Email this article Stability of a three-layer symmetric differential-difference scheme in the class of functions summable on a network-like domain
- Authors: Provotorov V.V.1, Hoang V.N.1
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Affiliations:
- Voronezh State University
- Issue: Vol 27, No 137 (2022)
- Pages: 80-94
- Section: Articles
- URL: https://bakhtiniada.ru/2686-9667/article/view/295005
- DOI: https://doi.org/10.20310/2686-9667-2022-27-137-80-94
- ID: 295005
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Abstract
In the paper, the stability conditions of a three-layer symmetric differential-difference scheme with a weight parameter in the class of functions summable on a network-like domain are obtained. To analyze the stability of the differential-difference system in the space of feasible solutions H , a composite norm is introduced that has the structure of a norm in the space H2 = H⊕H . Namely, for Y={Y 1 , Y 2 }∈ H2 , Yl ∈ H (l=1,2) , ∥ Y∥ H 2 = ∥ Y 1 ∥ 1, H 2 + ∥ Y 2 ∥ 2, H 2 , where ∥·∥ 1, H 2 ∥·∥ 2, H 2 are some norms in H . The use of such a norm in the description of the energy identity opens the way for constructing a priori estimates for weak solutions of the differential-difference system, convenient for practical testing in the case of specific differentialdifference schemes. The results obtained can be used to analyze optimization problems that arise when modeling network-like transfer processes with the help of formalisms of differentialdifference systems.
About the authors
Vyacheslav V. Provotorov
Voronezh State University
Email: wwprov@mail.ru
Doctor of Physical and Mathematical Sciences, Professor of the Partial Differential Equations and Probability Theory Department 1 Universitetskaya pl., Voronezh 394018, Russian Federation
Van N. Hoang
Voronezh State University
Email: fadded9x@gmail.com
Post-Graduate Student. Partial Differential Equations and Probability Theory Department 1 Universitetskaya pl., Voronezh 394018, Russian Federation
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