ABSTRACT Numerical investigation of a new similarity method (the Aldar-Kose method) for N-body simulations is described. Using this method we have carried out numerical simulations for two tasks: 1) calculation of the temporal behavior of different physical parameters of active galactic nuclei (AGN) containing a super massive black hole (SMBH), an accretion disk, and a compact stellar cluster; 2) calculation of the stellar capture rate to the central SMBH without accretion disk. The calculations show good perspectives for applications of the similarity method to optimize the evolution model calculations of large stellar systems and of AGN.
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