ORDER PROPERTIES AND CONSTRUCTION OF SYMPLECTIC RUNGE-KUTTA METHODS

The main results of this paper are as follows: (1) Suppose an s stage RungeKutta method is consistent, irreducible, non-confluent and symplectic. Then this method is of order at least 2P (1) provided that the simplifying conditions C(P) (or D(p) with non-zero weights) and B(2P 1) hold, where 0, 1, 2. (2) Suppose an s stage Runge-Kutta method is consistent, irreducible and non-confluent, and satisfies the simplifying conditions C(P) and D(p) with 0