High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods

摘要

On the basis of the previous work by Tang and Zhang [37], in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations. Instead of analyzing order conditions step by step as shown in the previous work, the new technique of this paper is using Legendre expansions to deal with the simplifying assumptions for order conditions. With the new technique, high-order symplectic integrators can be conveniently devised by truncating an orthogonal series.