The successive approximations method for the airfoil equation
type: Item
instance of: scholarly article
title: The successive approximations method for the airfoil equation
zbMATH Open document ID: 0662.76016
DOI: 10.1016/0377-0427(88)90271-3
author: S. H. Smith
published in: Journal of Computational and Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The successive approximations method for the solution of Fredholm equations of the second kind is applied in this paper, for the first time, and after an appropriate modification, to the airfoil equation [\textit{F. G. Tricomi}, Integral Equations (1957; Zbl 0078.094)]. Rather than giving just one more method for the solution of this equation, the aim of the paper is to show that a modification of the successive approximations method may be applied to the direct solution of some Cauchy type singular integral equations of the first kind. The numerical implementation of the method, by using Gaussian quadrature rules, is described in detail and applied to some simple cases. Numerical results verifying the accuracy and convergence of the method are displayed.
Mathematics Subject Classification ID: 76B10
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 4083169
zbMATH Keywords: convergence
zbMATH Keywords: Jacobi polynomial
zbMATH Keywords: Neumann iterations
zbMATH Keywords: uniform norm
zbMATH Keywords: successive approximations method
zbMATH Keywords: Fredholm equations of the second kind
zbMATH Keywords: airfoil equation
zbMATH Keywords: Cauchy type singular integral equations of the first kind
zbMATH Keywords: Gaussian quadrature rules
MaRDI profile type: Publication
full work available at URL: 0377-0427(88)90271-3
OpenAlex ID: W2094700851
cites work: Q4124250
cites work: The Deferred Approach to the Limit for Eigenvalues of Integral Equations
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cites work: On the numerical evaluation of derivatives of Cauchy principal value integrals
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cites work: Q3682937
cites work: Q3244632
description: scientific article; zbMATH DE number 4083169