Paper Title:

Error Bounds for Numerical Integration of Functions of Lower Smoothness and Gauss-Legendre Quadrature Rule

Author(s):

Samuel A. Surulere and Abiola O. Oladeji

Tshwane University of Technology
Department of Mathematics and Statistics
175, Nelson Mandela drive, Arcadia, Pretoria,
South Africa.
E-mail: samuel.abayomi.sas@gmail.com

Abstract:

The error bounds of the rectangular, trapezoidal and Simpson's rules which are commonly used in approximating the integral of a function (f(x)) over an interval ([a,b]) were estimated. The error bounds of the second, and third generating functions of the Gauss-Legendre quadrature rules were also estimated in this paper. It was shown that for an (f(t)) whose smoothness is increasing, the accuracy of the fourth, sixth and eighth error bound of the second, and third generating functions of the Gauss-Legendre quadrature rule does not increase. It was also shown that the accuracy of the fourth error bound of the Simpson's (1/3) and (3/8) rules does not increase.

Full Text PDF: