# EFFICIENT DERIVATIVE-BASED SIMPSON’S 1/3-TYPE SCHEME USING CENTROIDAL MEAN FOR RIEMANN-STIELTJES INTEGRAL

#### DOI NO:

https://doi.org/10.26782/jmcms.2021.03.00006

#### Keywords:

Quadrature rule,Riemann-Stieltjes integral,Centroidal Mean,Simpson’s 1/3 rule,Composite form,Local error,Global error,Cost-effectiveness,Time-efficiency,

#### Abstract

In this paper, a new efficient derivative-based quadrature scheme of Simpson’s 1/3-type is proposed using the centroidal mean for the approximation of Riemann-Stieltjes integral (RS-integral). Theorems are proved related to the basic form, composite form, local and global errors of the new scheme for the RS-integral. The reduction of the new proposed scheme is verified using g(t) = t for Riemann integral. The theoretical results of new proposed scheme have been proved by experimental work using programming in MATLAB against existing schemes. The order of accuracy, computational cost and average CPU time (in seconds) of the new proposed scheme are determined. The results obtained show the effectiveness of the proposed scheme compared to the existing schemes.

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