Error inequalities for an optimal 3-point quadrature formula of closed type
An optimal 3-point quadrature formula of closed type is derived. Various error inequalities are established. Applications in numerical integration are also given.
math.CA↗
arXiv subjects
Nenad Ujevic
Publications and source records attributed to Nenad Ujevic.
A corrected quadrature formula and applications
A straightforward 3-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.
math.NA↗
Peano-like bounds for some Newton-Cotes formulae
An error analysis for some Newton-Cotes quadrature formulae is presented. Peano-like error bounds are obtained. They are generally, but not always, better than the usual Peano bounds.
math.NA↗