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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

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Abstract

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.

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Authors and Affiliations

  1. Mari State University, pl. Lenina 1, Ioshkar Ola, 424001, Russia

    V. V. Klyuchev

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  1. V. V. Klyuchev
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Correspondence to V. V. Klyuchev.

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Original Russian Text © V.V. Klyuchev, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 4, pp. 56–60.

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Klyuchev, V.V. 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. Russ Math. 53, 45–48 (2009). https://doi.org/10.3103/S1066369X09040082

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  • DOI: https://doi.org/10.3103/S1066369X09040082

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