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Open Newton-Cotes Quadrature Rules with Derivatives

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Title: Open Newton-Cotes Quadrature Rules with Derivatives

Authors: Shehzad Abbas Khan

Journal: Physical Education, Health and Social Sciences

HEC Recognition History
Category From To
Y 2024-10-01 2025-12-31

Publisher: Wisdom Education & Research Hub

Country: Pakistan

Year: 2025

Volume: 3

Issue: 2

Language: en

DOI: 10.63163/jpehss.v3i2.512

Keywords: Numerical integrationopen Newton-Cotes formuladefined integralarithmetic meangeometric meannumerical examples.

Categories
Computer Science (14978) Numerical Analysis (431) Applied Mathematics (727) Calculus (39) Mathematics (5170)

Abstract

In this research paper, a new family of numerical integration of open Newton-Cotes isintroduced which uses the mean of arithmetic and geometric means at derivative value for the evaluation ofa certain integral. These quadrature methods are shown to be more efficient than the existing quadraturerules. The error terms are obtained by using the concept of precision. Finally, the accuracy of proposedmethod is verified with numerical examples and the results are compared with existing methods numericallyand graphically

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