An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems
An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems
复制标题
非线性哈密顿系统的高效谱 Petrov-Galerkin 方法
DOI：
10.4208/cicp.2019.js60.11
复制
发表时间：
2019-06
影响因子：
3.7
通讯作者：
Zhang Zhimin
中科院分区：
文献类型：
--
作者：
An Jing;Cao Waixiang;Zhang Zhimin
本文提出并研究了求解非线性Hamilton系统的一种有效的谱Petrov-Galerkin时间推进方法。讨论了该方法的守恒性质（包括辛结构守恒和能量守恒）。给出了离散非线性项的迭代算法，并证明了迭代算法的唯一性、稳定性和收敛性。最后，数值实验验证了算法的有效性。AMS科目分类：65 M15、65 M70、65 N30
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. AMS subject classifications: 65M15, 65M70, 65N30