A class of quadrature formulas of Chebyshev type for singular integrals
type: Item
instance of: scholarly article
title: A class of quadrature formulas of Chebyshev type for singular integrals
zbMATH Open document ID: 0567.65011
DOI: 10.1016/0022-247X(84)90091-X
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: We reprove and extend several quadrature formulas for singular integrals \(\int^{1}_{-1}g(t)/(t-x)(1-t^ 2)^{1/2}dt\quad (-1<x<1)\) or \(\int^{1}_{-1}g(x)(1-x^ 2)^{1/2}/(x-t)dx\quad (-1\leq t\leq 1)\) systematically by a unified method based on the corresponding formulas for ordinary integrals so that their remainders can be easily estimated. Using the same method, we also establish another set of formulas named Simpson-Chebyshev type which seems more effective when the density function g(x) has less order of smoothness as illustrated by an example.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 30E20
zbMATH DE Number: 3905730
zbMATH Keywords: quadrature formulas
zbMATH Keywords: singular integrals
zbMATH Keywords: Simpson-Chebyshev type
author: Jianke Lu
MaRDI profile type: Publication
cites work: Q5558293
cites work: Modified gauss-jacobi quadrature formulas for the numerical evaluation of cauchy type singular integrals
cites work: On the numerical solution of singular integral equations
cites work: Q5681646
cites work: Q3253343
cites work: Q5820804
cites work: Numerical integration methods for the solution of singular integral equations
description: scientific article; zbMATH DE number 3905730