Structure-preserving algorithms for autonomous Birkhoffian systems

Xin Lei Kong; Hui Bin Wu; Feng Xiang Mei

Structure-preserving algorithms for autonomous Birkhoffian systems

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

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhoffian systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.

Original language	English
Pages (from-to)	1-7
Number of pages	7
Journal	Journal of Beijing Institute of Technology (English Edition)
Volume	21
Issue number	1
Publication status	Published - Mar 2012

Keywords

Birkhoffian system
Discrete Birkhoffian equations
Structure-preserving algorithm

Cite this

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title = "Structure-preserving algorithms for autonomous Birkhoffian systems",

abstract = "The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhoffian systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.",

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AU - Wu, Hui Bin

AU - Mei, Feng Xiang

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N2 - The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhoffian systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.

AB - The Pfaff-Birkhoff variational principle is discretized, and based on the discrete variational principle the discrete Birkhoffian equations are obtained. Taking the discrete equations as an algorithm, the corresponding discrete flow is proved to be symplectic. That means the algorithm preserves the symplectic structure of Birkhoffian systems. Finally, simulation results of the given example indicate that structure-preserving algorithms have great advantage in stability and energy conserving.

KW - Birkhoffian system

KW - Discrete Birkhoffian equations

KW - Structure-preserving algorithm

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M3 - Article

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JF - Journal of Beijing Institute of Technology (English Edition)

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Structure-preserving algorithms for autonomous Birkhoffian systems

Abstract

Keywords

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