Pade Numerical Method For The Rosenau-hyman Compacton Equation

摘要

Three implicit finite difference methods based on Pade approximations in space are developed for the Rosenau-Hyman 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 Pade methods is shown.