On a Method of Constructing Quadrature Formulas for Computing Hypersingular Integrals

This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the or...

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Bibliographic Details
Published in:Numerical analysis and applications 2022-09, Vol.15 (3), p.203-218
Main Authors: Boikov, I. V, Boikova, A. I
Format: Article
Language:English
Subjects:
Convergence
Errors
Integrals
Mathematics
Mathematics and Statistics
Numerical Analysis
Quadratures
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Summary:This paper is devoted to constructing quadrature formulas for evaluating singular and hypersingular integrals. For evaluating integrals with weights ,   defined on   we have constructed quadrature formulas uniformly converging on [ ] to the original integral with weights ,   and converging to the original integral for   with weights ,  . In the latter case, a sequence of quadrature formulas converges to the integral uniformly on [ ], where   is arbitrarily small. We propose a method for constructing and estimating the errors of quadrature formulas to evaluate hypersingular integrals by transforming quadrature formulas to evaluate singular integrals. We also propose a method for estimating the errors of quadrature formulas for singular integral evaluation based on approximation theory methods. The results obtained have been extended to hypersingular integrals.
ISSN:1995-4239
1995-4247
DOI:10.1134/S199542392203003X