NEW SUFFICIENT CONDITIONS IN THE GENERALIZED SPECTRUM APPROACH TO DEAL WITH SPECTRAL POLLUTION
- Authors: Khellaf A.1
-
Affiliations:
- Universit.e 8 Mai 1945, Guelma
- Issue: Vol 23, No 124 (2018)
- Pages: 595-604
- Section: Articles
- URL: https://ogarev-online.ru/2686-9667/article/view/297267
- DOI: https://doi.org/10.20310/1810-0198-2018-23-124-595-604
- ID: 297267
Cite item
Full Text
Abstract
Full Text
Spectral approximation for differential operators takes place in different applications in conjunction with the study of the mathematical modeling, as the case of Schr¨odinger operator in the quantum physics.About the authors
Ammar Khellaf
Universit.e 8 Mai 1945, Guelma
Email: amarlasix@gmail.com; khellaf.ammar@univ-guelma.dz
Post-Graduate Student B.P. 401 Guelma Alg.erie
References
- Aslanyan A., Davies E.B. Spectral instability for some Schrodinger operators. arXiv:math/9810063v1 [math.SP].
- Rappaz J., Sanchez Hubert J., Sanchez Palencia E., Vassiliev D. On spectral pollution in the finite element approximation of thin elastic ’membrane’ shells // Numer. Math. 1997. vol. 75. P. 473-500.
- Davies E.B. Spectral enclosures and complex resonances for general selfadjoint operators // LMS J. Comput. Math. 1998. Vol. 1. P. 42-74.
- Davies E.B., Plum M. Spectral pollution. arXiv:math/0302145v1. 2002.
- Boffi D. et al. On the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form // Math. of Comp. 1999. Vol. 69. P. 121-140.
- Guebbai H. Generalized spectrum approximation and numerical computation of eigenvalues for schr.odinger’s operators // Lobachevskii Journal of Mathematics. 2013. Vol. 34. P. 45-60.
- Ahues M., Largillier A., Limaye B.V. Spectral Computations for Bounded Operators. N. Y.: Chapman and Hall/CRC, 2001.
- Marletta M., Scheichl R. Eigenvalues in Spectral Gaps of Differential Operators // J. Spectr. Theory. 2012. Vol. 2 (3). P. 293-320.
- Guebbai H., Largillier A. Spectra and Pseudospectra of Convection-Diffusion Operator// Integral Methods in Science and Engineering. Boston, 2011.
- Roach G.F. Green’s Functions. N. Y.: Cambridge University Press, 1982.
- Atkinson K.E. The Numerical Solution of Integral Equations of the Second Kind. Cambridge, Cambridge University Press, 1997.
- Trefethen L.N. Pseudospectra of Linear Operators // SIAM Review. 1997. Vol. 39. P. 383.
- Laub A.J. Matrix Analysis for Scientists and Engineers. California: SIAM, 2005. 172 p.
- Gohberg I., Goldberg S., Kaashoek M.A. Classes of Linear Operators. Vol. I. Basel: Springer, 1990.
- Kato T. Perturbation Theory of Linear Operators. Second edition. Berlin; Heidelberg; New York: Springer-Verlag, 1980.
Supplementary files
