Further reduction in the number of independent order conditions for symplectic, explicit Partitioned Runge-Kutta and Runge-Kutta-Nyström methods

Abstract

We are concerned with symplectic Partitioned Runge-Kutta and Runge-Kutta-Nyström methods for the numerical integration of Hamiltonian systems of ordinary differential equations. We show that for these methods, explicitness operates as a simplifying assumption for the study of the order conditions.