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Approximation of the Stieltjes integral and applications in numerical integration

Pietro Cerone, Sever Silvestru Dragomir (2006)

Applications of Mathematics

Some inequalities for the Stieltjes integral and applications in numerical integration are given. The Stieltjes integral is approximated by the product of the divided difference of the integrator and the Lebesgue integral of the integrand. Bounds on the approximation error are provided. Applications to the Fourier Sine and Cosine transforms on finite intervals are mentioned as well.

Asymptotic behaviors of intermediate points in the remainder of the Euler-Maclaurin formula.

Xu, Aimin, Cen, Zhongdi (2010)

Abstract and Applied Analysis

Asymptotic behaviour of fixed-order error constants of modified quadrature formulae for Cauchy principal value integrals.

Diethelm, Kai, Köhler, Peter (2000)

Journal of Inequalities and Applications [electronic only]

Asymptotic expressions for remainder terms of some quadrature rules

Nenad Ujević, Nataša Bilić (2008)

Open Mathematics

Asymptotic expressions for remainder terms of the mid-point, trapezoid and Simpson’s rules are given. Corresponding formulas with finite sums are also given.

Asymptotic Minimum Norm Quadrature Formulae.

A. Pinkus (1975)

Numerische Mathematik

Asymptotics for the remainder of a class of positive quadratures for integrands with an interior singularity.

Knut Petras (1993)