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://doi.org/10.4208/cicp.2019.js60.11
UR - https://global-sci.org/intro/article_detail/cicp/13264.html
KW - Nonlinear Hamiltonian system, spectral Petrov-Galerkin method, iterative algorithm, energy conservation, symplectic structure.
AB - <p style="text-align: justify;">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.</p>