Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms  

作　　者：孔新雷 吴惠彬 梅凤翔 

机构地区：[1]College of Science,North China University of Technology,Beijing 100144,China [2]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China [3]School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China

出　　处：《Chinese Physics B》2016年第1期407-411,共5页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11272050);the Excellent Young Teachers Program of North China University of Technology(Grant No.XN132);the Construction Plan for Innovative Research Team of North China University of Technology(Grant No.XN129)

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 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.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.

关 键 词：Birkhoffian equations Hamiltonian equations symplectic algorithm 

分 类 号：O175[理学—数学]