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DIFFERENCE SCHEMES FOR MOLECULAR DYNAMICS. 1. COMPARATIVE ANALYSIS OF STABILITY, ACCURACY, AND EFFICIENCY

V. N. Sofronov, K. S. Mokina, V. E. Shemarulin
VANT. Ser.: Mat. Mod. Fiz. Proc 2011. Вып.2. С. 18-32.

Investigations of accuracy have been performed for the most extensively used difference schemes for MD simulations. The paper concludes that difference schemes with canonicity of phase flow demonstrate the best ratio between the accuracy and efficiency.
The paper offers the RKN4 scheme, which is a three-stage difference scheme of the fourth order of approximation. It allows reduction (by 3 to 4 orders) in the amplitude error and total energy disbalance in comparison with the Verlet scheme very often used for the molecular dynamics problems. Thus, it becomes possible to reduce the problem runtime while preserving the given computation accuracy.

Keywords: molecular dynamics, Hamiltonian systems, phase error, splitting method, preservation of the phase flow canonicity, MD difference schemes.








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