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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
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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.
Received: 10.04.2008
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, Volume 53, Issue 4, Pages 45–48
DOI: https://doi.org/10.3103/S1066369X09040082
Bibliographic databases:
Document Type: Article
UDC: 517.983
Language: Russian
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
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\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{https://mathscinet.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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