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A generalization of Filon–Clenshaw–Curtis quadrature for highly oscillatory integrals

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Abstract

The Filon–Clenshaw–Curtis method (FCC) for the computation of highly oscillatory integrals is known to attain surprisingly high precision. Yet, for large values of frequency \(\omega \) it is not competitive with other versions of the Filon method, which use high derivatives at critical points and exhibit high asymptotic order. In this paper we propose to extend FCC to a new method, FCC\(+\), which can attain an arbitrarily high asymptotic order while preserving the advantages of FCC. Numerical experiments are provided to illustrate that FCC\(+\) shares the advantages of both familiar Filon methods and FCC, while avoiding their disadvantages.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China

    Jing Gao

  2. DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK

    Arieh Iserles

Authors
  1. Jing Gao
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  2. Arieh Iserles
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Correspondence to Jing Gao.

Additional information

Communicated by Tom Lyche.

The work is supported by the Projects of International Cooperation and Exchanges NSFC-RS (Grant No. 11511130052), the Key Science and Technology Program of Shaanxi Province of China (Grant No. 2016GY-080) and the Fundamental Research Funds for the Central Universities.

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Gao, J., Iserles, A. A generalization of Filon–Clenshaw–Curtis quadrature for highly oscillatory integrals. Bit Numer Math 57, 943–961 (2017). https://doi.org/10.1007/s10543-017-0682-9

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  • DOI: https://doi.org/10.1007/s10543-017-0682-9

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