Stability of Discrete Shocks for Difference Approximations to Systems of Conservation Laws

In this paper we analyse the stability of weak discrete stationary shocks. The difference approximation is conservative, dissipative and k-th order accurate (k = 1 or k = 3). In Sections 1-3, following the previous results of D. Michelson we adapt the multistep methods RungeKutta and Adams-Bashforth to solve systems of conservation laws. In section 4 we analyse the stability of the numerical method and provide maximal values for the Courant-Friederichs-Levy number. The numerical examples presented in Section 5 confirm the robustness of the algorithm. Subject Classification: 65M12, 65M06, 35L65, 35L67.