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.