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On the convergence of the solution of a three-layer perturbed difference scheme to the solution of an abstract ill-posed Cauchy problem

TitleOn the convergence of the solution of a three-layer perturbed difference scheme to the solution of an abstract ill-posed Cauchy problem
AuthorsM. A. Sultanov1
1Akhmet Yassawi International Kazakh-Turkish University
AnnotationA theorem on the convergence of the solution of a three-layered difference scheme with two weights to the solution of an abstract ill-posed Cauchy problem is proved. The proof of convergence is based on the stability theorem for a three-layer difference scheme with two weights, which is based on the concepts of finite stability and on difference a priori weight estimates of the Carleman type.
Keywordsill-posed problem, difference scheme, finite stability, Carleman estimate, operator, $l - $ well-posed problem, convergence
CitationSultanov M. A. ''On the convergence of the solution of a three-layer perturbed difference scheme to the solution of an abstract ill-posed Cauchy problem'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 90-96. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper13.pdf. - Date of access: 15.10.2019.