An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System
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 sche...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1863 |
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| author | Abdumauvlen Berdyshev Rakhmatillo Aloev Zhanars Abdiramanov Mohinur Ovlayeva |
| author_facet | Abdumauvlen Berdyshev Rakhmatillo Aloev Zhanars Abdiramanov Mohinur Ovlayeva |
| author_sort | Abdumauvlen Berdyshev |
| collection | DOAJ |
| description | 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 <i>l</i><sup>2</sup> norm, has been identified. |
| first_indexed | 2024-03-10T20:52:20Z |
| format | Article |
| id | doaj.art-fbe9a85af91c4897b49421cd49884102 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:52:20Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-fbe9a85af91c4897b49421cd498841022023-11-19T18:17:51ZengMDPI AGSymmetry2073-89942023-10-011510186310.3390/sym15101863An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic SystemAbdumauvlen Berdyshev0Rakhmatillo Aloev1Zhanars Abdiramanov2Mohinur Ovlayeva3Department of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050000, KazakhstanDepartment of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent 100174, UzbekistanDepartment of Mathematics and Mathematical Modelling, Institute of Mathematics, Physics and Informatics, Abai Kazakh National Pedagogical University, Almaty 050000, KazakhstanDepartment of Computational Mathematics and Information Systems, Faculty of Applied Mathematics and Intellectual Technology, Ulugbek National University of Uzbekistan, Tashkent 100174, UzbekistanIn 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 <i>l</i><sup>2</sup> norm, has been identified.https://www.mdpi.com/2073-8994/15/10/1863hyperbolic systemupwind difference schemeLyapunov stability |
| spellingShingle | Abdumauvlen Berdyshev Rakhmatillo Aloev Zhanars Abdiramanov Mohinur Ovlayeva An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System Symmetry hyperbolic system upwind difference scheme Lyapunov stability |
| title | An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System |
| title_full | An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System |
| title_fullStr | An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System |
| title_full_unstemmed | An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System |
| title_short | An Explicit–Implicit Upwind Difference Splitting Scheme in Directions for a Mixed Boundary Control Problem for a Two-Dimensional Symmetric t-Hyperbolic System |
| title_sort | explicit implicit upwind difference splitting scheme in directions for a mixed boundary control problem for a two dimensional symmetric t hyperbolic system |
| topic | hyperbolic system upwind difference scheme Lyapunov stability |
| url | https://www.mdpi.com/2073-8994/15/10/1863 |
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