Special stability advantages of position-Verlet over velocity-Verlet in multiple-time step integration

We present an analysis for a simple two-component harmonic oscillator that compares the use of position-Verlet to velocity-Verlet for multiple-time step integration. The numerical stability analysis based on the impulse-Verlet splitting shows that position-Verlet has enhanced stability, in terms of the largest allowable time step, for cases where an ample separation of time scales exists. Numerical investigations confirm the advantages of the position-Verlet scheme when used for the fastest time scales of the system. Applications to a biomolecule, a solvated protein, for both Newtonian and Langevin dynamics echo these trends over large outer time-step regimes.