesolutions, to yield numerical approximations which are increasingly accurate for large times whencomputing small perturbations of stable asymptotic states, respectively, around stationary solutionsand in the diffusion (Chapman–Enskog) limit.