Numerical evaluation of oscillatory-singular integrals

In this paper we consider an asymptotic-Filon-type method for computing the oscillatory Cauchy principal value integrals and end-points oscillatory-singular integrals. The method is constructed by using a Lagrange interpolating polynomial to approximate the non-oscillatory function so that it successfully avoids the singularity and solving the systems of equations. Numerical examples and theoretical results show the accuracy and efficiency of the proposed method.