Publications internationales

2020
MOHAMED HAIOUR, SALAH BOULAARAS, RAFIK GUEFAIFIA, AND FARES KAMACHE. (2020), EXISTENCE RESULT FOR A NEW CLASS OF KIRCHHOFF ELLIPTIC SYSTEM WITH VARIABLE PARAMETERS. Miskolc Mathematical Noteshttps://real.mtak.hu/119085/1/3380.pdf

Résumé: Abstract. The paper studies the existence result for a new class of Kirchhoff elliptic system with variable parameters in the right hand side. Sub-super solutions method are used for proving the main result. Our study is a natural improvement result of our previous one in (Boulaaras et al. in

2018
Sofiane Madi, Mohamed Cherif Bouras, Mohamed Haiour, Andreas Stahel. (2018), Pricing of American options, using the Brennan–Schwartz algorithm based on finite elements. Applied Mathematics and Computation : sciencedirect, https://www.sciencedirect.com/science/article/abs/pii/S0096300318305174

Résumé: Abstract A finite element method and implicit time steps are used to determine the price of an American option. The algorithm of Brennan and Schwartz is adapted to this situation and we prove convergence. Numerical tests confirm the theoretical result and lead to a smaller error for the same computational effort, compared to the finite difference method.

Salah Boulaaras * , Mohammed Cherif Bahi, Mohamed Haiour and Abderrahmane Zarai. (2018), The Maximum Norm Analysis of a Nonmatching Grids Method for a Class of Parabolic Equation∗ . Boletim da Sociedade Paranaense de Matemaica : Sociedade Paranaense de Matemática, https://scholar.google.com/citations?view_op=view_citation&hl=ar&user=OAk4xVUAAAAJ&citation_for_view=OAk4xVUAAAAJ:blknAaTinKkC

Résumé: Motivated by the idea which has been introduced by M. Haiour and S. Boulaaras (Proc. Indian Acad. Sci.(Math. Sci.) Vol. 121, No. 4, November 2011, pp. 481–493), we provide a maximum norm analysis of Euler combined with finite element Schwarz alternating method for a class of parabolic equation on with nolinear source terms two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a stability analysis on Euler scheme which given by our work in (App. Math. Comp., 217, 6443–6450 (2011)), we establish, on each subdomain, an optimal asymptotic behavior between the discrete Schwarz sequence and the asymptotic solution of parabolic differential equation

2017
Salah Boulaaras, Mohamed Haiour, Med Amine Bencheick Le hocine. (2017), l-error estimates of discontinuous Galerkin methods with theta time discretization scheme for an evolutionary HJB equations. Mathematical Methods in the Applied Sciences : WILEY, https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.4306

Résumé: Abstract The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton-Jacobi-Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd.

Mohamed Haiour Salah Boulaaras. (2017), Uniform Convergence of Schwarz Method for Elliptic Quasi-Variational Inequalities Related to Impulse Control Problem. An-Najah University Journal for Research - A (Natural Sciences)https://repository.najah.edu/items/c8a9873b-d65a-4522-b8ad-303e6c38fadb

Résumé: In this paper we provide a uniform convergence using an overlapping Schwarz method on nonmatching grids for quasi-variational inequalities related to impulse control problem. The discretization on every sub-domain converges in uniform norm was provided and a result of approximation in the -norm was given. في هذه الورقة نبين التقارب المنتظم بطريقة تداخل النطاقات (nonmatching grids) لشوارتز المطبقة على المتراجات شبه المتغيرة الناقصية أين يكون حاجز المسألة المنفصلة (المتقطعة) متعلق بالحل والمعرف بتحكم دفع مثالي (Impulse control problem).حيث بُرْهِن التقارب المنتظم للمسألة المنفصلة (المتقطعة) في كلتي النطاقين المقسمين وفق الطريقة العددية المذكورة سلفا وأعْطِيت نتيجتها التقريبية بواسطة النظيم المنتظم

2015
Salah Boulaaras, Mohamed Haiour. (2015), A new proof for the existence and uniqueness of the discrete evolutionary HJB equations. Applied Mathematics and Computation : sciencedirect, https://www.sciencedirect.com/science/article/abs/pii/S0096300315004099

Résumé: Abstract In this paper, we establish a new proof for the existence and uniqueness of the discrete solution of evolutionary HJB equations which can be approximated by a weakly coupled system of coercive elliptic quasi-variational inequalities (OVIs). For that some properties of the presented algorithm (cf., e.g., Boulaaras and Haiour, 2013; Boulbrachene and Haiour, 2001) using the theta-scheme with respect to the t-variable combined with a finite element spatial approximation are proved.

Salah Boulaaras, Mohamed Haiour. (2015), A General Case for the Maximum Norm Analysis of an Overlapping Schwarz Methods of Evolutionary HJB Equation with Nonlinear Source Terms with the Mixed Boundary Conditions. Applied Mathematics & Information Sciences : Natural Sciences Publish, https://scholar.google.com/citations?view_op=view_citation&hl=ar&user=OAk4xVUAAAAJ&citation_for_view=OAk4xVUAAAAJ:IWHjjKOFINEC

Résumé: Abstract: In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for evolutionary HJB equation with nonlinear source terms with the mixed boundary conditions and a general elliptic operator. Moreover, an asymptotic behavior in uniform norm is established.

