Derivative corrections for quadrature formulas
type: Item
instance of: scholarly article
title: Derivative corrections for quadrature formulas
zbMATH Open document ID: 0876.65008
DOI: 10.1007/BF02127701
author: William F. Ford
author: Yuesheng Xu
author: Yunhe Zhao
published in: Advances in Computational Mathematics
publication date: 1997-03-11T00:00:00Z
review text: This paper is concerned with the construction of quadrature rules that include approximations to derivative correction terms for standard formulas. The correction terms require only the use of the integrand values from the original formula. This is a standard method for improving simple quadrature formulas. What is new in this paper is that the quadrature formulas that are considered do not require the integrand values to be determined at equally spaced points. The main theoretical contributions of the paper are the derivation of some recursive formulas for the correction terms. The application of the new formulas is considered for both smooth and singular integrands. Two numerical examples are used to illustrate the new formulas.
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 989551
zbMATH Keywords: quadrature rules
zbMATH Keywords: correction terms
zbMATH Keywords: recursive formulas
zbMATH Keywords: singular integrands
zbMATH Keywords: numerical examples
reviewed by: A. Genz
MaRDI profile type: Publication
cites work: Q3323133
cites work: High-Order Corrected Trapezoidal Quadrature Rules for Singular Functions
cites work: End-point corrected trapezoidal quadrature rules for singular functions
cites work: Q3895980
cites work: Quadrature methods for periodic singular and weakly singular Fredholm integral equations
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description: scientific article; zbMATH DE number 989551