ORDER-PRESERVING MESH SPACING FOR COMPOUND QUADRATURE FORMULAS AND FUNCTIONS WITH ENDPOINT SINGULARITIES

摘要

For compound quadrature formulas for the numerical evaluation of integral(a)(b) w(x)f(x)dx, where the function f as well as the weight function w are allowed to have singularities at the endpoints a and b, we show how to preserve the order of convergence, which is obtained for smooth w and f, by an appropriate choice of the meshpoints. The main emphasis is on singularities of algebraic and logarithmic type. [References: 9]