On quadrature for Cauchy principal value integrals of oscillatory functions

The authors develop an algorithm for the numerical evaluation of Cauchy principal value integrals of oscillatory functions. The method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a Jacobi weight. A numerically stable procedure is obtained and the corresponding algorithm can be implemented in a fast way yielding satisfactory numerical results. Bounds of the error and of the amplification factor are also proved.