A Spectral Method for the Eigenvalue Problem for Elliptic Equations

Details A Spectral Method for the Eigenvalue Problem for Elliptic Equations A Spectral Method for the Eigenvalue Problem for Elliptic Equations

2009-09-19

arxiv.org/abs/0909.3607v1

Electronic Transactions on Numerical Analysis 37 (2010), pp. 386-412

Mathematics

Numerical Analysis

28 pages, 13 figures

Scientific paper

Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ 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 in [5],[6].

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