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计算数学  2011, Vol. 33 Issue (1): 77-86    DOI:
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牛顿科茨公式计算超奇异积分的误差估计
李金1,2, 余德浩2
1. 山东建筑大学理学院, 济南 250101;
2. LSEC, 中国科学院, 数学与系统科学研究院, 计算数学研究所, 北京 100080
THE ERROR ESTIMATE OF NEWTON-COTES METHODS TO COMPUTE HYPERSINGULAR INTEGRAL
Li Jin1,2, Yu Dehao2
1. School of Science, Shandong Jianzhu University, Jinan 250101, China;
2. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China
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摘要 

超奇异积分的数值计算是边界元方法中的重要的课题之一,本文得到了牛顿科茨公式计算任意阶超奇异积分误差估计, 当误差函数中的Sk(p)(τ)=0 时,便得到超收敛现象,并给出了Sk(p)(τ) 之间的相互关系.相应的数值算例验证了理论分析的正确性.

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关键词超奇异积分   牛顿科茨公式   误差展开式     
Abstract

The composite Newton-Cotes rules for the computation of hypersingular integral on interval is studied. The emphasis is placed on certain function, denoted by Sk(p)(τ), in the error functional, where τ is the local coordinate of the singular point. When Sk(p)(τ)=0 the so-called point wise superconvergence phenomenon occurs. Besides, the property of Sk(p)(τ) is presented. At last, numerical examples are provided to validate the theoretical analysis.

Key wordshypersingular integral   Newton-Cotes rule   error estimate   
收稿日期: 2009-12-11;
基金资助:

国家重点基础研究发展规划项目(No.2005CB321701)资助项目.

引用本文:   
. 牛顿科茨公式计算超奇异积分的误差估计[J]. 计算数学, 2011, 33(1): 77-86.
. THE ERROR ESTIMATE OF NEWTON-COTES METHODS TO COMPUTE HYPERSINGULAR INTEGRAL[J]. Mathematica Numerica Sinica, 2011, 33(1): 77-86.
 
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