{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T22:06:40Z","timestamp":1775167600051,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T00:00:00Z","timestamp":1696377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Committee of the Ministry of Science","award":["AP14872379"],"award-info":[{"award-number":["AP14872379"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce a numerical integration method for hyperbolic systems problems known as the splitting method, which serves as an effective tool for solving complex multidimensional problems in mathematical physics. The exponential stability of the upwind explicit\u2013implicit difference scheme split into directions is established for the mixed problem of a linear two-dimensional symmetric t-hyperbolic system with variable coefficients and lower-order terms. It is noteworthy that there are control functions in the dissipative boundary conditions. A discrete quadratic Lyapunov function was devised to address this issue. A condition for the problem\u2019s boundary data, ensuring the exponential stability of the difference scheme with directional splitting for the mixed problem in the l2 norm, has been identified.<\/jats:p>","DOI":"10.3390\/sym15101863","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T07:47:52Z","timestamp":1696405672000},"page":"1863","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Explicit\u2013Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1228-8246","authenticated-orcid":false,"given":"Abdumauvlen","family":"Berdyshev","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":"Institute of Information and Computational Technologies SC MES, Almaty 050010, Kazakhstan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4734-3070","authenticated-orcid":false,"given":"Rakhmatillo","family":"Aloev","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\/0000-0003-3820-7253","authenticated-orcid":false,"given":"Zhanars","family":"Abdiramanov","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"}]},{"given":"Mohinur","family":"Ovlayeva","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"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,4]]},"reference":[{"key":"ref_1","unstructured":"Godunov, S.K. 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