A reversible averaging integrator for multiple time-scale dynamics

This paper describes a new reversible staggered time-stepping method for si mulating long-term dynamics formulated on two or more time scales. By assum ing a partition into fast and slow variables, it is possible to design an i ntegrator that (1) averages the force acting on the slow variables over the fast motions and (2) resolves the fast variables on a finer time scale tha n the others. By breaking the harmonic interactions between slow and fast s ubsystems, this scheme formally avoids resonant instabilities and is stable to the slow-variable stability threshold. The method is described for Hami ltonian systems, but can also be adapted to certain types of non-Hamiltonia n reversible systems. (C) 2001 Academic Press.