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

We study properties of 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)...

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Veröffentlicht in:Russian mathematics Jg. 53; H. 4; S. 45 - 48
1. Verfasser: Klyuchev, V. V.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Heidelberg Allerton Press, Inc 01.04.2009
Schlagworte:
Mathematics
Mathematics and Statistics
sectorial condition
finite-difference approximation methods
sourcewise representation
Banach space
ill-posed problem
Cauchy problem
ISSN:1066-369X, 1934-810X
Online-Zugang:Volltext
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Zusammenfassung:We study properties of 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 an 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.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X09040082