The superconvergence of composite Newton–Cotes rules for Hadamard finite-part integral on a circle
The superconvergence of composite Newton–Cotes rules for Hadamard finite-part integral on a circle
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DOI：
10.1007/s00607-009-0048-5
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发表时间：
2009-07
期刊：
影响因子：
3.7
通讯作者：
Xiaoping Zhang;Jiming Wu;Dehao Yu
中科院分区：
文献类型：
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作者：
Xiaoping Zhang;Jiming Wu;Dehao Yu
本文研究了具有超奇异核的圆上Hadamard有限部分积分的一般（复合）Newton-Cotes规则，并着重研究了它们的逐点超收敛现象，即，当奇异点与某个先验已知点重合时，收敛速度高于全局可能收敛速度。我们证明了（复合）Newton-Cotes规则的超收敛速度发生在一个特殊函数的零点处，并证明了超收敛点的存在性。建立了Wu和Sun（Numer Math 109：143-165，2008）中定义的和之间的关系，并讨论了Cotes系数的有效计算。数值算例验证了理论分析的正确性。
We study the general (composite) Newton–Cotes rules for the computation of Hadamard finite-part integral on a circle with the hypersingular kerneland focus on their pointwise superconvergence phenomenon, i.e., when the singular point coincides with some a priori known point, the convergence rate is higher than what is globally possible. We show that the superconvergence rate of the (composite) Newton–Cotes rules occurs at the zeros of a special functionand prove the existence of the superconvergence points. The relation betweenanddefined in Wu and Sun (Numer Math 109:143–165, 2008) is established, and the efficient calculation of Cotes coefficients is also discussed. Several numerical examples are provided to validate the theoretical analysis.