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

Jing An, Waixiang Cao & Zhimin Zhang

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

Published online: 2019-08

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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.

  • Keywords

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

  • AMS Subject Headings

65M15, 65M70, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

aj154@163.com (Jing An)

caowx@bnu.edu.cn (Waixiang Cao)

zzhang@math.wayne.edu (Zhimin Zhang )

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@Article{CiCP-26-1249, author = {An , Jing and Cao , Waixiang and Zhang , Zhimin }, title = {An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {5}, pages = {1249--1273}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2019.js60.11}, url = {http://global-sci.org/intro/article_detail/cicp/13264.html} }
TY - JOUR T1 - An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems AU - An , Jing AU - Cao , Waixiang AU - Zhang , Zhimin JO - Communications in Computational Physics VL - 5 SP - 1249 EP - 1273 PY - 2019 DA - 2019/08 SN - 26 DO - http://dor.org/10.4208/cicp.2019.js60.11 UR - https://global-sci.org/intro/cicp/13264.html KW - Nonlinear Hamiltonian system, spectral Petrov-Galerkin method, iterative algorithm, energy conservation, symplectic structure. AB -

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.

Jing An, Waixiang Cao & Zhimin Zhang. (2019). An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems. Communications in Computational Physics. 26 (5). 1249-1273. doi:10.4208/cicp.2019.js60.11
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