A corrected quadrature formula and applications
Date
2004
Authors
Ujevic, N.
Roberts, A.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2004; 45:E41-E56
Statement of Responsibility
Nenad Ujevic and A.J. Roberts
Conference Name
Abstract
A straightforward three-point quadrature formula of closed type is derived that improves on Simpson’s rule. Just using the additional information of the integrand’s derivative at the two endpoints we show the error is sixth order in grid spacing. Various error bounds for the quadrature formula are obtained to quantify more precisely the errors. Applications in numerical integration are given. With these error bounds, which are generally better than the usual Peano bounds, the composite formulas can be applied to integrands with lower order derivatives.