NUMERICAL INTEGRATORS THAT CONTRACT VOLUME

ROBERT I. MCLACHLAN AND G. REINOUT W. QUISPEL

Abstract. We study numerical integrators that contract phase space volume even when the ODE does so at an arbitrarily small rate. This is done by a splitting into two-dimensional contractive systems. We prove a sufficient condition for Runge-Kutta methods to have the appropriate contraction property for these two-dimensional systems; the midpoint rule is an example.