A Theoretical Analysis of Simpson’s 1/3-Type Scheme for the Riemann-Stieltjes Integral Based on Geometric Mean Derivative
DOI:
https://doi.org/10.26692/surjss.v57i1.7711Keywords:
Quadrature rule, Geometric mean, Riemann-Stieltjes, Error terms. Local error, Global error.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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