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 计算数学  2011, Vol. 33 Issue (1): 77-86    DOI:
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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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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.

 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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