Generalized composite integration rules in the presence of a singularity
type: Item
instance of: scholarly article
title: Generalized composite integration rules in the presence of a singularity
zbMATH Open document ID: 0543.41031
DOI: 10.1007/BF02575594
published in: Calcolo
publication date: 1983-01-01T00:00:00Z
review text: A composite integration rule results from applying a basic integration rule exact for constants and with all abscissas in the integration interval to each of n equal subintervals of the interval of integration. A sequence of such composite rules converges to the interval for all Riemann-integrable functions and for functions with an endpoint singularity which are dominated by a monotonic improperly integrable function. These rules are generalized to allow a partition into unequal subintervals or different basic rules in each subinterval. In each of these situations, restrictions must be placed on the basic rule or rules or on the partition to ensure convergence in the singular case. Such restrictions also ensure the convergence of a modified rule in the case of an interior singularity.
reviewed by: R. S. Dahiya
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 3863802
zbMATH Keywords: composite integration rule
zbMATH Keywords: interior singularity
author: Philip Rabinowitz
MaRDI profile type: Publication
cites work: Ignoring the Singularity in Approximate Integration
cites work: Q4060253
cites work: On Ignoring the Singularity in Numerical Quadrature
cites work: Gaussian Integration in the Presence of a Singularity
cites work: Q3875201
description: scientific article; zbMATH DE number 3863802