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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. 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
  • 收稿日期:2009-12-11 出版日期:2011-02-15 发布日期:2011-03-08
  • 基金资助:

    国家重点基础研究发展规划项目(No.2005CB321701)资助项目.

李金, 余德浩. 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.

Li Jin, Yu Dehao. THE ERROR ESTIMATE OF NEWTON-COTES METHODS TO COMPUTE HYPERSINGULAR INTEGRAL[J]. Mathematica Numerica Sinica, 2011, 33(1): 77-86.

THE ERROR ESTIMATE OF NEWTON-COTES METHODS TO COMPUTE HYPERSINGULAR INTEGRAL

Li Jin1,2, Yu Dehao2   

  1. 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
  • Received:2009-12-11 Online:2011-02-15 Published:2011-03-08

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.

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.

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