Padé numerical method for the Rosenau–Hyman compacton equation

Three implicit finite difference methods based on Padé approximations in space are developed for the Rosenau–Hyman K(n,n)K(n,n) equation. The analytical solutions and their invariants are used to assess the accuracy of these methods. Shocks which develop after the interaction of compactons are shown to be independent of the numerical method and its parameters indicating that their origin may not be numerical. The accuracy in long-time integrations of high-order Padé methods is shown.