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This paper is devoted to different modifications of two standard softeningsof the gravitational attraction (namely the Plummer and Hernquist softenings),which are commonly used in cosmological simulations based on theparticle-particle (PP) method, and their comparison. It is demonstrated thatsome of the proposed alternatives lead to almost the same accuracy as in thecase of the pure Newtonian interaction, even despite the fact that the forceresolution is allowed to equal half the minimum interparticle distance. Therevealed way of precision improvement gives an opportunity to succeed insolving Gurzadyan's Problem 5 and bring modern computer codes up to a higherstandard.

Gurzadyan's Problem 5 and improvement of softenings for cosmological simulations using the PP method