Copyright © 2012 Cuicui Liao and Xiaohua Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the idea of nonstandard finite difference methods to derive the discrete variational integrators for multisymplectic PDEs. We obtain a nonstandard finite difference variational integrator for linear wave equation with a triangle discretization and two nonstandard finite difference variational integrators for the nonlinear Klein-Gordon equation with a triangle discretization and a square discretization, respectively. These methods are naturally multisymplectic. Their discrete multisymplectic structures are presented by the multisymplectic form formulas. The convergence of the discretization schemes is discussed. The effectiveness and efficiency of the proposed methods are verified by the numerical experiments.