Spectral decomposition of a finite-difference operator

SH Lui, PN Shivakumar - International Journal of Computer …, 2005 - Taylor & Francis
International Journal of Computer Mathematics, 2005Taylor & Francis
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.
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.
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