Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils  

作　　者：Fatima Aboud Francois Jauberteau Guy Moebs Didier Robert 

机构地区：[1]Mathematics Department,College of Science,University of Diyala,Baquba,Iraq [2]Laboratoire de Mathematiques Jean Leray,CNRS-UMR 6629,Universite de Nantes,France.

出　　处：《Journal of Mathematical Study》2020年第1期12-44,共33页数学研究（英文）

基　　金：supported by the research project DefiMaths of the Federation de Mathematiques des Pays de la Loire,CNRS FR 2962;supported by the CIMPA(International Center of Pure ans Applied Mathematics);Computations are done thanks to the computer of the CCIPL(Centre de Calcul Intensif des Pays de la Loire).

摘　　要：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 Schr¨odinger 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.

关 键 词：Nonlinear eigenvalue problems SPECTRA PSEUDOSPECTRA finite difference methods Galerkin spectral method Hermite functions. 

分 类 号：O17[理学—数学]