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Numerical Quadrature Methods for Integrals of Singular Periodic Functions and Their Application to Singular and Weakly Singular Integral Equations

机译：奇异周期函数积分的数值求积方法及其在奇异和弱奇异积分方程中的应用

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High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

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作者
Sidi, A.; Israeli, M.;
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年度 1986
页码 p.1-36
总页数 36
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Fredholm equations; Periodic functions; Singular integral equations; Numerical analysis; Boundary element method; Boundary value problems; Conformal mapping; Elastic properties;

机译：Fredholm方程;周期函数;奇异积分方程;数值分析;边界元法;边值问题;共形映射;弹性性质;

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专利

1. SINGULAR　INTEGRAL　OPERATORS　AND　SINGULAR　QUADRATURE　OPERATORS　ASSOCIATED　WITH　SINGULAR　INTEGRAL　EQUATIONS　OF　THE　FIRST　KIND　AND　THEIR　APPLICATIONS [J] . 杜金元数学物理学报：B辑英文版 . 1995,第002期

机译：奇异的积分运算符和奇异正交运算符与第一类及其应用的奇异积分方程相关联
2. Quadrature rules for weakly singular, strongly singular, and hypersingular integrals in boundary integral equation methods [J] . Tsalamengas John L. Journal of Computational Physics . 2015,第Null期

机译：边界积分方程方法中的弱奇异积分，强奇异积分和超奇异积分的正交规则
3. Singular integral operators and singular quadrature operators associated with singular integral equations [J] . Du Jinyuan Acta Mathematica Scientia . 1998,第2期

机译：与奇异积分方程相关的奇异积分算子和奇异正交算子
4. New higher order numeric quadratures for regular or singular functions on an interval: applications for the helmholtz integral equation [C] . Philippe Helluy, Sylvain Maire, Patrice Ravel ASME design engineering technical conferences;Biennial conference on mechanical vibration and noise . 1999

机译：区间上正则函数或奇异函数的新的高阶数字正交：亥姆霍兹积分方程的应用
5. CONVERGENCE AND SUPERCONVERGENCE OF NUMERICAL SOLUTIONS OF WEAKLY SINGULAR INTEGRAL AND DIFFERENTIAL EQUATIONS (GALERKIN, COLLOCATION, EIGENVALUES, EIGENVECTORS, SPLINES) [D] . LEBBAR, RACHID. 1986

机译：弱奇异积分和微分方程数值解的收敛性和超级度验收（Galerkin，Collocation，特征值，特征向量，花键）
6. Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations [O] . Michael Feischl, Gregor Gantner, Dirk Praetorius -1

机译：弱奇异积分方程的自适应IGA边界元方法的可靠高效后验误差估计
7. Application of global optimization and radial basis functions to numerical solutions of weakly singular volterra integral equations [O] . Galperin E.A, Kansa E.J 2002

机译：全局优化和径向基函数在弱奇异Volterra积分方程数值解中的应用

Numerical Quadrature Methods for Integrals of Singular Periodic Functions and Their Application to Singular and Weakly Singular Integral Equations

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