Conditional stability of a solution of a difference scheme for an ill-posed Cauchy problem
Texas State University, Department of Mathematics
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.
Carleman estimates, Ill-posed Cauchy problems, Finite stability, Difference operator, Numerical solution
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.