Absolute stability of a difference scheme for the multidimensional time-dependently identification telegraph problem

Ashyralyev A. Al-Hazaimeh H. Ashyralyyev C.
December 2023 Springer Nature

Computational and Applied Mathematics
2023 #42 Issue 8

In 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.

Absolute stability , Difference schemes , Source identification problems , Telegraph equations

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Department of Mathematics, Bahcesehir University, Istanbul, 34353, Turkey
Peoples’ Friendship University of Russia (RUDN University), Moscow, 10587, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Near East University, TRNC, Mersin 10, Nicosia, Turkey
National University of Uzbekistan named after Mirzo Ulugbek, Tashkent, 100174, Uzbekistan
Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, 161200, Kazakhstan

Department of Mathematics
Peoples’ Friendship University of Russia (RUDN University)
Institute of Mathematics and Mathematical Modeling
Near East University
National University of Uzbekistan named after Mirzo Ulugbek
Khoja Akhmet Yassawi International Kazakh-Turkish University

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