A new proof of the Euler-Maclaurin expansion for quadrature over implicitly defined curves
type: Item
instance of: scholarly article
title: A new proof of the Euler-Maclaurin expansion for quadrature over implicitly defined curves
zbMATH Open document ID: 0938.65004
DOI: 10.1016/S0377-0427(98)00198-8
author: Muhammed Syam
published in: Journal of Computational and Applied Mathematics
publication date: 2000-06-28T00:00:00Z
review text: This paper provides a short proof of the existence of an expansion in even powers of the grid parameter \(h\) for the error in a remarkable simple integraton rule for line integrals. The integration rule is a natural generalization of the trapezoidal rule. The generalized rule can be used for integration of a smooth \(n\)-dimensional vector-valued integrand along a smooth parameterized curve in \(n\) dimensions. The derivations given in the paper are based on the use of Taylor series combined with one-dimensional Euler-Maclaurin expansions.
Mathematics Subject Classification ID: 65B15
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 1367880
zbMATH Keywords: Euler-Maclaurin expansion
zbMATH Keywords: line integral
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: Taylor series
reviewed by: A. Genz
MaRDI profile type: Publication
cites work: Q3998344
cites work: Q3139554
cites work: Approximation of Integrals for Boundary Element Methods
cites work: Quadrature Over Curved Surfaces by Extrapolation
cites work: The modified trapezoidal rule for line integrals
description: scientific article; zbMATH DE number 1367880