Hermite interpolation and a method for evaluating Cauchy principal value integrals of oscillatory kind

G. E. Okecha

Kragujevac Journal of Mathematics, Tome 29 (2006) no. 1.

Résumé

An alternative method to the method proposed in [10] for the numerical evaluation of integrals of the form $\int_{-1}^1e^{i\phi t}f(t)dt$, where $f(t)$ has a simple pole in $(-1,1)$ and $\phi\in R$ may be large, has been developed. The method is based on a special case of Hermite interpolation polynomial and it is comparatively simpler and entails fewer function evaluations and thus faster, but the two methods are comparable in accuracy. The validity of the method is demonstrated in the provision of two numerical experiments and their results.