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

Based on -transformation, some parametric symplectic partitioned Runge–Kutta (PRK) methods depending on a real parameter are developed. For , the corresponding methods become the usual PRK methods, including Radau and Lobatto methods as examples. For any , the corresponding methods are symplectic and there exists a value 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.