Commun. Comput. Phys., 2 (2007), pp. 662-683.


Explicit Multi-Symplectic Methods for Hamiltonian Wave Equations

Jialin Hong 1*, Shanshan Jiang 2, Chun Li 2, Hongyu Liu 3

1 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China.
2 State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China/Graduate School, Chinese Academy of Sciences, Beijing 100080, P. R. China.
3 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.

28 July 2006; Accepted (in revised version) 25 October 2006
Available online 15 January 2007

Abstract

In this paper, based on the multi-symplecticity of concatenating symplectic Runge-Kutta-Nystr\"om (SRKN) methods and symplectic Runge-Kutta-type methods for numerically solving Hamiltonian PDEs, explicit multi-symplectic schemes are constructed and investigated, where the nonlinear wave equation is taken as a model problem. Numerical comparisons are made to illustrate the effectiveness of our newly derived explicit multi-symplectic integrators.

AMS subject classifications: 65L06, 65M06, 65M12

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Key words: Hamiltonian wave equations, multi-symplectic integration, symplectic Runge-Kutta methods, symplectic Runge-Kutta-Nystrom methods.

*Corresponding author.
Email: hjl@lsec.cc.ac.cn (J. Hong), jiangss@lsec.cc.ac.cn (S. Jiang), lichun@lsec.cc.ac.cn (C. Li), hyliu@math.cuhk.edu.hk (H. Liu)
 

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