Geodesic
A spectral method for the eigenvalue problem for elliptic equations
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 386-412.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $\Omega $be an open, simply connected, and bounded region in Rd, d $\geq 2$, 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 by Atkinson, Chien, and Hansen [Adv. Comput. Math, 33 (2010), pp. 169-189, and to appear].
Classification : 65M70
Keywords: elliptic equations, eigenvalue problem, spectral method, multivariable approximation 
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     author = {Atkinson, Kendall and Hansen, Olaf},
     title = {A spectral method for the eigenvalue problem for elliptic equations},
     journal = {Electronic transactions on numerical analysis},
     pages = {386--412},
     publisher = {mathdoc},
     volume = {37},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a1/}
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Atkinson, Kendall; Hansen, Olaf. A spectral method for the eigenvalue problem for elliptic equations. Electronic transactions on numerical analysis, Tome 37 (2010), pp. 386-412. http://geodesic.mathdoc.fr/item/ETNA_2010__37__a1/