Fatima Aboud

• PhD
• Assistant Professor at University of Diyala

In this article we are interested for 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 eignevalues. This leads to solve nonlinear eigenvalue problems. In introduction we begin with a review of theo...

In this paper, we present a novel method for solving an inverse problem that involves determining an unknown defect D compactly contained in a simply-connected bounded domain \(\varOmega \), given the Dirichlet temperature data u, the Neumann heat flux data \(\partial _\nu u\) on the boundary \(\partial \varOmega \), and a Dirichlet boundary condit...

The objective of this paper is to solve numerically a Cauchy problem defined on a two-dimensional domain occupied by a material satisfying the Helmholtz type equations and verifying additional Cauchy-type boundary conditions on the accessible part of the boundary. A meshless numerical method using an approximation of the solution based on the polyn...

Abstract. Data completion known as Cauchy problem is one most investigated inverse problems. In this work we consider a Cauchy problem associated with Helmholtz equation. Our concerned is the convergence of the well-known alternating iterative method [25]. Our main result is to restore the convergence for the classical iterative algorithm (KMF) whe...

In this article we propose a new demonstration of the convergence of the relaxed iterative JN algorithm for solving the inverse Cauchy problem. We give in particular the convergence interval as well as the interval of the convergence acceleration of KMF algorithm.

This paper is concerned with the Cauchy problem for the Helmholtz equation. Recently, some new works asked the convergence of the well‐known alternating iterative method. Our main result is to propose a new alternating algorithm based on relaxation technique. In contrast to the existing results, the proposed algorithm is simple to implement, conver...

In this work, the finite difference method was used to calculate the heat distribution during cooling by the boundary part of a cylindrical material subjected to high temperature. A mathematical model of the process was formulated using cylindrical coordinates. The heat transfer coefficient occurring in the Robin condition at the cooled boundary is...

In this work, the finite difference method was used to calculate the heat distribution during cooling by the boundary part of a cylindrical material subjected to high temperature. A mathematical model of the process was formulated using cylindrical coordinates. The heat transfer coefficient occurring in the Robin condition at the cooled boundary is...

In this paper, two relaxation algorithms on the Dirichlet Neumann boundary condition, for solving the Cauchy problem governed to the Modified Helmholtz equation are presented and compared to the classical alternating iterative algorithm. The numerical results obtained using our relaxed algorithm and the finite element approximation show the numeric...

In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given for the pseudospectra. Then we present the numerical methods and results obtained for eigenvalues computation...

In this paper we consider generalized eigenvalue problems for a family of operators with a quadratic dependence on a complex parameter. Our model is L(λ)=−△+(P2(x)−λ) in L2(Rd) where P is a positive elliptic polynomial in Rd of degree m⩾2. It is known that for d even, or d=1, or d=3 and m⩾6, there exist λ∈C and u∈L2(Rd), u≠0, such that L(λ)u=0. In...

Ce travail porte sur l'étude de familles polynomiales d'opérateurs de la forme : L(z)=H_0+z H_1+...+ zm-1Hm-1+zm , où H0,H1,...,Hm-1 sont des opérateurs définis sur l'espace de Hilbert H et z est un paramètre complexe. On s'intéresse au spectre de la famille L(z). Le problème L(z)u(x)=0 est un problème aux valeurs propres non-linéaires lorsque m≥2...

In this paper we consider generalized eigenvalue problems for a family of operators with a quadratic dependence on a complex parameter. Our model is $L(\lambda)=-\triangle +(P(x)-\lambda)^2$ in $L^2(\R^d)$ where $P$ is a positive elliptic polynomial in $\R^d$ of degree $m\geq 2$. It is known that for $d$ even, or $d=1$, or $d=3$ and $m\geq 6$, ther...