Paper Info
Title
Unified error bounds for all Newton-Cotes quadrature rules.
Abstract
It is well-known that the remaining term of a classical n-point Newton-Cotes quadrature depends on at least an n-order derivative of the integrand function. Discounting the fact that computing an n-order derivative requires a lot of differentiation for large n, the main problem is that an error bound for an n-point Newton-Cotes quadrature is only relevant for a function that is n times differentiable, a rather stringent condition. In this paper, by defining two specific linear kernels, we resolve this problem and obtain new error bounds for all closed and open types of Newton-Cotes quadrature rules. The advantage of the obtained bounds is that they do not depend on the norms of the integrand function and are very general such that they cover almost all existing results in the literature. Some illustrative examples are given in this direction.
Year
DOI
Venue
2015
10.1515/jnma-2015-0006
JOURNAL OF NUMERICAL MATHEMATICS
Keywords
Field
DocType
Closed and open types of Newton-Cotes quadrature rules,error bounds,linear kernels,normed spaces,Simpson and Milne integration formulae
Gauss–Kronrod quadrature formula,Applied mathematics,Mathematical analysis,Clenshaw–Curtis quadrature,Newton–Cotes formulas,Quadrature (mathematics),Mathematics
Journal
Volume
Issue
ISSN
23
1
1570-2820
Citations 
PageRank 
References 
0
0.34
0
Authors
1
Name
Order
Citations
PageRank
Mohammad Masjed-Jamei1158.03