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Publication Metadata only Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem(SPRINGER HEIDELBERG, 2023) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Ashyralyyev, Charyyar; Bahcesehir University; Institute of Mathematics & Mathematical Modeling; Near East University; National University of Uzbekistan; Akhmet Yassawi International Kazakh-Turkish UniversityIn the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated.Publication Metadata only An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems(MDPI, 2023) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Bahcesehir University; Peoples Friendship University of Russia; Institute of Mathematics & Mathematical Modeling; Near East UniversityThis article is devoted to the study of the stability of time-dependent source identification telegraph type differential problems with dependent coefficients. Time-dependent source identification problems (SIPs) for telegraph differential equations (TDEs) with constant coefficients can be solved by classical integral-transform methods. However, these classical methods can be used, basically, in cases where the differential equation has constant coefficients. We establish the basic theorem of the stability of the time-dependent SIPs for the second-order linear differential equation (DE) in a Hilbert space with a self-adjoint positive definite operator (SAPDO) and damping term. In practice, stability estimates for the solution of the three types of SIPs for one-dimensional and for multidimensional TDEs with dependent coefficients and classic and non-classic conditions are obtained.Publication Open Access STABILITY OF THE TIME-DEPENDENT IDENTIFICATION PROBLEM FOR THE TELEGRAPH EQUATION WITH INVOLUTION(Academic Publications Ltd., 2022) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Ashyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Al-Hazaimeh, Haitham, Department of Mathematics, Yakın Doğu Üniversitesi, Nicosia, CyprusIn the present paper, a time-dependent source identification problem for a one dimensional telegraph equation with involution is studied. Theorems on the stability estimates for the solution of this problem are established © 2022 Elsevier B.V., All rights reserved.Publication Metadata only Numerical Solution of the Time-Dependent Source of Identification Problem for the Telegraph Equation with Nonlocal Condition(American Institute of Physics Inc., 2023) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Aripov, M.M.; Ashyralyev, A.; Ashyralyev, A.; Ashyralyyev, C.; Ashyralyyev, C.; Erdogan, A.S.; Kabulov, A.; Karimov, E.; Khudoyberdiyev, A.; Ashyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Al-Hazaimeh, Haitham, Department of Mathematics, Yakın Doğu Üniversitesi, Nicosia, CyprusIn the present paper, a time-dependent source of identification p roblem f or a o ne d imensional t elegraph equation with nonlocal conditions is studied. The first o rder o f a ccuracy s table d ifference s cheme f or t his s ource i dentification problem is presented. The numerical results are presented, and are compared with the exact solution to verify the accurate nature of our method. © 2023 Elsevier B.V., All rights reserved.Publication Open Access An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems(Multidisciplinary Digital Publishing Institute (MDPI), 2023) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Ashyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, Department of Mathematics, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Al-Hazaimeh, Haitham, Department of Mathematics, Yakın Doğu Üniversitesi, Nicosia, CyprusThis article is devoted to the study of the stability of time-dependent source identification telegraph type differential problems with dependent coefficients. Time-dependent source identification problems (SIPs) for telegraph differential equations (TDEs) with constant coefficients can be solved by classical integral-transform methods. However, these classical methods can be used, basically, in cases where the differential equation has constant coefficients. We establish the basic theorem of the stability of the time-dependent SIPs for the second-order linear differential equation (DE) in a Hilbert space with a self-adjoint positive definite operator (SAPDO) and damping term. In practice, stability estimates for the solution of the three types of SIPs for one-dimensional and for multidimensional TDEs with dependent coefficients and classic and non-classic conditions are obtained. © 2023 Elsevier B.V., All rights reserved.Publication Metadata only An a pproximation to the solution of two dimensional source identification telegraph problem with Dirichlet condition(American Institute of Physics Inc., 2023) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Ashyralyyev, Charyyar; Cakalli, H.; Kocinac, L.D.R.; Ashyralyev, A.; Harte, R.; Dik, M.; Canak, I.; Kandemir, H.S.; Tez, M.; Ozay, G.; Savas, E.; Aral, N.D.; Ucgun, F.C.; Ashyralyyev, C.; Akay, K.U.; Ashyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Al-Hazaimeh, Haitham, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey; Ashyralyyev, Charyyar, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, UzbekistanIn this paper, the first order of accuracy absolutely stable difference scheme for the approximate solution of the identification problem for the telegraph equation with the Dirichlet condition is proposed. Numerical results have been provided for the solution of time-dependent source identification problems for telegraph differential equations in the two-dimensional case. © 2023 Elsevier B.V., All rights reserved.Publication Metadata only Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem(Springer Nature, 2023) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Ashyralyyev, Charyyar; Ashyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Al-Hazaimeh, Haitham, Yakın Doğu Üniversitesi, Nicosia, Cyprus; Ashyralyyev, Charyyar, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, Uzbekistan, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, KazakhstanIn the present study, a new implicit absolute stable difference scheme (DS) for an approximate solution of the time-dependent source identification problem (SIP) for the telegraph equation (TE) is presented. The stability of difference problem is established. In applications of abstract results in a Hilbert space with a self-adjoint positive definite operator (SAPDO), theorems on stability estimates for the solution of DSs for approximate solutions of the multidimensional time-dependent SIPs for telegraph equations are obtained. Finally, these DSs are tested on stability in both two- and three-dimensional examples with different boundary conditions and some computational results are illustrated. © 2023 Elsevier B.V., All rights reserved.Publication Metadata only A Study on Approximate Solution of the Two Dimensional Source Identification Telegraph Problem with Neumann Condition(American Institute of Physics Inc., 2024) Ashyralyev, Allaberen; Al-Hazaimeh, Haitham; Ashyralyyev, Charyyar; Ashyralyev, A.; Ashyralyev, A.; Ashyralyyev, C.; Ashyralyyev, C.; Erdogan, A.S.; Sadybekov, M.; Ashyralyev, Allaberen, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, RUDN University, Moscow, Russian Federation, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan; Al-Hazaimeh, Haitham, Department of Mathematics, Yakın Doğu Üniversitesi, Nicosia, Cyprus; Ashyralyyev, Charyyar, Department of Mathematics, Bahçeşehir Üniversitesi, Istanbul, Turkey, National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, UzbekistanIn the current work, two-dimensional source identification problem for the telegraph equation with Neumann boundary condition is investigated. The first order of accuracy absolute stable difference scheme to find the numerical solution of the two-dimensional identification problem for the telegraph equation with the second kind boundary condition is solved. A numerical example of the time-dependent source identification problem has been carried out to check the accuracy and effectiveness of the presented technique. © 2024 Elsevier B.V., All rights reserved.