Improvement of the asymptotic behaviour of the Euler–Maclaurin formula for Cauchy principal value and Hadamard finite‐part integrals
Improvement of the asymptotic behaviour of the Euler–Maclaurin formula for Cauchy principal value and Hadamard finite‐part integrals
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DOI：
10.1002/nme.1077
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发表时间：
2004-09
影响因子：
2.9
通讯作者：
U. Choi;Shin-wook Kim;B. Yun
中科院分区：
文献类型：
--
作者：
U. Choi;Shin-wook Kim;B. Yun
在最近的著作中（Commun. Numer. Meth. Engng 2001；17：881；即将出现），包含实参数 b ≠ 0 的非线性变换的优越性已在弱奇异积分的数值计算中得到了证明。基于这些变换，我们定义了所谓的参数 sigmoidal 变换，并使用它通过 Euler-Maclaurin 公式来计算 Cauchy 主值和 Hadamard 有限部分积分。由于参数 sigmoidal 变换的突出特性，其在 x = 0 附近的局部行为由参数 b 控制，因此预计会得到更好的近似。
In the recent works (Commun. Numer. Meth. Engng 2001; 17: 881; to appear), the superiority of the non‐linear transformations containing a real parameter b ≠ 0 has been demonstrated in numerical evaluation of weakly singular integrals. Based on these transformations, we define a so‐called parametric sigmoidal transformation and employ it to evaluate the Cauchy principal value and Hadamard finite‐part integrals by using the Euler–Maclaurin formula. Better approximation is expected due to the prominent properties of the parametric sigmoidal transformation of whose local behaviour near x = 0 is governed by parameter b.