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A Theoretical Analysis of Simpson’s 1/3-Type Scheme for the Riemann-Stieltjes Integral Based on Geometric Mean Derivative

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Title: A Theoretical Analysis of Simpson’s 1/3-Type Scheme for the Riemann-Stieltjes Integral Based on Geometric Mean Derivative

Authors: MUHAMMAD MUJTABA SHAIKH, KASHIF MEMON, SARA MAHESAR, OWAIS ALI RAJPUT

Journal: Sindh University Research Journal - Science Series (SURJ)

HEC Recognition History
Category From To
Y 2024-10-01 2025-12-31
Y 2023-07-01 2024-09-30
Y 2021-07-01 2022-06-30

Publisher: University of Sindh, Jamshoro

Country: Pakistan

Year: 2025

Volume: 57

Issue: 1

Language: en

DOI: 10.26692/surjss.v57i1.7711

Keywords: Quadrature ruleGeometric meanRiemann-StieltjesError terms. Local errorGlobal error.

Categories
Numerical Analysis (431) Applied Mathematics (727) Calculus (39) Mathematics (5170) Computational Mathematics (14)

Abstract

This research aims to discuss the theoretical analysis of a three-point numerical scheme used to approximate a Riemann-Stieltjes integral (RSI) by incorporating derivative in each strip at the geometric mean of the ending points of the interval of integration. The suggested scheme is discussed in terms of its basic and composite versions for the RSI. The error analysis of the scheme is also presented in theorems. Additionally, the reduction of the suggested scheme is discussed for the Riemann integral by using g(t) = t.

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