Convergence of the invariant scheme of the method of fundamental solutions for two-dimensional potential problems in a Jordan region

被引：0

作者：

Hidenori Ogata

Masashi Katsurada

机构：

[1] The University of Electro-Communications,The Department of Communication Engineering and Informatics, Graduate School of Informatics and Engineering

[2] Meiji University,The Department of Mathematics, School of Science and Technology

来源：

Japan Journal of Industrial and Applied Mathematics | 2014年 / 31卷

关键词：

Method of fundamental solutions; Charge simulation method; Laplace equation; Invariant scheme; Conformal mapping; 65N80; 65N35; 65N12; 35J05; 35J08;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We examine the invariant scheme of the method of fundamental solutions for two-dimensional potential problems, that is, Dirichlet boundary value problems of the Laplace equation in a Jordan region, with the charge points and the collocation points obtained by a conformal mapping of the exterior of a disk to the exterior of the problem region. By a theoretical error analysis, we show that the approximate solution of the invariant scheme converges to the exact solution exponentially and some unnatural assumptions needed in the conventional scheme are removed in the convergence theorem of the invariant scheme.

引用

页码：231 / 262

页数：31

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