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

Gao, Jing; Iserles, Arieh

doi:10.1090/mcom/3797

On an extended Filon method for highly oscillatory integrals over a simplex
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by Jing Gao and Arieh Iserles;

Math. Comp. 92 (2023), 867-893

DOI: https://doi.org/10.1090/mcom/3797

Published electronically: November 10, 2022

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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.

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