Cost and Time Efficient Derivative Based Midpoint Closed Newton-Cotes Quadrature

Abstract

A variety of methods, collectively known as "numerical integration," are employed in numerical analysis to approximate the value of a definite integral. Among these, the Newton-Cotes formulas represent a key category of numerical techniques for evaluating such integrals. These methods are especially valuable for integrating functions that involve singularities or nonlinearities. The primary aim of this research is to propose more efficient techniques using centroid mean that offer higher accuracy, greater precision, and reduced errors. The study also emphasizes the theoretical analysis of errors, including theorems related to the order of accuracy and error terms for the developed methods. To assess the effectiveness of the new methods, comparisons are made with other classical approaches through numerical tests on various commonly used integrals, as reported in existing literature. The methods are implemented using MATLAB (R2018b) for high-level computer programming. All results were noted in Intel(R) Core(TM) i3-4010U with RAM 4.00GB Laptop and processing speed of 1.70GHz.