A spectral method for the eigenvalue problem for elliptic equations - Atkinson, Kendall; Hansen, Olaf (Electronic transactions on numerical analysis, 2010)
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