High precision solutions of two fourth order eigenvalue problems
type: Item
instance of: scholarly article
title: High precision solutions of two fourth order eigenvalue problems
zbMATH Open document ID: 0940.65119
author: Petter E. Bjørstad
author: B. P. Tjøstheim
published in: Computing
publication date: 2000-07-19T00:00:00Z
review text: Using a highly accurate spectral Legendre-Galerkin method, the authors solve the biharmonic eigenvalue problem \(\Delta^2u=\lambda u\) and the buckling plate problem \(\Delta^2u= -\lambda\Delta u\) on the unit square under Dirichlet boundary conditions. In both cases they study for the first eigenfunction the nodal lines occurring near a corner. Five sign changes are computed, where the eigenfunction exhibits a self-similar pattern as one approaches the corner. The numerical results are compared with the known asymptotic expansion of the solution near a corner. This comparison shows complete agreement between the numerical and the analytical results already from the first sign change.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 1383910
zbMATH Keywords: fourth-order eigenvalue problems
zbMATH Keywords: numerical examples
zbMATH Keywords: spectral Legendre-Galerkin method
zbMATH Keywords: biharmonic eigenvalue problem
zbMATH Keywords: buckling plate problem
reviewed by: Waldemar Velte
MaRDI profile type: Publication
full work available at URL: s006070050053
OpenAlex ID: W2049145900
DOI: 10.1007/S006070050053
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description: scientific article; zbMATH DE number 1383910