Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

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 e...

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Bibliographic Details
Published inChinese physics B Vol. 25; no. 1; pp. 407 - 411
Main Author 孔新雷 吴惠彬 梅凤翔
Format Journal Article
LanguageEnglish
Published 01.01.2016
Subjects
Algorithms
Birkhoff方程
Birkhoff系统
Construction
Inverse
Mathematical analysis
Mathematical models
Oscillators
Preserving
Transformations (mathematics)
保结构算法
哈密顿方程
差分格式
操作过程
线性阻尼
辛算法
Online AccessGet full text
ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/25/1/010203

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Summary: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 Birkhoftian 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.
Bibliography:Birkhoffian equations, Hamiltonian equations, symplectic algorithm
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 Birkhoftian 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.
11-5639/O4
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/25/1/010203