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

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology