A Modified Derivative-BasedScheme for the Riemann-Stieltjes Integral

Abstract

In this researchpaper, a new efficient midpoint derivative-based quadrature scheme of trapezoid-type is developed for the approximation of the Riemann-Stieltjes integral. The proposed quadrature scheme is an efficient modification of Zhao etal.midpoint derivative-based schemefor the Riemann-Stieltjes integral. The performance of proposed scheme, Zhao etal. scheme and the original Trapezoid scheme for the Riemann-Stieltjesintegral are comparedusing MATLAB. Ithas been noticed that the numerical error is smallerusing proposed schemeincomparisontootherschemes.