Year: 2025
Author: Fatima Aboud, François Jauberteau, Didier Robert
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 2 : pp. 155–175
Abstract
In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the eigenvalues. This leads to solve nonlinear eigenvalue problems. In introduction we begin with a review of theoretical results and numerical results obtained for the one dimensional case. Then we present the numerical methods developed to compute the spectra (finite difference discretization) for the two and three dimensional cases. The numerical results obtained are presented and analyzed. One difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are unstable. This work is in continuity of a previous work in one spatial dimension [3].
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aam.OA-2024-0026
Annals of Applied Mathematics, Vol. 41 (2025), Iss. 2 : pp. 155–175
Published online: 2025-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Non-self adjoint quadratic operators nonlinear eigenvalue problems spectra finite difference methods.