Summary: A SPECTRAL METHOD FOR THE EIGENVALUE PROBLEM FOR
KENDALL ATKINSON AND OLAF HANSEN
Abstract. Let be an open, simply connected, and bounded region in Rd, d 2, and assume
its boundary is smooth. Consider solving the eigenvalue problem Lu = u for an elliptic partial
differential operator L over 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 , .
Key words. elliptic equations, eigenvalue problem, spectral method, multivariable approxima-
AMS subject classification. 65M70
1. INTRODUCTION. We consider the numerical solution of the eigenvalue