FURTHER REDUCTION IN THE NUMBER OF INDEPENDENT ORDER CONDITIONS FOR SYMPLECTIC, EXPLICIT PARTITIONED RUNGE-KUTTA AND RUNGE-KUTTA-NYSTROM METHODS

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