Source identification problems for hyperbolic differential and difference equations

Author:

Ashyralyev Allaberen1ORCID,Emharab Fathi2

Affiliation:

1. Department of Mathematics , Near East University , Nicosia , TRNC, Mersin 10 , Turkey ; and Peoples’ Friendship University of Russia (RUDN University), Moscow 117198, Russia; and Institute of Mathematics and Mathematical Modeling, 050010, Almaty, Kazakhstan

2. Department of Mathematics , Near East University , Nicosia , TRNC, Mersin 10 , Turkey ; and Department of Mathematics, Omar Al-Mukhtar University, El-Beida, Libya

Abstract

Abstract In the present study, a source identification problem for a one-dimensional hyperbolic equation is investigated. Stability estimates for the solution of the source identification problem are established. Furthermore, a first-order-of-accuracy difference scheme for the numerical solution of the source identification problem is presented. Stability estimates for the solution of the difference scheme are established. This difference scheme is tested on an example, and some numerical results are presented.

Funder

Ministry of Education and Science of the Republic of Kazakhstan

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Reference37 articles.

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4. Y. E. Anikonov and M. V. Neshchadim, On analytical methods in the theory of inverse problems for hyperbolic equations. I, J. Appl. Ind. Math. 5 (2011), no. 4, 506–518.

5. Y. E. Anikonov and M. V. Neshchadim, On analytical methods in the theory of inverse problems for hyperbolic equations. II, J. Appl. Ind. Math. 6 (2012), no. 1, 6–11.

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