A novel method for integrating the equations of motion in molecular dynamics simulations of many-particle systems is proposed. It is based on canonical transformations of the phase space and high-accuracy reversible decompositions of the time evolution propagator into terms with different time scales. This allows one to efficiently overcome the limitations imposed on the efficiency of the integration in standard multiple time stepping algorithms. As is demonstrated for a particular case of the Lennard-Jones fluids, the precision of the simulations within the method presented can be increased by several orders of magnitude already at typical computational costs and time steps.

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