Error inequalities for a quadrature formula and applications

Several error inequalities for a quadrature formula with a parameter and applications

In this paper, we will derive several error inequalities for a quadrature formula with a parameter, which will not only provide some generalizations of the known results, but also give some other interesting quadrature formulae as special cases. Furthermore, sharp upper and lower error bounds for the double error inequalities are obtained. Applications in numerical integration are also given. ©...

An Error Estimate for Stenger's Quadrature Formula

The basis of this paper is the quadrature formula where q = exp(2A), h being a chosen step length. This formula has been derived from the Trapezoidal Rule formula by F. Stenger. An explicit form of the error is given for the case where the integrand has a factor of the form (1 — x)a(\ + x)P, a,ß> -1. Application is made to the evaluation of Cauchy principal value integrals with endpoint singula...

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 ...

Error inequalities for an optimal 3-point quadrature formula of closed type

In recent years a number of authors have considered an error analysis for quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson rules have been investigated more recently ([2], [4], [5], [6], [11]) with the view of obtaining bounds on the quadrature rule in terms of a variety of norms involving, at most, the first derivative. In the mentioned papers explicit...

Asymptotic Error Estimates for the Gauss Quadrature Formula