A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration

Abstract

In this work, a newfour-pointclosed quadraturerule is proposed for numerical integration.The proposed quadrature rule appears to be an efficient modification of Zhao and Li’s mid-point derivative based Simpson’s 3/8 rule (MDS38) which used fourth order mid-point derivative in each strip of integration. While the proposed Simpson’s 3/8 rule uses only the second order mid-point derivative in each strip of integration, we show through numerical experiments that it results in smallest error bounds as compared to the Zhao and Li’s MDS38 rule and the original Newton-Cote’s Simpson’s 3/8 rule (Original S38).