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

A theoretical study of a two-component harmonic oscillator that compares the position-Verlet to velocity-Verlet for multiple-time step integration was carried out. The stability analysis suggested better numerical behavior for position-Verlet results when the inner time step approached its Verlet stability limit. Numerical analysis also indicated the advantages of the position-Verlet scheme for fastest time scales of the system. Similar trends were obtained for a biomolecular system, a solvated protein and Newtonian and Langevin dynamics.