Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils (Journal of Mathematical Study, 2020)
In this article we are interested in the numerical computation of spectra ofnon-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 analyzedand compared with the theoretical results. The main difficulty here is that we have tocompute eigenvalues of strongly non-self-adjoint operators which are very unstable.