Thèses de Doctorat "Mathématique"

URI permanent de cette collection

https://dspace.univ-oran1.dz/handle/123456789/77

Parcourir par

Parcourir la collection Thèses de Doctorat "Mathématique" par Sujet "Advection-diffusion operator"

Voici les éléments 1 - 1 sur 1
  • Item
    Discretization of certain operators and their spectral and pseudo-spectral study
    (2022-07-03) DERKAOUI Rafik
    The project of this thesis treated one of the most important and newest topics in functional analysis. In the present study , we focused on several aspects, such as the theory of spectrum, the demand for this result arise in the solution of linear equations and in many other mathematics and physics problems. The pseudo-spectrum discovered by the numerical scientist Lioyd Nicholas Trefthen in the early of 90s plays an important role in the study of non-normal operators. Also, in order to understand the perturbations of spectral objects, we set a point in pseudo-spectrum. Moreover, we discussed "The Numerical Range of an Operator", particularly the numerical range of matrices, with clarifying examples. The relevant of the latest result that it can be applied to many mathematical disciplines such as the Theory of Linear Operators, Matrix Polynomials, and applications in various fields including C-algebras. In the present work, we studied the discretization of some operators and their spectral and pseudo-spectral studies by providing examples of some operators by resorting to numerical methods. In the first example , we study of the discretization of the operator of Benilov et al, then the spectral and pseudo-spectral study of this discretization, while, in the second example, we discretize the advection-diffusion operator that we have established its spectrum and pseudo-spectrum.