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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 Numerical Solution of Delay Nonlinear Parabolic Differential Equations with Nonlocal Conditions(American Institute of Physics Inc., 2024) Ashyralyev, Allaberen; Mu’azu, Sa’Adu Bello; 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; Mu’azu, Sa’Adu Bello, 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 this paper, the numerical solution of delay nonlinear parabolic differential equations is studied. The first and second order of accuracy difference schemes for the solution of one dimensional nonlinear parabolic equation with time delay and nonlocal conditions are presented. Numerical results have been provided and compared with the exact solution to show the efficiency of the proposed numerical method. © 2024 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.