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

Date

2018-01-23

Authors

Sultanov, Murat
Akylbaev, Musabek
Ibragimov, Raskul

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

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.

Description

Keywords

Carleman estimates, Ill-posed Cauchy problems, Finite stability, Difference operator, Numerical solution

Citation

Sultanov, M. A., Akylbaev, M. I., & Ibragimov, R. (2018). Conditional stability of a solution of a difference scheme for an ill-posed Cauchy problem. <i>Electronic Journal of Differential Equations, 2018</i>(33), pp. 1-17.

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Attribution 4.0 International

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