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2012 Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs
Cuicui Liao, Xiaohua Ding
J. Appl. Math. 2012: 1-22 (2012). DOI: 10.1155/2012/705179

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.

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Cuicui Liao. Xiaohua Ding. "Nonstandard Finite Difference Variational Integrators for Multisymplectic PDEs." J. Appl. Math. 2012 1 - 22, 2012. https://doi.org/10.1155/2012/705179

Information

Published: 2012
First available in Project Euclid: 2 January 2013

zbMATH: 1264.65176
MathSciNet: MR2997262
Digital Object Identifier: 10.1155/2012/705179

Rights: Copyright © 2012 Hindawi

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