On the evaluation of Cauchy principal value integrals of oscillatory functions

✍ Scribed by Haiyong Wang; Shuhuang Xiang

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 409 KB
• Volume: 234
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.12.007

✦ Synopsis

The problem of the numerical evaluation of Cauchy principal value integrals of oscillatory functions 1 -1 e iωx f (x)

x-τ dx, where -1 < τ < 1, has been discussed. Based on analytic continuation, if f is analytic in a sufficiently large complex region G containing [-1, 1], the integrals can be transformed into the problems of integrating two integrals on [0, +∞) with the integrand that does not oscillate, and that decays exponentially fast, which can be efficiently computed by using the Gauss-Laguerre quadrature rule. The validity of the method has been demonstrated in the provision of two numerical experiments and their results.