|
| Numerical Approaches to ComputeSpectra of Non-Self Adjoint Operatorsin Two and Three Dimensions |
| Fatima Aboud,Fran?cois Jauberteau,Didier Robert |
| (Mathematics Department, College of Science, University of Diyala, Iraq;;Laboratoire de Math′ematiques Jean Leray, CNRS-UMR 6629, Nantes
Universit′e, France) |
| DOI： |
| Abstract: |
| In this article we are interested in the numerical computation of
spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the
location of the eigenvalues. This leads to solve nonlinear eigenvalue problems. In
introduction we begin with a review of theoretical results and numerical results
obtained for the one dimensional case. Then we present the numerical methods
developed to compute the spectra (finite difference discretization) for the two
and three dimensional cases. The numerical results obtained are presented and
analyzed. One difficulty here is that we have to compute eigenvalues of strongly
non-self-adjoint operators which are unstable. This work is in continuity of a
previous work in one spatial dimension [3]. |
| Key words: Non-self adjoint quadratic operators, nonlinear eigenvalue problems, spectra,
finite difference methods. |