Trapezoidal Rule for Computing Supersingular Integral on a Circle

被引：7
|
作者：
Li, Jin [1 ,2 ]
Rui, Hongxing [2 ]
Yu, Dehao [3 ,4 ]
机构：
[1] Shandong Jianzhu Univ, Sch Sci, Jinan 250101, Peoples R China
[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China
[3] Xiamen Univ, Sch Math, Xiamen 361005, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100080, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2016年 / 66卷 / 02期
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Supersingular integral; Composite trapezoidal rule; Error expansion; Superconvergence; Boundary element methods; CAUCHY PRINCIPAL VALUE; BOUNDARY-ELEMENT METHODS; COMPOSITE SIMPSONS RULE; FINITE-PART INTEGRALS; HYPERSINGULAR INTEGRALS; GAUSSIAN QUADRATURE; SINGULAR-INTEGRALS; SUPERCONVERGENCE; APPROXIMATIONS; EXTRAPOLATION;
D O I：
10.1007/s10915-015-0042-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The computation of trapezoidal rule for the supersingular integrals on a circle in boundary element methods is discussed. When the singular point coincides with some priori known point, the convergence rate of the trapezoidal rule is higher than the global one which is considered as the superconvergence phenomenon. Then the error functional of density function is derived and the superconvergence phenomenon of composite trapezoidal rule occurs at certain local coordinate of each subinterval. At last, several numerical examples are provided to validate the theoretical analysis and show the efficiency of the algorithms.
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页码：740 / 760
页数：21
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