Symplectic wavelet collocation method for Hamiltonian wave equations

Authors:
Huajun Zhu;Lingyan Tang;Songhe Song;Yifa Tang;Desheng Wang
Affiliations:
Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan 410073, China;Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan 410073, China;Department of Mathematics and System Science, Science School, National University of Defense Technology, Changsha, Hunan 410073, China;LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Science, P.O. Box 2719, Beijing 100190, China;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

This paper introduces a novel symplectic wavelet collocation method for solving nonlinear Hamiltonian wave equations. Based on the autocorrelation functions of Daubechies compactly supported scaling functions, collocation method is conducted for the spatial discretization, which leads to a finite-dimensional Hamiltonian system. Then, appropriate symplectic scheme is employed for the integration of the Hamiltonian system. Under the hypothesis of periodicity, the properties of the resulted space differentiation matrix are analyzed in detail. Conservation of energy and momentum is also investigated. Various numerical experiments show the effectiveness of the proposed method.