Quadrature Rules for Stieltjes Integrals and Numerical Solution of Renewal-Type Integral Equations

This paper introduces closed Newton-Cotes quadratic rules for Stieltjes integrals. These rules use directly the measure determined on the line by the Stieltjes integral, and do not use any numerical differentiation. They are used to construct simple algorithms for numerical convolution of cumulative distribution functions, and for the solution of integral equations of renewal type. Numerical analysis of these algorithms is presented.