Long-time Asymptotic Behavior of Lax-Friedrichs Scheme

In this paper we investigate the asymptotic stability of the discrete shocks of the Lax-Friedrichs scheme for hyperholic systems of conservation laws. For single equations, we show that the discrete shocks of the Lax-Friedrichs scheme are asymptotically stable in the sense of I³ and I¹. For the systems of conservation laws, if the summation of initial perturbations equals to zero, we show the l² stability and l¹ boundedness.