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A Numerical Method to Verify the Elliptic Eigenvalue Problems Including a Uniqueness Property
Authors:K. Nagatou
Affiliation:(1) Graduate School of Mathematics, Kyushu University, Fukuoka, 812-8581, Japan, e-mail: nagatou@math.kyushu-u.ac.jp , JP
Abstract:We propose a numerical method to enclose the eigenvalues and eigenfunctions of second-order elliptic operators with local uniqueness. We numerically construct a set containing eigenpairs which satisfies the hypothesis of Banach's fixed point theorem in a certain Sobolev space by using a finite element approximation and constructive error estimates. We then prove the local uniqueness separately of eigenvalues and eigenfunctions. This local uniqueness assures the simplicity of the eigenvalue. Numerical examples are presented. Received: November 2, 1998; revised June 5, 1999
Keywords:AMS Subject Classifications:35P15   65N25.
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