A Spectral Method for the Eigenvalue Problem for Elliptic Equations. (arXiv:0909.3607v1 [math.NA])

Let $Omega$ be an open, simply connected, and bounded region in
$mathbb{R}^{d}$, $dgeq2$, and assume its boundary $partialOmega$ 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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Original source : http://arxiv.org/abs/0909.3607...