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

Based on WW-transformation, some parametric symplectic partitioned Runge–Kutta (PRK) methods depending on a real parameter αα are developed. For α=0α=0, the corresponding methods become the usual PRK methods, including Radau IA–IA¯ and Lobatto IIIA–IIIB methods as examples. For any α≠0α≠0, the corresponding methods are symplectic and there exists a value α∗α∗ 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.