A FAST ALGORITHM FOR SOLVING THE GENERALIZED AIRFOIL EQUATION

被引：62

作者：

BERTHOLD, D ^{[1
]}

HOPPE, W ^{[1
]}

SILBERMANN, B ^{[1
]}

机构：

[1] TECH UNIV CHEMNITZ, FACHBEREICH MATH, O-9010 KARL MARX STADT, GERMANY

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1992年 / 43卷 / 1-2期

关键词：

CAUCHY-TYPE SINGULAR INTEGRAL EQUATION; SOBOLEV SPACES; CLASSICAL COLLOCATION METHOD; FAST ALGORITHMS;

D O I：

10.1016/0377-0427(92)90266-Z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper is devoted to the quadrature method for Cauchy-type singular integral equations on [-1, 1] with an additional logarithmic singularity of the kernel. An algorithm being based on this method is given whose realization only requires a computational work of O(n ln n) operations in order to determine n unknown coefficients of the approximate solution. Furthermore, in a scale of weighted Sobolev-like spaces on [-1, 1] (having analogous properties like the classical Sobolev spaces on the unit circle) the order of convergence is optimal.

引用

页码：185 / 219

页数：35

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