Derivative‐Based Trapezoid Rule for the Riemann‐Stieltjes Integral

Abstract

The derivative‐based trapezoid rule for the Riemann‐Stieltjes integral is presented which uses 2 derivative values at the endpoints. 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 derivative‐based trapezoid rule for Riemann‐Stieltjes integral is demonstrated.