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This strategy is applied to derive reversible reference system propagator algorithms (RESPA) that greatly accelerate simulations of systems with a separation of time scales or with long range forces. The new algorithms have all of the advantages of previous RESPA integrators but are reversible, and more stable than those methods. These methods are applied to a set of paradigmatic systems and are shown to be superior to earlier methods. It is shown how the new RESPA methods are related to predictor–corrector integrators. 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