Abstract In this article, we briefly review the random choice method (RCM) and ADER methods for solving one two-dimensional hyperbolic conservation laws. The main advantage of RCM is that it computes discontinuities with infinite resolution. method, original problem reduced to a set local Riemann problems (RPs). exact solutions these RPs are used form solution problem. However, has following di...

This paper studies the asymptotic stability of traveling relaxation shock profiles for hyperbolic systems of conservation laws. Under a stability condition of subcharacteristic type the large time relaxation dynamics on the level of shocks is shown to be determined by the equilibrium conservation laws. The proof is due to the energy principle, using the weighted norms, the interaction of waves ...

We consider a multi-dimensional triangular system of conservation laws. This system arises as a model of three-phase flow in porous media and includes multi-dimensional conservation laws with discontinuous coefficients as a special case. The system is neither strictly hyperbolic nor symmetric. We propose an Engquist-Osher type scheme for this system and show that the approximate solutions gener...