An Efficient Spectral Petrov-Galerkin Method for Nonlinear Hamiltonian Systems (Communications in Computational Physics, 2019)
In this paper, an efficient spectral Petrov-Galerkin time-stepping method forsolving nonlinear Hamiltonian systems is presented and studied. Conservation properties of the proposed method (including symplectic structure preserving and energyconservation) are discussed. Iterative algorithm on how to discretize the nonlinearterm is introduced and the uniqueness, stability and convergence properties of the iterative algorithm are also established. Finally, numerical experiments are presented toverify the efficiency of our algorithm.