Comparison of a Spectral Collocation Method and Symplectic Methods for Hamiltonian Systems

Abstract

We conduct a systematic comparison of a spectral collocation method with some symplectic methods in solving Hamiltonian dynamical systems. Our main emphasis is on non-linear problems. Numerical evidence has demonstrated that the proposed spectral collocation method preserves both energy and symplectic structure up to the machine error in each time (large) step, and therefore has a better long time behavior.