A spectral method for the eigenvalue problem for elliptic equations

Let Ω be an open, simply connected, and bounded region in [R.sup.d] d ≥ 2, and assume its boundary δΩ is smooth. Consider solving the eigenvalue problem [L.sub.u] = [[lam[B.sub.d]a].sub.u] for an elliptic partial differential operator L over Ω with zero values for either Dirichlet or Neumann boundar...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 37; p. 386
Main Authors Atkinson, Kendall, Hansen, Olaf
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.01.2010
Online AccessGet full text
ISSN1068-9613
1097-4067

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Summary:Let Ω be an open, simply connected, and bounded region in [R.sup.d] d ≥ 2, and assume its boundary δΩ is smooth. Consider solving the eigenvalue problem [L.sub.u] = [[lam[B.sub.d]a].sub.u] for an elliptic partial differential operator L over Ω 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]. Key words. elliptic equations, eigenvalue problem, spectral method, multivariable approximation AMS subject classifications. 65M70
ISSN:1068-9613
1097-4067