This work is devoted to finding an estimate of the convergence rate of an algorithm for numerically solving the optimal control problem for the three-dimensional heat equation. An important aspect of the work is not only the establishment of convergence of solutions of a sequence of discrete problems to the solution of the original differential problem, but the determination of the order of convergence, which plays a very important role in applications. The paper uses the discretization method of the differential problem and the method of integral estimates. The reduction of a differential multidimensional mixed problem to a difference one is based on the approximation of the desired solution and its derivatives by difference expressions, for which the error of such an approximation is known. The idea of using integral estimates is typical for such problems, but in the multidimensional case significant technical difficulties arise. To estimate errors, we used multidimensional analogues of the integration formula by parts, Friedrichs and Poincare inequalities. The technique used in this work can be applied under some additional assumptions, and for nonlinear multidimensional mixed problems of parabolic type. To find a numerical solution, the variable direction method is used for the difference problem of a parabolic type equation. The resulting algorithm is implemented using program code written in the Python 3.7 programming language.

The paper proposes methods for designing and building information systems for distributed processing of streaming data and their application for organizing and analyzing trade at financial sites. Typical approaches to organizing scalable systems are considered.

To date, the turbojet dual-circuit engine (turbojet) is the most common air-jet aircraft engine due to low fuel consumption and a number of other advantages. The purpose of this work is to develop a software package for calculating the parameters of the flow part of the turbojet with an intuitive and user-friendly modern interface that allows further expansion of the functionality due to the modular architecture. The developed software package is allowed to raise the process of designing the flow part of the turbojet to a higher level, thereby reducing not only the time of its development, but also the costs.