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Reference: Korsunsky, AM, (1998). Gauss-Chebyshev quadrature formulae for strongly singular integrals. QUARTERLY OF APPLIED MATHEMATICS, 56 (3), 461-472.Citable link to this page:

 

Gauss-Chebyshev quadrature formulae for strongly singular integrals

Abstract: This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e. one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. The quadrature formulae are derived from those for Cauchy singular integrals.The resulting discretizations are valid at a number of fixed points, determined as the zeros of a certain Jacobi polynomial. As in all Gaussian quadratures, the final quadrature formulae involve fixed nodal points and provide exact results for polynomials of degree 2n − 1, where n is the number of nodes. These properties make this approach rather attractive for applications to fracture mechanics problems, where often numerical solution of integral equations with strongly singular kernels is the objective. Numerical examples of the application of the Gauss-Chebyshev rule to some plane and axisymmetric crack problems are given.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Accepted ManuscriptNotes:First published in the Quarterly of Applied Mathematics 56 (3) in 1998. © 1998 Brown University.

Bibliographic Details

Publisher: Division of Applied Mathematics, Brown University

Publisher Website: http://www.dam.brown.edu/

Journal: QUARTERLY OF APPLIED MATHEMATICSsee more from them

Issue Date: 1998-9

pages:461-472Identifiers

Urn: uuid:f932ce88-8185-49c2-bf35-6c1f5295a7f7

Source identifier: 62719

Issn: 0033-569X Item Description

Type: Journal article;

Language: eng

Version: Accepted ManuscriptSubjects: Engineering and allied sciences Tiny URL: pubs:62719

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Author: Korsunsky, AM - institutionUniversity of Oxford Oxford, MPLS, Engineering Science - - - - Bibliographic Details Publisher: Divisi

Source: https://ora.ox.ac.uk/objects/uuid:f932ce88-8185-49c2-bf35-6c1f5295a7f7



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