Parametric symplectic partitioned Runge-Kutta methods with energy-preserving properties for Hamiltonian systems

Based on W-transformation, some parametric symplectic partitioned Runge-Kutta (PRK) methods depending on a real parameter alpha are developed. For alpha = 0, the corresponding methods become the usual PRK methods, including Radau IA-I (A) over bar and Lobatto IIIA-IIIB methods as examples. For any alpha not equal 0, the corresponding methods are symplectic and there exists a value alpha* such that energy is preserved in the numerical solution at each step. The existence of the parameter and the order of the numerical methods are discussed. Some numerical examples are presented to illustrate these results. (C) 2012 Elsevier B.V. All rights reserved.