AHO schemes for Dissipative Hyperbolic Systems

We study finite difference schemes which approximate linear one dimensional dissipative hyperbolic systems. We introduce suitable modifications of standard upwinding schemes to keep into account the long-time behaviour of the solutions, which consist in some schemes which are increasingly accurate for large times. This property of accuracy is required in order to get better results for large time simulations when computing perturbations of some given stable states, both in the steady state and in the diffusion limit