 
Summary: HighOrder Quadratures for Integral Operators with
Singular Kernels
Bradley K. Alpert
3
Abstract
A numerical integration method that has rapid convergence for integrands with
known singularities is presented. Based on endpoint corrections to the trapezoidal
rule, the quadratures are suited for the discretization of a variety of integral equations
encountered in mathematical physics. The quadratures are based on a technique in
troduced by Rokhlin (Computers Math. Applic. 20, pp. 5162, 1990). The present
modication controls the growth of the quadrature weights and permits higherorder
rules in practice. Several numerical examples are included.
Abbreviated Title. Quadratures for Integral Equations
Key Words. numerical integration, singular kernels, quadrature rules, corrected trape
zoidal rules
AMS(MOS) subject classications. 65D30, 65B15, 65R20
1 Introduction
The discretization of a linear Fredholm integral equation of the second kind,
f(x)+
Z b
