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论文类型：期刊论文

发表时间：2012-01-27

发表刊物：INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

收录刊物：SCIE、EI、Scopus

卷号：89

期号：4

页面范围：438-508

ISSN号：0029-5981

关键字：symplectic; Hamiltonian system; principle of least action; generating function; dual

摘要：In this paper, the principle of least action and generating functions are used to construct symplectic numerical algorithms for finite dimensional autonomous Hamiltonian systems. The approximate action is obtained by approximating the generalized coordinates and momentums by Lagrange polynomials and performing Gaussian quadrature. Based on the principle of least action and the requirements of a canonical transformation, different types of symplectic algorithms have been constructed by choosing different types of independent variables at two ends of the time step. The symmetric property of the four types of symplectic algorithms proposed in this paper is discussed, and the exact linear stability domain for small m, n and g is discussed. The linear stability and precision of different types of symplectic algorithms are tested using numerical examples. Copyright (c) 2011 John Wiley & Sons, Ltd.