A sinc-Hunter quadrature rule for Cauchy principal value integrals

Abstract

A Sinc function approach is used to derive a new Hunter type quadrature rule for the evaluation of Cauchy principal value integrals of certain analytic functions. Integration over a general arc in the complex plane is considered. Special treatment is given to integrals over the interval ( − 1 , 1 ) ( - 1,1) . It is shown that the quadrature error is of order O ( e − c N ) O({e^{ - c\sqrt N }}) , where N is the number of nodes used, and where c is a positive constant which is independent of N. An application of the rule to the approximate solution of Cauchy singular integral equations is also discussed. Numerical examples are included to illustrate the performance of the rule.