IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v442y2023ics0096300322008268.html
   My bibliography  Save this article

Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis

Author

Listed:
  • Kang, Hongchao
  • Xu, Qi

Abstract

In this article, we propose and analyze the Clenshaw–Curtis–Filon-type method for computing many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities at the endpoints. First, by using integration by parts and the characteristics of Chebyshev polynomials, four useful recursive relationships of the required modified moments are deduced. We perform the strict error analysis on the presented method and acquire asymptotic error estimations in inverse powers of frequency ω. Our method has the following advantages: when the interpolation node is fixed, the accuracy improves considerably as either the frequency or the interpolated multiplicities at endpoints increase. Numerical experiments verify the efficacy and correctness of the presented method.

Suggested Citation

  • Kang, Hongchao & Xu, Qi, 2023. "Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis," Applied Mathematics and Computation, Elsevier, vol. 442(C).
  • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008268
    DOI: 10.1016/j.amc.2022.127758
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322008268
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2022.127758?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kang, Hongchao & An, Congpei, 2015. "Differentiation formulas of some hypergeometric functions with respect to all parameters," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 454-464.
    2. He, Guo & Zhang, Chuanlin, 2017. "On the numerical approximation for Fourier-type highly oscillatory integrals with Gauss-type quadrature rules," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 96-104.
    3. Kang, Hongchao & Wang, Ruoxia & Zhang, Meijuan & Xiang, Chunzhi, 2023. "Efficient and accurate quadrature methods of Fourier integrals with a special oscillator and weak singularities," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kang, Hongchao, 2019. "Efficient calculation and asymptotic expansions of many different oscillatory infinite integrals," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 305-318.
    2. Li, Bin & Kang, Hongchao & Chen, Songliang & Ren, Shanjing, 2023. "On the approximation of highly oscillatory Volterra integral equations of the first kind via Laplace transform," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 92-113.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008268. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.