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Registration Number

0223U003887, 0122U201304 , R & D reports

Title

Modern methods of mathematical modeling in theoretical, technical and natural problems. Actual problems of studying mathematics in higher education

Head

Kholkin Oleksandr М., Доктор фізико-математичних наук

Registration Date

18-07-2023

Organization

State Higher Educational Institution "Azov State Technical University"

Description

 The object of research is mathematical and computer modeling for abstract, technical and economic objects, methods of teaching mathematics at a technical university. The purpose of the work is to study processes in various fields of natural science, economics, and technology using the creation of mathematical models, their analysis using mathematical methods and computer modeling. Development of new methods of teaching mathematics. The research method is analytical and numerical modeling. Methodological developments, such as testing students using information and computer technologies. Research results: The application of the symplectic integration method to the system of point vortices in an ideal fluid was investigated. The Tao method of doubling the phase space is used. Research indicates that the symplectic method conserves the energy (Hamiltonian) of the vortices, while the 2nd-order Runge-Kutta method yields energy reduction. The relationship between the oscillatory properties of the solution of the boundary value problem and the levels in the gap of the boundary spectrum for a differential equation of arbitrary order is established. Considered alternative methods of symmetric regression, in particular: orthogonal regression and regression of the geometric mean. The derivation of each method is made efficient by using Ehrenberg's formula for the ordinary least squares error and by extracting a weight function that characterizes the regression. The operation of the multi-channel mass service system in stationary mode is considered: a semi-Markov operating device is constructed, the asymptotic behavior of the probabilities of group failures at one recovery interval of the control device is analyzed. Numerical analysis of the determination of resonant frequencies and characteristics of the wave field for the problem of harmonic oscillations of a piecewise inhomogeneous region consisting of three interconnected rectangles with different elastic properties was

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