High order symplectic integrators based on continuous stage Runge Kutta Nystrom methods
On the basis of the previous work by Tang Zhang (Appl. Math. Comput. 323, 2018, p. 204 219) 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.
Appl. Math. Comput.