A new Simpson's 1/3-type quadrature scheme with geometric mean derivative for the Riemann-Stieltjes integral | [Sindh University Research Journal • 2021]

Author(s):

1. Kashif Memon: Institute of Mathematics and Computer Science, University of Sindh Jamshoro, Pakistan

2. M. M. Shaikh: Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro.Pakistan

3. K. Malik: Department of Mathematics, Government College University, Hyderabad, Pakistan

4. M. S. Chandio: Institute of Mathematics and Computer Science, University of Sindh Jamshoro, Pakistan

5. A. W. Shaikh: Institute of Mathematics and Computer Science, University of Sindh Jamshoro, Pakistan

Abstract:

The main purpose of this research is to develop and improve the Simpson's 1/3-type quadrature scheme numerically utilizing the geometric mean derivative for the RiemannStieltjes integral. The proposed scheme of Simpson's 1/3-type is described in basic form and also in composite form. The performance of the proposed scheme is compared with existing schemes by experimental results using MATLAB. It has been noted in numerical results that the performance of new proposed scheme is more efficient against the existing schemes in terms of errors, computational cost, and average CPU time.

Page(s): 39-45

DOI: DOI not available

Published: Journal: Sindh University Research Journal, Volume: 53, Issue: 4, Year: 2021

Keywords:

Computational Cost , RiemannStieltjes integral , Time efficiency , Simpsons 13 rule , geometric mean

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