Uniform approximations to Cauchy principal value integrals of oscillatory functions

摘要

This paper presents an interpolatory type integration rule for the numerical evaluation of Cauchy principal value integrals of oscillatory integrands (sic)(-1)(1) e(i omega x)f(x)/x-tau dx, where -1 < tau < 1 for a given smooth function f(x). The proposed method is constructed by interpolating f(x) at practical Chebyshev points and subtracting out the singularity. A numerically stable procedure is obtained and the corresponding algorithm can be implemented by fast Fourier transform. The validity of the method has been demonstrated by several numerical experiments.