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...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of computational physics Ročník 279; s. 80 - 102
Hlavní autori: Gong, Yuezheng, Cai, Jiaxiang, Wang, Yushun
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.12.2014
Predmet:
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
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.09.001