On some questions in computer modeling of the reachability sets constructing problems

The research considers the problem of constructing the reachability sets of non-linear dynamical system in n-dimensional Euclidean space on the fixed time interval. The approximate solution methods of the reachability sets constructing are considered in this research as well as the accuracy estimation for this methods is given. The research contains the computational experiments on computer modeling of described reachability sets constructing methods, which use the algorithms implemented for two computation technologies CPU as well as GPU (using CUDA technology). In this research the description and comparison of approaches to the computer modeling of the problem are given. Furthermore, the CPU-based computer modeling result comparison with the result obtained on GPU based on CUDA technology are presented. Besides, this research discusses some the side issues appeared during computer modeling, the issues raised during the computer algorithms implementation, as well as the ways to eliminate these issues or reduce their impact.