Characterizations of Symmetric Multistep Runge-Kutta Methods

Abstract

Some characterizations for symmetric multistep Runge-Kutta (RK) methods are obtained. Symmetric two-step RK methods with one and two-stages are presented. Numerical examples show that symmetry of multistep RK methods alone is not sufficient for long time integration for reversible Hamiltonian systems. This is an important difference between one-step and multistep symmetric RK methods.