Title | On the convergence of the solution of a three-layer perturbed difference scheme to the solution of an abstract ill-posed Cauchy problem |
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Authors | M. A. Sultanov^{1}^{1}Akhmet Yassawi International Kazakh-Turkish University |

Annotation | A 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. |

Keywords | ill-posed problem, difference scheme, finite stability, Carleman estimate, operator, $l - $ well-posed problem, convergence |

Citation | Sultanov 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: 24.06.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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