Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs

Many PDEs can be recast into the general multi-symplectic formulation possessing three local conservation laws. We devote the present paper to some systematic methods, which hold the discrete versions of the local conservation laws respectively, for the general multi-symplectic PDEs. For the origina...

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Bibliographic Details
Published inComputer physics communications Vol. 235; pp. 210 - 220
Main Authors Cai, Jiaxiang, Wang, Yushun, Jiang, Chaolong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2019
Subjects
Conservation law
Discrete gradient
Dispersion relation
Multi-symplectic Hamiltonian PDE
Structure-preserving algorithm
Conservation law
Multi-symplectic Hamiltonian PDE
Structure-preserving algorithm
Dispersion relation
Discrete gradient
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ISSN0010-4655
1879-2944
DOI10.1016/j.cpc.2018.08.015

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Summary:Many PDEs can be recast into the general multi-symplectic formulation possessing three local conservation laws. We devote the present paper to some systematic methods, which hold the discrete versions of the local conservation laws respectively, for the general multi-symplectic PDEs. For the original problem subjected to appropriate boundary conditions, the proposed methods are globally conservative. The proposed methods are successfully applied to many one-dimensional and multi-dimensional Hamiltonian PDEs, such as KdV equation, G–P equation, Maxwell’s equations and so on. Numerical experiments are carried out to verify the theoretical analysis.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2018.08.015