Year: 2020
Author: Fatima Aboud, François Jauberteau, Guy Moebs, Didier Robert
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 12–44
Abstract
In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators. This leads to solve nonlinear eigenvalue problems. We begin with a review of theoretical results for the spectra of quadratic operators, especially for the Schrödinger pencils. Then we present the numerical methods developed to compute the spectra: spectral methods and finite difference discretization, in infinite or in bounded domains. The numerical results obtained are analyzed and compared with the theoretical results. The main difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are very unstable.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v53n1.20.02
Journal of Mathematical Study, Vol. 53 (2020), Iss. 1 : pp. 12–44
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Nonlinear eigenvalue problems spectra pseudospectra finite difference methods Galerkin spectral method Hermite functions.