It is known that accelerator physics technology has made essential contributions to other branches of science and technology. Experiments realized on linear and circular accelerators have made remarkable discoveries about the basic nature of matter. In particular, there are now two accelerator projects. The first of them is already realized - the Large Hadron Collider, the second - the pilot project for future dedicated EDM machine. These and other similar projects (i. e., the project NICA, JINR, Dubna) demand some special requirements for simulation methods and technologies. Indeed, the successful functioning of these accelerators requires essential advancement in theory and technology leading to new particle accelerators capabilities. The complexity of accelerator physics problems makes comprehensive use of modern analytical, numerical, and symbolic methods. Only if we integrate these approaches the corresponding computational technologies will be effective. In the present report, we discuss some problems of correlation between symbolic and numerical manipulation. The main approach for beam dynamics is based on Lie algebraic methods and corresponding matrix formalism as presentation tools. All suggested approaches are realized using symbolic algorithms, and the corresponding symbolic formulae are assumed as a basis of numerical algorithms. This approach allows to realize the necessary numerical modeling using parallel and distributed computational systems for some practical problems.