Fast Integration for Cauchy Principal Value Integrals of Oscillatory Kind

In this paper we give a simple, but high order and rapid convergence method for computing the Cauchy principal value integrals of the form and its error bounds, where f(x) is a given smooth function, omega aR (+) may be large and -1 <tau < 1. The proposed method is constructed by approximating by using the special Hermite interpolation polynomial, which is a Taylor series. The validity of the method has been demonstrated by the results of several numerical experiments and the comparisons with other methods.