Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

Xin Lei Kong*, Hui Bin Wu, Feng Xiang Mei

*此作品的通讯作者

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3 引用 (Scopus)

摘要

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation, applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities.

源语言英语
文章编号010203
期刊Chinese Physics B
25
1
DOI
出版状态已出版 - 8 12月 2015

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