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快速配置法中数值积分的误差控制策略
引用本文:陈仲英,巫斌,许跃生.快速配置法中数值积分的误差控制策略[J].东北数学,2005,21(2):233-252.
作者姓名:陈仲英  巫斌  许跃生
作者单位:Department of Scientific Computing,Zhongshan University,Guangzhou,510275,Department of Scientific Computing,Zhongshan University,Guangzhou,510275,Department of Mathematics,Syracuse University,Syracuse,NY 13244,U.S.A. and Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100080
摘    要:We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.

关 键 词:弗雷德霍姆积分函数  快速排列法  二次准则  误差控制

Error Control Strategies for Numerical Integrations in Fast Collocation Methods
CHEN Zhong-ying,WU Bin,XU Yue-sheng.Error Control Strategies for Numerical Integrations in Fast Collocation Methods[J].Northeastern Mathematical Journal,2005,21(2):233-252.
Authors:CHEN Zhong-ying  WU Bin  XU Yue-sheng
Institution:[1]DepartmentofScientificComputing,ZhongshanUniversity,Guangzhou,510275 [2]DepartmentofMathematics,SyracuseUniversity,Syracuse,NY13244,U.S.A.andAcademyofMathematicsandSystemsScience,ChineseAcademyofSciences,Beijing,100080
Abstract:We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.
Keywords:Fredholm integral equation of the second kind  fast collocation method  quadrature rule  error control
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