Electron. J. Differential Equations, Vol. 2018 (2018), No. 33, pp. 1-17.

Conditional stability of a solution of a difference scheme for an ill-posed Cauchy problem

Murat A. Sultanov, Musabek I. Akylbaev, Raskul Ibragimov

In this article, we obtain criteria for stability of two-layer difference schemes for an abstract ill-posed Cauchy problem. Method of proof is based on obtaining a priori difference weighted Carleman type estimates. Stability conditions for solutions of two-layer difference schemes are used to prove the theorem of conditional stability of a solution of three-layer scheme that approximates an ill-posed Cauchy problem for an integral-differential equation associated with a coefficient inverse problem.

Submitted July 5, 2017. Published January 23, 2018.
Math Subject Classifications: 35R30, 65M12.
Key Words: Carleman estimates; Ill-posed Cauchy problems; finite stability; Difference operator; numerical solution.

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Murat A. Sultanov
Department of Mathematics
Akhmet Yasawi International Kazakh-Turkish University
str. Sattarkhanov, 29, 161200 Turkistan, Kazakhistan
email: murat.sultanov@ayu.edu.kz
Musabek I. Akylbaev
Department of Computer Science and Mathematics
Kazakhstan Engineering and Pedagogical University of Friendship of Peoples
str. Tole bi 32, 160000, Shymkent, Kazakhstan
email: akyl-bek@mail.ru
Raskul Ibragimov
Department of Physics and Mathematics
South Kazakhstan State Pedagogical Institute
str. Baitursynov 13, 160000, Shymkent, Kazakhstan
email: raskul1953@mail.ru

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