MIDPOINT DERIVATIVE-BASED TRAPEZOID RULE FOR THE RIEMANN-STIELTJES INTEGRAL - Zhao, Weijing; Zhang, Zhaoning; Ye, Zhijian (Italian Journal of Pure and Applied Mathematics, 2014)
In this paper, the midpoint derivative-based trapezoid rule for the Riemann-Stieltjes integral is presented which uses derivative value at the midpoint. This kind of quadrature rule obtains an increase of two orders of precision over the trapezoid rule for the Riemann-Stieltjes integral and the error term is investigated. At last, the rationality of the generalization of midpoint derivative-based trapezoid rule for Riemann-Stieltjes integral is demonstrated.