A Reversible Averaging Integrator for Multiple Time-Scale Dynamics

This paper describes a new reversible staggered time-stepping method for simulating long-term dynamics formulated on two or more time scales. By assuming a partition into fast and slow variables, it is possible to design an integrator 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 than the others. By breaking the harmonic interactions between slow and fast subsystems, this scheme formally avoids resonant instabilities and is stable to the slow-variable stability threshold. The method is described for Hamiltonian systems, but can also be adapted to certain types of non-Hamiltonian reversible systems.