Symplectic algorithm for solving Hamiltonian systems of the water-wave problem under long-wave approximation

doi:10.7523/j.issn.2095-6134.2013.05.001

›› 2013, Vol. 30 ›› Issue (5): 577-584.DOI: 10.7523/j.issn.2095-6134.2013.05.001

Symplectic algorithm for solving Hamiltonian systems of the water-wave problem under long-wave approximation

LIU Cheng-Bao, CHEN Yu-Fu

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2012-12-13 Revised:2013-03-21 Online:2013-09-15
Contact: 刘成保,E-mail:liuchengbao08@mails.ucas.ac.cn
Supported by:
Supported by the National Natural Science Foundation of China(11271363)

Abstract

Abstract: An symplectic algorithm is presented for solving the Hamiltonian systems of the water-wave problem under long-wave approximation. Firstly, the generating function method is generalized to infinite-dimensional Hamiltonian systems, and then symplectic schemes are deduced directly from the Hamiltonian function of infinite-dimensional system, rather than from a Hamiltonian function of finite-dimensional approximate system. Finally, the spatial discretization of these schemes is used in simulation. Compared with the known results by un-symplectic algorithms, the numerical solutions by the symplectic algorithm are stable in long-time simulation. Compared with the traditional symplectic algorithm for solving infinite-dimensional systems, our algorithm is more efficient and more accurate.

Key words: symplectic algorithm, Hamiltonian system, water-wave problem, generating function method, long-wave approximation

CLC Number:

LIU Cheng-Bao, CHEN Yu-Fu. Symplectic algorithm for solving Hamiltonian systems of the water-wave problem under long-wave approximation[J]. , 2013, 30(5): 577-584.

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Symplectic algorithm for solving Hamiltonian systems of the water-wave problem under long-wave approximation

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