Abstract
This paper presents an overview of the regularization algorithms for modeling the central regions of galaxies having black holes. We are looking at the following algorithms: Logarithmic Hamiltonian (LogH), Time-Transformed Leapfrog (TTL), and the Graph-based Activity Regularization (GAR) [1]. In the data algorithms, you can use the system coordinate that is a good sign. The distortion of circular distances may be the main problem in the algorithm, where the coordinates of the corresponding body are measured from the split head. In the baseline, TTL algorithm is only used for some types of regularization for the random closest collisions of the very small bodies. Next, a hybrid algorithm, called ϕGRAPEch code, was investigated to simulate the central regions of galaxies containing one or more massive black holes. The ϕGRAPE code is based on a sequential implementation and includes a regularization scheme for the Mikkola and Merritt algorithmic chain for processing orbits near the central black hole with high accuracy. This algorithm divides particles into two groups: particles associated with massive objects and included in the chain, and particles outside the chain that move according to the Hermite ϕGRAPE scheme. The hybrid code provides better energy saving in less computation time than the standard fourth-order Hermite integration scheme.