On an extended Filon method for highly oscillatory integrals over a simplex

Abstract

We study a Filon-type method for the computation of multivariate highly oscillatory integrals over a general simplex. A new kind of multivariate Hermite interpolation is proposed. The existence of the multivariate Hermite interpolation leads towards the construction of an extended Filon-type methods. Such methods attain good accuracy for all values of the oscillatory parameter when increasing, as required, the interpolation order. Numerical experiments are provided to illustrate the effectiveness of our approach.