An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems

Authors

  • Jing An School of Mathematical Science, Xiamen University, Xiamen 361005, P. R. China
  • Waixiang Cao School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China.
  • Zhimin Zhang Key Laboratory of Computational and Stochastic Mathematics and Its Applications, Universities of Hunan Province, Hunan Normal University, Changsha 410081, China

DOI:

https://doi.org/10.4208/cicp.2019.js60.11

Keywords:

Nonlinear Hamiltonian system, spectral Petrov-Galerkin method, iterative algorithm, energy conservation, symplectic structure.

Abstract

In this paper, an efficient spectral Petrov-Galerkin time-stepping method for solving nonlinear Hamiltonian systems is presented and studied. Conservation properties of the proposed method (including symplectic structure preserving and energy conservation) are discussed. Iterative algorithm on how to discretize the nonlinear term is introduced and the uniqueness, stability and convergence properties of the iterative algorithm are also established. Finally, numerical experiments are presented to verify the efficiency of our algorithm.

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Published

2019-08-27

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Issue

Vol. 26 No. 5 (2019)

Section

Articles

How to Cite

An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems. (2019). Communications in Computational Physics, 26(5), 1249-1273. https://doi.org/10.4208/cicp.2019.js60.11