Volume 26, Issue 5
An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems

Jing An ,  Waixiang Cao and Zhimin Zhang


Commun. Comput. Phys., 26 (2019), pp. 1249-1273.

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  • 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.

  • History

Published online: 2019-08

  • AMS Subject Headings

65M15, 65M70, 65N30

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