{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:05:15Z","timestamp":1760144715981,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T00:00:00Z","timestamp":1715904000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP14872379"],"award-info":[{"award-number":["AP14872379"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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 \u21132-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 \u21132-norm with respect to a discrete perturbation is proved.<\/jats:p>","DOI":"10.3390\/axioms13050334","type":"journal-article","created":{"date-parts":[[2024,5,17]],"date-time":"2024-05-17T12:02:23Z","timestamp":1715947343000},"page":"334","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Exponential Stability of the Numerical Solution of a Hyperbolic System with Nonlocal Characteristic Velocities"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4734-3070","authenticated-orcid":false,"given":"Rakhmatillo Djuraevich","family":"Aloev","sequence":"first","affiliation":[{"name":"Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050000, Kazakhstan"},{"name":"Department of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent 100174, Uzbekistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1228-8246","authenticated-orcid":false,"given":"Abdumauvlen Suleimanovich","family":"Berdyshev","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050000, Kazakhstan"},{"name":"Institute of Information and Computational Technologies SC MES, Almaty 050010, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-5966-3039","authenticated-orcid":false,"given":"Vasila","family":"Alimova","sequence":"additional","affiliation":[{"name":"Department of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent 100174, Uzbekistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7552-1789","authenticated-orcid":false,"given":"Kymbat Slamovna","family":"Bekenayeva","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050000, Kazakhstan"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2646","DOI":"10.1137\/120902203","article-title":"Output Feedback Stabilization for a Scalar Conservation Law with a Nonlocal Velocity","volume":"45","author":"Coron","year":"2013","journal-title":"SIAM J. 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