Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
519070 | Journal of Computational Physics | 2014 | 23 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Yuezheng Gong, Jiaxiang Cai, Yushun Wang,