RESONANCE IN THE DYNAMICS OF CHEMICAL-SYSTEMS SIMULATED BY THE IMPLICIT MIDPOINT SCHEME

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- (Delta t) dependent resonances and we predict approximate values of Delta t where they will occur. The particular case of a third-order resonance (Delta t approximate to 7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Delta t > 10 fs the energy errors remain bound.