NED University Journal of Research
ISSN 2304-716X
E-ISSN 2706-5758




HERONIAN MEAN DERIVATIVE-BASED OPEN NEWTON-COTES QUADRATURE RULES

Author(s): Sara Mahesar1, Muhammad Mujtaba Shaikh2, Muhammad Saleem Chandio3, Abdul Wasim Shaikh4
1Assistant Professor, Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan, Ph. +92(0)22-2772250, Fax: +92(0)22-2772250, Email: Sara.mahesar@faculty.muet.edu.pk.
2 Associate Professor, Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan, Ph. +92(0)22-2772250, Fax: +92(0)22-2772250, Email: mujtaba.shaikh@faculty.muet.edu.pk.
3 Ex-professor, Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Pakistan, Ph. +92(0)22-9213181, Fax: +92(0)22-9213181, Email: saleem.chandio@usindh.edu.pk.
4 Professor, Institute of Mathematics and Computer Science, University of Sindh, Jamshoro, Pakistan, Ph. +92(0)22-9213181, Fax: +92(0)22-9213181, Email: wasim.shaikh@usindh.edu.pk.

https://doi.org/10.35453/NEDJR-ASCN-2023-0028.R1


Volume: XX

No. 4

Pages: 31-45

Date: December 2023

Abstract:
A novel family of open Newton-Cotes (ONC) formulas is devised for evaluating the definite integrals. The new family is developed by using the Heronian mean in the first-order derivatives of the integrand within the interval [a, b]. The devised Heronian mean derivative-based quadrature rules (HRMDONC) achieve two orders of accuracy enhancement over the conventional ONC quadrature rules. These formulas are derived using the idea of degree of precision. Theorems regarding the degree of precision and order of accuracy are also derived along with the local and global error terms. In addition, the computational order of accuracy of each method is computed confirming the theoretical results. Computational cost and absolute error drops are also determined for three different integrals from the literature which demonstrate the superiority of the proposed HRMDONC methods over the classical ONC.

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