A finite difference scheme for the K(2, 2) compacton equation
Journal of Computational Physics
A numerical study of compactons
Mathematics and Computers in Simulation
Particle methods for dispersive equations
Journal of Computational Physics
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics
Method of lines study of nonlinear dispersive waves
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
Self-similar radiation from numerical Rosenau-Hyman compactons
Journal of Computational Physics
Adiabatic perturbations for compactons under dissipation and numerically-induced dissipation
Journal of Computational Physics
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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.