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An efficient quadrature rule for weakly and strongly singular integrals

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  • Liu, Guidong
  • Xiang, Shuhuang

Abstract

In this paper, we consider the weakly and strongly singular integrals that arose from physical and engineering problems with corners. A fast and stable quadrature rule is designed for such integrals with nodes following a Clenshaw–Curtis distribution (i.e., extreme points of the Chebyshev polynomials). By a recurrence relation for the moments involved and Fast Fourier Transform (FFT), the presented quadrature rule can be implemented in O(nlogn) operations. Particular error estimates of the proposed algorithm are studied and verified by ample numerical illustrations. Finally, a specific Nyström method with the presented quadrature is applied to the two-dimensional scattering problem.

Suggested Citation

  • Liu, Guidong & Xiang, Shuhuang, 2023. "An efficient quadrature rule for weakly and strongly singular integrals," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    • Handle: RePEc:eee:apmaco:v:447:y:2023:i:c:s009630032300070x
    DOI: 10.1016/j.amc.2023.127901
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    References listed on IDEAS

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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.
    2. 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.
    3. Shuhuang Xiang & Guo He & Haiyong Wang, 2014. "On Fast and Stable Implementation of Clenshaw-Curtis and Fejér-Type Quadrature Rules," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, August.
    4. 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.
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