**Efficient recursive Adams-Bashforth methods in molecular dynamics
simulations of N-body systems interacting through pairwise potentials**

J Marti and B Diaz, MOLECULAR SIMULATION, 46, 1248-1254 (2020).

DOI: 10.1080/08927022.2020.1815730

A recursive multistep Adams-Bashforth method applied to the Molecular Dynamics simulations of N-body systems interacting through pairwise force fields is introduced and analysed. Equations of motion are obtained using a set of Cartesian coordinates solved by means of an Adams-Bashforth numerical integration scheme of orders, which requires the iterative computation of function time derivatives. The proposed algorithm has been implemented using a programming approach that makes it possible to re-use a source code resulting in small codes, easy to maintain. Practical examples and benchmarks that illustrate the performance of these implementations are included. The study of its performance gives clues to evaluate its efficiency and precision. Numerical tests for a N-particle system are made on the equilibrium configuration of liquid argon near its triple point at 86.5 K and 0.021 angstrom(-3). In most cases, the algorithms here presented outperform those implemented traditionally as the Gear corrector-predictor or the Verlet family, leading to important savings in terms of total computation times and significantly increasing the numerical precision obtained with standard algorithms.

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