Geodesic
A spectral method for the eigenvalue problem for elliptic equations
Electronic transactions on numerical analysis, Tome 37 (2010), pp. 386-412
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 
@article{ETNA_2010__37__a1,
     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},
     year = {2010},
     volume = {37},
     zbl = {1206.65235},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__37__a1/}
}
TY  - JOUR
AU  - Atkinson,  Kendall
AU  - Hansen,  Olaf
TI  - A spectral method for the eigenvalue problem for elliptic equations
JO  - Electronic transactions on numerical analysis
PY  - 2010
SP  - 386
EP  - 412
VL  - 37
UR  - http://geodesic.mathdoc.fr/item/ETNA_2010__37__a1/
LA  - en
ID  - ETNA_2010__37__a1
ER  - 
%0 Journal Article
%A Atkinson,  Kendall
%A Hansen,  Olaf
%T A spectral method for the eigenvalue problem for elliptic equations
%J Electronic transactions on numerical analysis
%D 2010
%P 386-412
%V 37
%U http://geodesic.mathdoc.fr/item/ETNA_2010__37__a1/
%G en
%F ETNA_2010__37__a1
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/