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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On an extended Filon method for highly oscillatory integrals over a simplex
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by Jing Gao and Arieh Iserles PDF
Math. Comp. 92 (2023), 867-893 Request permission

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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Additional Information
  • Jing Gao
  • Affiliation: School of Mathematics and Statistics, Xi’an Jiaotong University, People’s Republic of China
  • Email: jgao@xjtu.edu.cn
  • Arieh Iserles
  • Affiliation: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, UK
  • MR Author ID: 91725
  • Email: ai10@cam.ac.uk
  • Received by editor(s): September 6, 2021
  • Received by editor(s) in revised form: May 5, 2022, and August 23, 2022
  • Published electronically: November 10, 2022
  • Additional Notes: The work was supported by Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2020JM-026) and National Natural Science Foundation of China (Grant No. 12071368).
    The first author is the corresponding author
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 867-893
  • MSC (2020): Primary 65D30, 65D32
  • DOI: https://doi.org/10.1090/mcom/3797