Volume 53, Issue 1
Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils

Fatima Aboud, François Jauberteau, Guy Moebs & Didier Robert

J. Math. Study, 53 (2020), pp. 12-44.

Published online: 2020-03

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  • 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 Schrodinger 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.

  • Keywords

Nonlinear eigenvalue problems, spectra, pseudospectra, finite difference methods, Galerkin spectral method, Hermite functions.

  • AMS Subject Headings

47A75, 47F05, 65N06, 65N25, 65N35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

Fatima.Aboud@sciences.uodiyala.edu.iq (Fatima Aboud)

francois.jauberteau@univ-nantes.fr (François Jauberteau)

guy.moebs@univ-nantes.fr (Guy Moebs)

didier.robert@univ-nantes.fr (Didier Robert)

  • BibTex
  • RIS
  • TXT
@Article{JMS-53-12, author = {Aboud , Fatima and Jauberteau , François and Moebs , Guy and Robert , Didier}, title = {Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {1}, pages = {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 Schrodinger 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n1.20.02}, url = {http://global-sci.org/intro/article_detail/jms/15206.html} }
TY - JOUR T1 - Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils AU - Aboud , Fatima AU - Jauberteau , François AU - Moebs , Guy AU - Robert , Didier JO - Journal of Mathematical Study VL - 1 SP - 12 EP - 44 PY - 2020 DA - 2020/03 SN - 53 DO - http://doi.org/10.4208/jms.v53n1.20.02 UR - https://global-sci.org/intro/article_detail/jms/15206.html KW - Nonlinear eigenvalue problems, spectra, pseudospectra, finite difference methods, Galerkin spectral method, Hermite functions. AB -

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 Schrodinger 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.

Fatima Aboud , François Jauberteau , Guy Moebs & Didier Robert . (2020). Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils. Journal of Mathematical Study. 53 (1). 12-44. doi:10.4208/jms.v53n1.20.02
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