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Updated: Jul 11, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Trotter derivation of algorithms for Brownian and dissipative particle dynamics
Fabrice Thalmann1, Jean Farago
1Institut Charles Sadron, CNRS UPR 22, 67083 Strasbourg Cedex, France, and Université Louis Pasteur, 4 rue Blaise Pascal, F-67070 Strasbourg Cedex, France. thalmann@ics.u-strasbg.fr
Abstract:
This paper focuses on the temporal discretization of the Langevin dynamics, and on different resulting numerical integration schemes. Using a method based on the exponentiation of time dependent operators, we carefully derive a numerical scheme for the Langevin dynamics, which we found equivalent to the proposal of Ermak and Buckholtz [J. Comput. Phys. 35, 169 (1980)] and not simply to the stochastic version of the velocity-Verlet algorithm. However, we checked on numerical simulations that both algorithms give similar results, and share the same "weak order two" accuracy. We then apply the same strategy to derive and test two numerical schemes for the dissipative particle dynamics. The first one of them was found to compare well, in terms of speed and accuracy, with the best currently available algorithms.
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