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Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels

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  • Li, Bin
  • Xiang, Shuhuang

Abstract

In this paper, we present a special Clenshaw–Curtis Filon (CCF) type scheme for approximation of highly oscillatory integrals with weak and hypersingular kernels. The non-oscillatory and nonsingular part of the integrand is replaced by a special Hermite interpolation polynomial. Error bounds with respect to the frequency k and the number of the Clenshaw–Curtis points N are considered. The overall computational complexity for the scheme is O(Nlog (N)). Numerical experiments support the theoretical analysis.

Suggested Citation

  • Li, Bin & Xiang, Shuhuang, 2019. "Efficient methods for highly oscillatory integrals with weakly singular and hypersingular kernels," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:18
    DOI: 10.1016/j.amc.2019.06.013
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    1. Liu, Guidong & Xiang, Shuhuang, 2019. "Clenshaw–Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 251-267.
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    Cited by:

    1. Xu, Zhenhua & Geng, Hongrui & Fang, Chunhua, 2020. "Asymptotics and numerical approximation of highly oscillatory Hilbert transforms," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Liu, Guidong & Xiang, Shuhuang, 2023. "An efficient quadrature rule for weakly and strongly singular integrals," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    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).

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