A generalization of the pre-Grüss inequality is presented. It is applied to estimations of remainders of some quadrature formulas.

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. ©...

We study the construction of a quadrature rule which allows the simultaneous integration of a given function with respect to different weights. This construction is built on the basis of simultaneous Padé approximation of a Nikishin system of functions. The properties of these approximants are used in the proof of convergence of the quadratures and positivity of the corresponding quadrature coe...

An evaluation of the derivative of spherical Bessel functions of order n + 1 2 at its zeros is obtained. Consequently, an explicit quadrature formula for entire functions of exponential type is given.

Abstract This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As matter of fact, the (VFD) that has been used is in Caputo sense. The first step this constructive on construction using shifted Legendre–Laguerre polynomials unknown coefficients. second involves combination collocation method and operatio...

This article focuses on the process of approximating a definite integral from values of the integrand when exact mathematical integration is not available. This problem arises in statistics when marginal density functions or expected values of random variables are required. The article describes classical univariate quadrature methods including the trapezoidal rule, Simpson’s rule, Newton-Cotes...

Cotes, J. E., Dabbs, J. M., Hall, A. M., Axford, A. T., and Laurence, K. M. (1973). Thorax, 28, 709-715. Lung volumes, ventilatory capacity, and transfer factor in healthy British boy and girl twins. Normal values are reported for the lung volumes, ventilatory capacity, and transfer factor of 212 healthy British twin children aged 8 to 16 years. The boys and the girls share a common relationshi...