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
Abstract:
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
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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
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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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