A new Simpson’s 1/3-type quadrature scheme with geometric mean derivative for the Riemann-Stieltjes integral

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 Riemann- Stieltjes 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.