A SPECTRAL METHOD FOR THE EIGENVALUE PROBLEM FOR ELLIPTIC EQUATIONS

被引：0

作者：

Atkinson, Kendall ^{[1
,2
]}

Hansen, Olaf ^{[3
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Univ Iowa, Dept Comp Sci, Iowa City, IA 52242 USA

[3] Calif State Univ San Marcos, Dept Math, San Marcos, CA 92096 USA

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2010年 / 37卷

关键词：

elliptic equations; eigenvalue problem; spectral method; multivariable approximation; NUMERICAL-SOLUTION; APPROXIMATION;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Omega be an open, simply connected, and bounded region in R-d, d >= 2, and assume its boundary partial derivative Omega is smooth. Consider solving the eigenvalue problem Lu = lambda u for an elliptic partial differential operator L over Omega with zero values for either Dirichlet or Neumann boundary conditions. We propose, analyze, and illustrate a 'spectral method' for solving numerically such an eigenvalue problem. This is an extension of the methods presented earlier by Atkinson, Chien, and Hansen [Adv. Comput. Math, 33 (2010), pp. 169-189, and to appear].

引用

页码：386 / 412

页数：27

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