Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs

Many partial differential equations (PDEs) can be written as a multi-symplectic Hamiltonian system, which has three local conservation laws, namely multi-symplectic conservation law, local energy conservation law and local momentum conservation law. In this paper, we give several systematic methods...

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Veröffentlicht in:Journal of computational physics Jg. 279; S. 80 - 102
Hauptverfasser: Gong, Yuezheng, Cai, Jiaxiang, Wang, Yushun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.12.2014
Schlagworte:
Algorithms
Average vector field method
Conservation
Energy conservation law
Energy-preserving
Fourier pseudospectral method
Hamiltonian PDEs
Law
Local structure-preserving
Mathematical analysis
Mathematical models
Momentum-preserving
Partial differential equations
Schroedinger equation
Momentum-preserving
Energy-preserving
Fourier pseudospectral method
Hamiltonian PDEs
Average vector field method
Local structure-preserving
ISSN:0021-9991, 1090-2716
Online-Zugang:Volltext
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Zusammenfassung:Many partial differential equations (PDEs) can be written as a multi-symplectic Hamiltonian system, which has three local conservation laws, namely multi-symplectic conservation law, local energy conservation law and local momentum conservation law. In this paper, we give several systematic methods for discretizing general multi-symplectic formulations of Hamiltonian PDEs, including a local energy-preserving algorithm, a class of global energy-preserving methods and a local momentum-preserving algorithm. The methods are illustrated by the nonlinear Schrödinger equation and the Korteweg–de Vries equation. Numerical experiments are presented to demonstrate the conservative properties of the proposed numerical methods.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.09.001