Email this article Projector Approach to Constructing the Asymptotics of Solution of Initial Value Problems for Weakly Nonlinear Discrete Systems with Small Step in the Critical Case
- Authors: Kurina G.A1,2, Khoay N.T.3
-
Affiliations:
- Voronezh State University, Voronezh, 394018, Russia
- Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia
- VNU University of Science, Vietnam National University, Ha Noi, Viet Nam
- Issue: Vol 59, No 1 (2023)
- Pages: 73-84
- Section: Articles
- URL: https://journals.rcsi.science/0374-0641/article/view/144901
- DOI: https://doi.org/10.31857/S0374064123010077
- EDN: https://elibrary.ru/OCIIXC
- ID: 144901
Cite item
Open Access
Access granted
Subscription Access
Abstract
An algorithm for constructing an asymptotic solution containing boundary functions for an initial value problem for a weakly nonlinear system of discrete equations with small step in the critical case under certain conditions is given in the article by V.F. Butuzov and A.B. Vasil’eva in Differ. Uravn., 1970, vol. 6, no. 4, pp. 650–664. In the present paper, orthogonal projectors are used to construct the asymptotics of the solution of this problem. This projector approach greatly simplifies the understanding of the algorithm for constructing the asymptotics and permits explicitly writing the problems from which one can find the terms of any order in the asymptotics of the solution.
About the authors
G. A Kurina
Voronezh State University, Voronezh, 394018, Russia; Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333, Russia
Email: kurina@math.vsu.ru
Nguen Tkhi Khoay
VNU University of Science, Vietnam National University, Ha Noi, Viet Nam
Author for correspondence.
Email: nguyenthihoai@hus.edu.vn
References
- Бутузов В.Ф., Васильева А.Б. Дифференциальные и разностные системы уравнений с малым параметром в случае, когда невозмущённая (вырожденная) система расположена на спектре // Дифференц. уравнения. 1970. T. 6. № 4. С. 650-664.
- Васильева А.Б., Бутузов В.Ф. Сингулярно возмущенные уравнения в критических случаях. М., 1978.
- Kurina G.A., Dmitriev M.G., Naidu D.S. Discrete singularly perturbed control problems (a survey) // Dyn. Contin. Discrete Impuls. Syst. Ser. B: Appl. Algorithms. 2017. V. 24. P. 335-370.
- Sibuya Y. Some global properties of matrices of functions of one variable // Math. Ann. 1965. V. 161. P. 67-77.
- Kurina G. Projector approach to constructing asymptotic solution of initial value problems for singularly perturbed systems in critical case // Axioms. 2019. V. 8. № 2. P. 56-60.
- Курина Г.А., Хоай Н.Т. Проекторный подход к алгоритму Бутузова-Нефедова асимптотического решения одного класса сингулярно возмущённых задач в критическом случае // Журн. вычислит. математики и мат. физики. 2020. Т. 60. № 12. С. 2073-2084.
- Kurina G.A., Hoai N.T. Projector approach for constructing the zero order asymptotic solution for the singularly perturbed linear-quadratic control problem in a critical case // AIP Conf. Proc. Int. Conf. Analysis and Applied Mathematics (ICAAM 2018). 2018. V. 1997. P. 430-436.
- Каto T. Perturbation Theory for Linear Operators. Berlin, Heidelberg, 1966.
- Гайшун И.В. Системы с дискретным временем. Минск, 2001.
- Horn R.A., Johnson C.R. Matrix Analysis. Cambridge, 2013.
