Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities

Author:

Aloev Rakhmatillo Djuraevich12ORCID,Berdyshev Abdumauvlen Suleimanovich13ORCID,Alimova Vasila2ORCID,Bekenayeva Kymbat Slamovna1ORCID

Affiliation:

1. Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050000, Kazakhstan

2. Department of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent 100174, Uzbekistan

3. Institute of Information and Computational Technologies SC MES, Almaty 050010, Kazakhstan

Abstract

In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary control for the specified hyperbolic system is given. A difference scheme is constructed for the numerical solution of the considered initial boundary value problem. The definition of the exponential stability of the numerical solution in ℓ2-norm with respect to a discrete perturbation of the equilibrium state of the initial boundary value difference problem is given. A discrete Lyapunov function for a numerical solution is constructed, and a theorem on the exponential stability of a stationary solution of the initial boundary value difference problem in ℓ2-norm with respect to a discrete perturbation is proved.

Funder

Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan

Publisher

MDPI AG

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