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Velocity autocorrelation functions (VAF) of the fluids are studied on short-and long-time scales within a unified approach. This approach is based on aneffective summation of the infinite continued fraction at a reasonableassumption about convergence of relaxation times of the high order memoryfunctions, which have purely kinetic origin. The VAFs obtained within ourmethod are compared with computer simulation data for the liquid Ne atdifferent densities and the results, which follow from the Markovianapproximation for the highest order kinetic kernels. It is shown that in allthe thermodynamic points and at the chosen level of the hierarchy, our resultsagree much better with the MD data than those of the Markovian approximation.The density dependence of the transition time, needed for the fluid to attainthe hydrodynamic stage of evolution, is evaluated. The common and distinctivefeatures of our method are discussed in their relations to the generalizedcollective mode (GCM) theory, the mode coupling theory (MCT), and some othertheoretical approaches.

A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches