Quadrature rules for Prandtl's integral equation
type: Item
instance of: scholarly article
title: Quadrature rules for Prandtl's integral equation
zbMATH Open document ID: 0576.65014
DOI: 10.1007/BF02252732
author: V. Pennacchietti
author: G. Monegato
published in: Computing
publication date: 1986-01-01T00:00:00Z
review text: We construct an interpolatory quadrature formula of the type \[ \int^{1}_{-1}f'(x)/(y-x)dx\approx \sum^{n}_{i=1}w_{ni}(y)f(x_{ni}), \] where \(f(x)=(1- x)^{\alpha}(1+x)^{\beta}f_ 0(x)\), \(\alpha,\beta >0\), and \(\{x_{ni}\}\) are the n zeros of the n-th degree Chebyshev polynomial of the first kind, \(T_ n(x)\). We also give a convergence result and examine the behavior of the quantity \(\sum^{n}_{i=1}| w_{ni}(y)|\) as \(n\to \infty\).
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 45E05
zbMATH DE Number: 3921809
zbMATH Keywords: Prandtl's integral equation
zbMATH Keywords: interpolatory quadrature formula
zbMATH Keywords: Cauchy principal value integral
zbMATH Keywords: convergence
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02252732
OpenAlex ID: W1717552839
description: scientific article; zbMATH DE number 3921809