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Asymptotic error expansions and splitting extrapolation algorithm for two classes of two-dimensional Cauchy principal-value integrals

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  • Ma, Yanying
  • Huang, Jin

Abstract

This paper proposes numerical quadrature rules for two-dimensional Cauchy principal-value integrals of the forms ∫∫Ωf(x,y)(x−s)2+(y−t)2dydx and ∫∫Ωf(x,y)(x−s)(y−t)dydx. The derivation of these quadrature rules is based on the Euler–Maclaurin error expansion of a modified trapezoidal rule for one-dimensional Cauchy singular integrals. The corresponding error estimations are investigated, and the convergence rates O(hm2μ+hn2μ) are obtained for the proposed quadrature rules, where hm and hn are partition sizes in x and y directions, μ is a positive integer determined by integrand. To further improve accuracy, a splitting extrapolation algorithm is developed based on the asymptotic error expansions. Several numerical tests are performed to verify the effectiveness of the proposed methods.

Suggested Citation

  • Ma, Yanying & Huang, Jin, 2019. "Asymptotic error expansions and splitting extrapolation algorithm for two classes of two-dimensional Cauchy principal-value integrals," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 107-118.
    • Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:107-118
    DOI: 10.1016/j.amc.2019.03.056
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    References listed on IDEAS

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    1. P. S. Theocaris, 1983. "Modified Gauss-Legendre, Lobatto and Radau cubature formulas for the numerical evaluation of 2-D singular integrals," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 6, pages 1-21, January.
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    Cited by:

    1. Beong In Yun, 2020. "Rational Transformations for Evaluating Singular Integrals by the Gauss Quadrature Rule," Mathematics, MDPI, vol. 8(5), pages 1-15, May.
    2. Bo Wang & Tiancheng Wang & Mao Yang & Chao Han & Dawei Huang & Dake Gu, 2023. "Ultra-Short-Term Prediction Method of Wind Power for Massive Wind Power Clusters Based on Feature Mining of Spatiotemporal Correlation," Energies, MDPI, vol. 16(6), pages 1-16, March.
    3. Zhang, Jiaan & Liu, Dong & Li, Zhijun & Han, Xu & Liu, Hui & Dong, Cun & Wang, Junyan & Liu, Chenyu & Xia, Yunpeng, 2021. "Power prediction of a wind farm cluster based on spatiotemporal correlations," Applied Energy, Elsevier, vol. 302(C).

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