Spectral decomposition of a finite-difference operator

Abstract

We give asymptotic expansions of the eigenvalues of the second derivative operator with Sommerfeld boundary conditions in one dimension. In terms of these eigenvalues, eigenpairs of the associated second-order finite-difference operator can be inferred. Eigenpairs of the Laplacian operator on a disk with absorbing boundary conditions are also derived.

Keywords:

• Eigenvalue
• Finite difference
• Sommerfeld
• Absorbing boundary conditions

Acknowledgements

This work was partially supported by a grant from NSERC Canada.