Reference modeling as a method for solving nonlinear problems
https://doi.org/10.37493/2307-910X.2023.2.2
Abstract
In this paper, the method of reference modeling is considered, designed for calculation, analysis and mathematical modeling of nonlinear physical phenomena and technological processes. The advantages of this method, the possibility of its application in the entire range of basic parameters of a nonlinear problem, the uniformity of the design scheme for all types of problems are formulated. The proposed method is used to create models of convective diffusion in an inhomogeneous medium, scattering of thermal electrons in a field with central symmetry, and the behavior of electrical conductivity depending on temperature and dielectric permittivity of wide-band semiconductors. The problem of calculating the transparency of a potential barrier that a particle hits, considered as a test, gave a good result (an error in the range of 0.8-1.2%). In this paper, the main features of using the reference modeling method for solving nonlinear differential equations are demonstrated. The obtained results of analysis and modeling allow us to confidently assess the reliability of the general ideas of the reference modeling method, its design scheme, as well as the convergence of its decompositions, the similarity criteria of the system under study and the selected model. The method proposed in this paper, taking into account its approbation in various conditions, can serve as a basis for application in the study of nonlinear problems of various nature, finding approximate solutions to nonlinear differential equations.
About the Authors
A. B. Cheboksarov
Stavropol State Pedagogical Institute, Branch in Essentuki
Russian Federation
Russian Federation
Cheboksarov Alexander Borisovich - Candidate of Physical and Mathematical Sciences, Associate Professor, Head of the Department of Mathematics, Computer Science
N. Yu. Botvineva
Stavropol State Pedagogical Institute, Branch in Essentuki
Russian Federation
Russian Federation
Botvineva Natalia - Candidate of Pedagogical Sciences, Associate Professor, Associate Professor of the Department of Mathematics, Computer Science
V. A. Cheboksarov
Pyatigorsk Institute (branch) of North-Caucasus Federal University
Russian Federation
Russian Federation
Cheboksarov Victor Aleksandrovich - teacher of computer science at NCFU College and Shame
E. V. Polovinko
Pyatigorsk Institute (branch) of North-Caucasus Federal University
Russian Federation
Russian Federation
Polovinko Ekaterina Vladimirovna - Associate Professor of the Department of Management Systems and Information Technologies
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Review
For citations:
Cheboksarov A.B., Botvineva N.Yu., Cheboksarov V.A., Polovinko E.V. Reference modeling as a method for solving nonlinear problems. Modern Science and Innovations. 2023;(2):20-32. (In Russ.) https://doi.org/10.37493/2307-910X.2023.2.2
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