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Symplectic algorithms based on the principle of least action and generating functions
Author(s) -
Gao Q.,
Tan S.J.,
Zhang H.W.,
Zhong W.X.
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3245
Subject(s) - symplectic geometry , action (physics) , algorithm , computer science , algebra over a field , mathematics , pure mathematics , physics , quantum mechanics
SUMMARY 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 © 2011 John Wiley & Sons, Ltd.