Multisymplectic schemes for the nonlinear Klein-Gordon equation

Authors:
Yu Shun Wang;Meng Zhao Qin
Affiliations:
Lasg, Institute of Atmosphere Physics Chinese Academy of Sciences Beijing 100029, P.R. China and School of Mathematics and Computer Sciences Nanjing Norml University, P.R. China;Academy of Mathematics and Systems Sciences Chinese Academy of Scineces P.O. Box 2719, Beijing 100080, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2002

Citing 3
Cited 1

Analysis of four numerical schemes for a nonlinear Klein-Gordon equation

Applied Mathematics and Computation
Finite difference calculus invariant structure of a class of algorithms for the nonlinear Klein-Gordon equation

SIAM Journal on Numerical Analysis
Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations

Journal of Computational Physics

Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions

International Journal of Computer Mathematics

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Abstract

In this paper, we derive the multisymplectic structure of the nonlinear Klein-Gordon equation directly from the variational principle and show the connection between the relative theories of Bridges-Reich's and Marsdon-Partrick-Shkoller's. In the numerical aspect, we construct a series of multisymplectic schemes for the nonlinear Klein-Gordon equation. Among these schemes, some are the classical, such as the five points scheme and the Preissman box scheme, some are new which we never encountered in the literature. Some numerical results are also reported to show the effectiveness of the schemes.