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Conditional stability of a solution of a difference scheme for an ill-posed Cauchy problem. (English) Zbl 1387.35624
Summary: 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.
MSC:
35R30 Inverse problems for PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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