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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 47

Identification of a Mathematical Model of Economic Development of Two Regions of the World

Author(s)
Mikhail V. Bezgachev1,2,4, Maxim A. Shishlenin1,2,4, Alexander V. Sokolov3,4

1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russian Federation

2Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

3Institute of Economics and Industrial Production Organization SB RAS, Novosibirsk, Russian Federation

4Novosibirsk State University, Novosibirsk, Russian Federation

Abstract
This paper is devoted to solving the inverse problem (determining the parameters of a system of ordinary differential equations based on additional information determined at discrete points in time) and analyzing its solution for a mathematical model describing the dynamics of changes in the population and capital of two regions of the world. The inverse problem is reduced to the problem of minimizing the target functional and is solved by the method of differential evolution. A numerical method for solving direct and inverse problems is implemented. The developed method was tested on model and real data for countries such as Russia, China, India and the USA.
About the Authors

Mikhail V. Bezgachev, Novosibirsk State University, Sobolev Institute of Mathematics SB RAS, Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, 630090, Russian Federation, m.bezgachev@g.nsu.ru

Maxim A. Shishlenin, Dr. Sci. (Phys.–Math.), Prof. RAS, Sobolev Institute of Mathematics SB RAS, Novosibirsk State University, Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, 630090, Russian Federation, mshishlenin@ngs.ru

Alexander V. Sokolov, Cand. Sci. (Econ.), Assoc. Prof., Institute of Economics and Industrial Engineering, Novosibirsk State University, Novosibirsk, 630090, Russian Federation, alsokolov@ieie.nsc.ru

For citation
Bezgachev M. V., Shishlenin M. A., Sokolov A. V. Identification of a Mathematical Model of Economic Development of Two Regions of the World. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 47, pp. 12–30. https://doi.org/10.26516/1997-7670.2024.47.12
Keywords
mathematical model, system of ordinary differential equations, population, economic development, inverse problem, direct problem
UDC
519.622
MSC
34A55, 65L05, 65L09, 65K10, 91B62
DOI
https://doi.org/10.26516/1997-7670.2024.47.12
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