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The numerical evaluation of one-dimensional Cauchy principal value integrals

Giovanni Monegato
- 01 Dec 1982 - 
- Vol. 29, Iss: 4, pp 337-354
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TLDR
This paper examines the numerical integration (in the Cauchy principal value sense) of functions having (several) first order real poles and proposes an alternative algorithm for the numerical evaluation of integrals of the form.
Abstract: 
In this paper we examine the numerical integration (in the Cauchy principal value sense) of functions having (several) first order real poles. We give a survey of results concerning some quadrature formulas of interpolatory type proposed by Delves, Hunter, Elliott and Paget, and several other authors; along with the description we present some minor generalizations and make comments on the computational aspects. Finally, we propose an alternative algorithm for the numerical evaluation of integrals of the form Open image in new window

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Citations
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Numerical Solution of Singular Integral Equations.

Frank Stenger
TL;DR: In this paper, the authors have developed methods for solving integral equations which work well in spite of the presence of singularities, in which the new approximation methods which were developed do work well for singularities.
Journal ArticleDOI

Numerical evaluation of hypersingular integrals

Giovanni Monegato
- 20 May 1994 - 
TL;DR: Boundary integral equations which employ integrals which exist only if defined in the Cauchy principal value sense or as the Hadamard finite part are currently used with success to solve many two-and three-dimensional problems of applied mechanics as mentioned in this paper.
Journal ArticleDOI

On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives

Nikolaos Ioakimidis
- 01 Jan 1985 - 
TL;DR: The convergence of the aforementioned quadrature rules for integrands possessing H6lder-continuous derivatives of an appropriate order is proved to be uniform and not only pointwise as mentioned in this paper.
Journal ArticleDOI

An automatic quadrature for Cauchy principal value integrals

Takemitsu Hasegawa, +1 more
- 01 Apr 1991 - 
TL;DR: In this paper, an automatic quadrature is presented for computing Cauchy principal value integrals Q(f; c) = Faf(t)/(t c) dt, a < c < b, for smooth functions f(t).
Journal ArticleDOI

The evaluation of cauchy principal value integrals in the boundary element method-a review

Massimo Guiggiani
- 01 Apr 1991 - 
TL;DR: Several methods of dealing with Cauchy Principal Value integrals in advanced boundary element methods are discussed and compared in this paper, and an attempt is made to present a comprehensive description of these methods in a unified, systematic manner.
References
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Journal ArticleDOI

Handbook of Mathematical Functions

Milton Abramowitz, +2 more
- 01 Feb 1966 - 
Journal ArticleDOI

Methods of Numerical Integration.

John F. Monahan, +2 more
- 01 Dec 1985 - 
Book

Methods of Numerical Integration

Philip J. Davis, +1 more
Journal ArticleDOI

Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints

K. S. Kölbig, +1 more
- 13 Jan 1972 - 
Journal ArticleDOI

On the numerical solution of singular integral equations

Fazil Erdogan, +1 more
- 01 Jan 1972 - 
TL;DR: In this paper, a pair of Gauss-Chebyshev integration formulas for singular integrals are developed and a simple numerical method for solving a system of singular integral equations is described.