An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System
Berdyshev A. Aloev R. Abdiramanov Z. Ovlayeva M.
October 2023Multidisciplinary Digital Publishing Institute (MDPI)
Symmetry
2023#15Issue 10
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–implicit 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’s boundary data, ensuring the exponential stability of the difference scheme with directional splitting for the mixed problem in the l2 norm, has been identified.
hyperbolic system , Lyapunov stability , upwind difference scheme
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Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty, 050000, Kazakhstan
Institute of Information and Computational Technologies SC MES, Almaty, 050010, Kazakhstan
Department of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent, 100174, Uzbekistan
Department of Mathematics and Mathematical Modelling
Institute of Information and Computational Technologies SC MES
Department of Computational Mathematics and Information Systems
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