Kashif Memon ,Muhammad Mujtaba Shaikh,Muhammad Saleem Chandio,Abdul Wasim Shaikh,




Quadrature rule,Riemann-Stieltjes,Simpson’s 1/3 rule,Composite form,Local error,Global error,Cost-effectiveness,Time-efficiency,


In this research paper, a new derivative-free Simpson 1/3-type quadrature scheme has been proposed for the approximation of the Riemann-Stieltjes integral (RSI). The composite form of the proposed scheme on the RSI has been derived using the concept of precision. The theorems concerning basic form, composite form, local and global errors of the new scheme have been proved theoretically. For the trivial case of the integrator in the proposed RS scheme, successful reduction to the corresponding Riemann scheme is proved. The performance of the proposed scheme has been tested by numerical experiments using MATLAB on some test problems of RS integrals from literature against some existing schemes. The computational cost, the order of accuracy and average CPU times (in seconds) of the discussed rules have been computed to demonstrate cost-effectiveness, time-efficiency and rapid convergence of the proposed scheme under similar conditions.


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