Rational function approximations in the numerical solution of Cauchy-type singular integral equations
type: Item
instance of: scholarly article
title: Rational function approximations in the numerical solution of Cauchy-type singular integral equations
zbMATH Open document ID: 0627.65139
DOI: 10.1016/0898-1221(85)90099-9
author: Michael A. Driscoll
author: R. P. Srivastav
publication date: 1985-01-01T00:00:00Z
review text: From authors' summary: Cauchy-type singular integral equations of the second kind with constant coefficients are solved via rational and polynomial approximations. Rational functions, similar to that of polynomials, have the property that for r(t) rational and for many of the weight functions w(t) encountered in practice, \(R(x)\equiv \int^{1}_{-1}w(t)r(t)/(t-x)dt\) is also rational. Hence, approximations by rational functions is feasible. Rational function approximations in the solution of the dominant equation results in a linear algebraic system which possesses block-diagonal structure. It is further shown that the determinant of the coefficient matrix is bounded below away from zero and stability is ensured under fairly non- restrictive conditions. For the complete Cauchy-type singular integral equation, i.e. the equation with both the principal and regular parts, Gaussian quadrature in conjunction with the rational function method is synthesized in the construction of a ``hybrid'' scheme. Error estimates and convergence are established. A variety of problems from aero-dynamics and fracture mechanics are solved and presented as a basis of comparison to polynomial-based schemes.
reviewed by: Douglas Quinney
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 76G25
Mathematics Subject Classification ID: 74R99
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 4020427
zbMATH Keywords: Cauchy-type singular integral equations of the second kind
zbMATH Keywords: Rational function approximations
zbMATH Keywords: stability
zbMATH Keywords: Gaussian quadrature
zbMATH Keywords: ``hybrid'' scheme
zbMATH Keywords: error estimates
zbMATH Keywords: convergence
zbMATH Keywords: aero-dynamics
zbMATH Keywords: fracture mechanics
zbMATH Keywords: comparison
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90099-9
OpenAlex ID: W1989460443
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4020427