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Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 4, Pages 56–60 (Mi ivm1321)  

Brief communications

The necessary and sufficient conditions for the qualified convergence of difference methods for approximate solution of the ill-posed Cauchy problem in a Banach space

V. V. Klyuchev

Mari State University

Abstract: We study properties of the finite-difference methods for approximate solution of the ill-posed Cauchy problem for a homogeneous equation of the first order with a sectorial operator in a Banach space. We obtain the necessary and sufficient conditions for the qualified (with respect to the step of grid) uniform (on a segment) convergence of approximations to the exact solution of the problem. These conditions represent a priori data about the segment, where a solution exists, or about the sourcewise representation of a certain value of the desired solution.

Keywords: Cauchy problem, ill-posed problem, finite-difference approximation methods, sectorial condition, Banach space, sourcewise representation.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:4, 45–48

Bibliographic databases:

UDC: 517.983
Received: 10.04.2008

Citation: V. V. Klyuchev, “The necessary and sufficient conditions for the qualified convergence of difference methods for approximate solution of the ill-posed Cauchy problem in a Banach space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 4, 56–60; Russian Math. (Iz. VUZ), 53:4 (2009), 45–48

Citation in format AMSBIB
\Bibitem{Kly09}
\by V.~V.~Klyuchev
\paper The necessary and sufficient conditions for the qualified convergence of difference methods for approximate solution of the ill-posed Cauchy problem in a~Banach space
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 4
\pages 56--60
\mathnet{http://mi.mathnet.ru/ivm1321}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2581475}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 4
\pages 45--48
\crossref{https://doi.org/10.3103/S1066369X09040082}


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