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Approximate Methods for Solving Hypersingular Integral Equations

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Topics in Integral and Integro-Differential Equations

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 340))

Abstract

The work is devoted to a review of analytical and numerical methods for solving linear hypersingular integral equations. Hypersingular integral equations of the first and second kind on closed and open integration intervals are considered. Particular attention is paid to equations with second-order singularities, since these equations are most in demand in applications. The proofs of the convergence of approximate methods are based on the general theory of approximate methods of analysis and on the continuous method for solving operator equations. Easily visible sufficient conditions for the solvability of computational schemes and estimates of the accuracy of the proposed methods are obtained.

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Authors and Affiliations

  1. Penza State University, Penza, Russia

    Ilya Boykov

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  1. Ilya Boykov
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Correspondence to Ilya Boykov .

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Editors and Affiliations

  1. Department of Mathematics, Post Graduate College, Ghazipur, Uttar Pradesh, India

    Harendra Singh

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Departamento de Matemática, Universidade Estadual de Maringá, Maringá, Brazil

    Marcelo M. Cavalcanti

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Boykov, I. (2021). Approximate Methods for Solving Hypersingular Integral Equations. In: Singh, H., Dutta, H., Cavalcanti, M.M. (eds) Topics in Integral and Integro-Differential Equations. Studies in Systems, Decision and Control, vol 340. Springer, Cham. https://doi.org/10.1007/978-3-030-65509-9_3

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