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 - <p style="text-align: justify;">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.</p>