The eigenvalue problem for −Δu=λu with dirichlet boundary conditions for a certain class of two-dimensional regions
✍ Scribed by K. Hashimoto
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 676 KB
- Volume
- 112
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
By using the Weinstein method, eigenvalues and eigenfunctions ofthe equation -zau = Au with Dirichlet boundary conditions are calculated for a certain class of regions. The regions are composed of unions of rectangles, and include L-shaped, single-notched and crossed rectangles. The method consists of determining the zeros of the Weinstein determinant W,(A). This function W,(A) in turn is determined by the eigenvalues and eigenfunctions of -zlu = Au with mixed boundary conditions (Dirichlet and Neumann) for each component rectangle of the given region, which are easily calculated, and by trial functions P~,P2 .... ,p, which are easily chosen. Numerical results for two examples, an asymmetrical L-shaped region and a symmetrical single-notched region, are given, and are shown to be reasonably precise by comparison with results available in the literature. The method is applicable to many problems for a certain class of regions.