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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 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 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.