High order symplectic integrators based on continuous-stage Runge-Kutta Nystrom methods
For researchers in numerical analysis and computational physics, this work provides a streamlined approach to building high-order symplectic integrators, though it is an incremental improvement over existing methods.
This paper presents a more effective method for constructing high-order symplectic integrators for second-order Hamiltonian equations, using Legendre expansions to simplify order conditions. The new technique allows convenient derivation of high-order integrators by truncating an orthogonal series.
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.