Numerical analysis for Cauchy principal value integrals of oscillatory kind

Abstract

In this paper, a new quadrature of Cauchy principal value integrals of the form has been discussed, where f(x) is a given smooth function, ω∈R may be large and−1<τ<1. In the present study, to avoid the singularity of the problem, firstly the integral is transformed to . Then the proposed method is constructed by interpolating at the Chebyshev points in practice. The validity of the method has been demonstrated in the provision of several numerical experiments and their results.

Keywords:

• Cauchy principal value
• Hermite interpolation
• oscillatory integral
• approximation
• numerical quadrature

2000 AMS Subject Classifications :

• 65D32
• 65D30

Acknowledgements

This work was supported by Start-up Projects of Guangdong Ocean University (No. E09230).