Abstract
In this research paper, a new harmonic mean derivative-based Simpson’s 1/3 scheme has been presented for the Riemann-Stieltjes integral (RS-integral). The basic and composite forms of the proposed scheme with local and global error terms have been derived for the RS-integral. The proposed scheme has been reduced using g(t) = t for Riemann integral. Experimental work has been discussed to verify the theoretical results of the new proposed scheme against existing schemes using MATLAB. The order of accuracy, computational cost and average CPU time (in seconds) of the new proposed scheme have been computed. Finally, it is observed from computational results that the proposed scheme is better than existing schemes
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