The talk is devoted to mathematical modelling of spherically symmetric gravitating configurations of a scalar field with minimal coupling. The authors find analytical generalisation of the methods of restored scalar potential and propose a general classification of scalar configurations. A comparative analytical and numerical analysis of vacuum black holes and static gravitating configurations of a classical scalar field (black holes, naked singularities, wormholes, and topological geons) is implemented. Scalar gravitating configurations are of interest as models of the space-time geometry in the close vicinity of massive, strongly gravitating objects at the centres of galaxies, while the scalar field is considered as an effective dark matter model. The main observed effects are primarily related to the motion of test particles (solar-mass stars) around the attracting centres, therefore, a significant part of this study is devoted to the numerical analysis of the parameters of their orbits. Secondly, models of tidal disruption of stars are constructed and it is shown that the mechanism of so-called tidal disruption events is completely different for black holes and naked singularities. In our numerical calculations, in particular, the method of covariant series in normal coordinates is used. When calculating the coefficients of covariant expansions of tensor fields in the normal neighbourhood of a submanifold, an original algorithm was developed, and its computational complexity was estimated. The algorithm is implemented in the form of a software set.