Fast Integration for Cauchy Principal Value Integrals of Oscillatory Kind

Authors:
Ruyun Chen
Affiliations:
College of Science, Guangdong Ocean University, Zhanjiang, China 524088
Venue:
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Year:
2013

Citing 4
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Abstract

In this paper we give a simple, but high order and rapid convergence method for computing the Cauchy principal value integrals of the form $\int_{-1}^{1}e^{i\omega x}\frac{f(x)}{x-\tau}dx$ and its error bounds, where f(x) is a given smooth function, 驴驴R + may be large and 驴1驴 $(\frac{f(x)-f(\tau)}{x-\tau})^{(s)}$ 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.