A Modified Derivative-BasedScheme for the Riemann-Stieltjes Integral

In this research paper, 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 scheme for the Riemann-Stieltjes integral. The performance of proposed scheme, Zhao etal. scheme and the original Trapezoid scheme for the Riemann-Stieltjesintegral are compared using MATLAB. Ithas been noticed that the numerical error is smaller using proposed scheme in comparison to other schemes.