Piecewise-Polynomial Quadratures for Cauchy Singular Integrals

In this paper, we propose piecewise-polynomial methods for the approximation of Cauchy principal value integrals and develop a simple, efficient and numerically stable algorithm for the evaluation of the weights of the resulting piecewise-polynomial quadratures. We present two examples to illustrate...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1986-08, Vol.23 (4), p.891-902
Main Author: Gerasoulis, Apostolos
Format: Article
Language:English
Subjects:
Approximation
Exact sciences and technology
Gaussian quadratures
Integrals
Mathematical integrals
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Numerical quadratures
Perceptron convergence procedure
Polynomials
Recursion
Sciences and techniques of general use
Series convergence
Singular integral equations
Weighting functions
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Summary:In this paper, we propose piecewise-polynomial methods for the approximation of Cauchy principal value integrals and develop a simple, efficient and numerically stable algorithm for the evaluation of the weights of the resulting piecewise-polynomial quadratures. We present two examples to illustrate the advantages of these quadratures versus the Gauss-Jacobi quadratures.
ISSN:0036-1429
1095-7170
DOI:10.1137/0723057