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- W2930995293 abstract "Abstract This paper proposes numerical quadrature rules for two-dimensional Cauchy principal-value integrals of the forms ∫ ∫ Ω f ( x , y ) ( x − s ) 2 + ( y − t ) 2 d y d x and ∫ ∫ Ω f ( x , y ) ( x − s ) ( y − t ) d y d x . 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 ( h m 2 μ + h n 2 μ ) 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." @default.
- W2930995293 created "2019-04-11" @default.
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- W2930995293 date "2019-09-01" @default.
- W2930995293 modified "2023-10-17" @default.
- W2930995293 title "Asymptotic error expansions and splitting extrapolation algorithm for two classes of two-dimensional Cauchy principal-value integrals" @default.
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- W2930995293 doi "https://doi.org/10.1016/j.amc.2019.03.056" @default.
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