Exponential stability of a numerical solution of a hyperbolic system with negative nonlocal characteristic velocities and measurement error
Aloev R. Berdyshev A. Alimova V.
2025Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan
Uzbek Mathematical Journal
2025#69Issue 47 - 14 pp.
In this work, the problem of stabilizing the equilibrium state for a hyperbolic system with negative nonlocal characteristic velocities and measurement error is investigated. A mixed problem is considered for such systems, when a limited perturbation of measurement errors is taken into account in the boundary conditions. The study is based on the use of the adequacy between the stability for a mixed problem for the original hyperbolic system of linear differential equations and the stability of the initial-boundary difference problem for it. When analyzing the initial-boundary difference problems constructed in this way, the properties of logarithmic norms are used. Algorithms are proposed that make it possible to obtain sufficient conditions for the exponential stability of a numerical solution of an initial-boundary difference problem with nonlocal coefficients and limited perturbation of measurement errors in boundary conditions. Sufficient conditions are presented in the form of matrix inequalities, which involve matrices of boundary conditions. The results are presented in the form of an a priori estimate of the numerical solution in the norm through the norms of the functions of the initial data and the norms of perturbation of measurement errors.
hyperbolic system , Lyapunov stability , Lyapunov’s function , nonlocal characteristic velocity
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Department of Computational Mathematics and Information Systems, National University of Uzbekistan, Tashkent, Uzbekistan
Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty, Kazakhstan
Department of Computational Mathematics and Information Systems
Department of Mathematics and Mathematical Modelling
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