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Well-Posedness and Uniform Approximations of the Solution of a Boundary Value Problem for a Singular Integro-Differential Equation

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Abstract

On a real segment, we consider a boundary value problem for a singular integro-differential equation of the first kind with the Cauchy kernel in the characteristic part. The well-posedness of this problem, established by the authors on a pair of specially selected spaces, allows to use approximate methods for its solving. We propose a general projection method, establish the conditions for its convergence in the chosen spaces and estimates the error of approximate solutions. As a result, uniform error estimates are obtained. A computational scheme of the wavelet collocation method is constructed, its theoretical substantiation is carried out, the results of a numerical experiment are presented on a model example.

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Authors and Affiliations

  1. N. I. Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga Region) Federal University, 420008, Kazan, Tatarstan, Russia

    A. V. Ozhegova

  2. Institute of Computational Mathematics and Information Technologies, Kazan (Volga Region) Federal University, 420008, Kazan, Tatarstan, Russia

    L. E. Khairullina

Authors
  1. A. V. Ozhegova
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  2. L. E. Khairullina
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Correspondence to A. V. Ozhegova or L. E. Khairullina.

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(Submitted by F. G. Avkhadiev)

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Ozhegova, A.V., Khairullina, L.E. Well-Posedness and Uniform Approximations of the Solution of a Boundary Value Problem for a Singular Integro-Differential Equation. Lobachevskii J Math 41, 2239–2247 (2020). https://doi.org/10.1134/S1995080220110177

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  • DOI: https://doi.org/10.1134/S1995080220110177

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