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.

1. Y. E. Anikonov, A uniqueness theorem for the solution of the inverse problem for the wave equation, Mat. Zametki 19 (1976), no. 2, 211–214.

2. Y. E. Anikonov, Analytical representations of solutions to multidimensional inverse problems for evolutionary equations, J. Inverse Ill-Posed Probl. 3 (1995), no. 4, 259–267.

3. Y. E. Anikonov, Formulas for solutions and coefficients of second-order differential equations, Sib. Math. J. 37 (1996), no. 3, 415–422.

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.

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3