Uniform approximations to Cauchy principal value integrals of oscillatory functions

作者：Wang, Haiyong^*; Xiang, Shuhuang

来源：Applied Mathematics and Computation, 2009, 215(5): 1886-1894.

DOI：10.1016/j.amc.2009.07.041

• Cauchy principal value
• Clenshaw-Curtis method
• Stability
• Oscillatory integral

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.

• 出版日期2009-11-1
• 单位中南大学