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Registration Number

0222U004472, 0121U113493 , R & D reports

Title

Mathematical methods for solving natural and technical problems. Actual problems of studying mathematics in higher education

Head

Kholkin Oleksandr M., Доктор фізико-математичних наук

Registration Date

11-08-2022

Organization

State Higher Educational Institution "Azov State Technical University"

Description

 Research method - analytical and numerical modeling. Methodological developments, such as testing students with the help of information and computer technologies. A numerical scheme for calculating the nonstationary laminar boundary layer was proposed and the separation point on the cylinder was calculated. The scheme can be used to find the point of viscous separation on smooth bodies with subsequent use in the method of discrete vortices to model the formation of free vortices. It was found that the result of the calculation depends significantly on the time step. An oscillation theorem for a problem with boundary conditions of general form is proved for the differential equation of arbitrary pair order with operator coefficients. In the framework of the modified superposition method, the solution of the problem of harmonic oscillations of a piecewise inhomogeneous region consisting of three interconnected rectangles with different elastic properties is constructed. A study of the peculiarities of the wave field near the singular point of the boundary at the junction of rectangles. The technologies, methods and algorithms for creating an information system for visualization of hydrodynamic processes with elements of intelligent interface are considered in the work. Both classical methods of visualization with the help of flow lines and labeled particles, as well as modern solutions based on textural visualization are considered and developed. To study one-dimensional discrete dynamic systems with one parameter, Kaskad was written in the Python programming language for the Windows operating system. With the help of the program you can explore the basic characteristics of a discrete dynamical system, namely: find fixed points, points of boundary cycles, Lyapunov exponent, phase space and bifurcation diagram.

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Bulanchuk Halyna H
Grafov Viktor Vyacheslavovych
Desyatsky Sergey P
Kirkina Tetyana Yuriivna
Litvin Anna M
Lopatenko Elena V
Nosovsky Svetlana E
Ostapenko Artem O
Kholkin Oleksandr M.