Salah Boulaaras, Khaled Habita & Mohamed Haiour . (2015), Asymptotic behavior and a posteriori error estimates for the generalized overlapping domain decomposition method for parabolic equation. Boundary Value Problems : springer., https://link.springer.com/article/10.1186/s13661-015-0398-1

Résumé: In this paper, a posteriori error estimates for the generalized overlapping domain decomposition method with Dirichlet boundary conditions on the interfaces, for parabolic variational equation with second order boundary value problems, are derived using the semi-implicit-time scheme combined with a finite element spatial approximation. Furthermore a result of asymptotic behavior in uniform norm is given using Benssoussan-Lions’ algorithm.

2014
Salah Boulaaras, Mohamed Haiour. (2014), The theta time scheme combined with a finite-element spatial approximation in the evolutionary hamilton–jacobi–bellman equation with linear source terms. Computational Mathematics and Modeling : Springer US, https://link.springer.com/article/10.1007/s10598-014-9237-y

Résumé: This paper is an extension and generalization of the previous results, cf. [2–4]. It is devoted to the theta-scheme with respect to the t -variable combined with a finite-element spatial approximation of the evolutionary Hamilton–Jacobi–Bellman equations (HJB equation) and involves a weakly coupled discrete system of parabolic quasi-variational inequalities (PQVs). Its relation to time energy behavior is proved. In addition, the PQVs are transformed into a coercive discrete system of elliptic quasi-variational inequalities. A new iterative discrete algorithm is also proposed to show the existence and uniqueness of the discrete solution. Moreover, its convergence is established. Then a simple proof to an asymptotic behavior in uniform norm is given. Furthermore the proposed approach is based on a discrete L ∞-stability property with respect to the right-hand side and the boundary conditions.

Salah Boulaaras1, Med Amine Bencheikh le Hocine2, and Mohamed Haiour3. (2014), THE FINITE ELEMENT APPROXIMATION IN A SYSTEM OF PARABOLIC QUASI-VARIATIONAL INEQUALITIES RELATED TO MANAGEMENT OF ENERGY PRODUCTION WITH MIXED BOUNDARY CONDITION. Computational Mathematics and Modeling : springer., https://www.researchgate.net/profile/Salah-Boulaaras/publication/266324373_The_Finite_Element_Approximation_in_a_System_of_Parabolic_Quasi-Variational_Inequalities_Related_to_Management_of_Energy_Production_with_Mixed_Boundary_Condition/links/5432ae710cf225bddcc7c54a/The-Finite-Element-Approximation-in-a-System-of-Parabolic-Quasi-Variational-Inequalities-Related-to-Management-of-Energy-Production-with-Mixed-Boundary-Condition.pdf

Résumé: This paper deals with a system of parabolic quasi-variational inequalities related to the management of energy production with mixed boundary condition. A quasi-optimal L1 -error estimate is established using a new discrete algorithm based on a theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L1 -stability property with respect to the right-hand side.

2013
Salah Boulaaras, Mohamed Haiour. (2013), The finite element approximation of evolutionary Hamilton–Jacobi–Bellman equations with nonlinear source terms . Indagationes Mathematicae : sciencedirect, https://www.sciencedirect.com/science/article/pii/S0019357712000626

Résumé: Abstract This paper deals with the semi-implicit scheme with respect to the -variable combined with a finite element spatial approximation of evolutionary Hamilton–Jacobi–Bellman equations with nonlinear source terms. We establish a convergence and a quasi-optimal -asymptotic behavior, involving a weakly coupled system of discrete parabolic quasi-variational inequalities (PQVIs), for the solution of which an iterative discrete scheme of monotone kind is introduced and analyzed. Furthermore, the simple numerical example shows that the estimates introduced in this paper are efficient.

Salah Boulaaras, Mohamed Haiour. (2013), The finite element approximation in parabolic quasi-variational inequalities related to impulse control problem with mixed boundary conditionsFootnote . Journal of Taibah University for Science : Taylor & Francis, https://www.tandfonline.com/doi/full/10.1016/j.jtusci.2013.05.005

Résumé: This paper is an extension for our previous results [3–5], and it deals with the finite element approximation of a parabolic quasi-variational inequalities with mixed boundary conditions. A quasi-optimal L∞-error estimate is established using a new discrete algorithm stands in theta time scheme combined with a finite element spatial approximation. Our approach stands on a discrete L∞-stability property with respect to the right-hand side where the obstacle defined as an impulse control problem.

2011
Salah Boulaaras a, Mohamed Haiour b. (2011), L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem. Applied Mathematics and Computation : sciencedirect, https://www.sciencedirect.com/science/article/abs/pii/S0096300311000415

Résumé: Abstract In this paper, the parabolic quasi-variational inequalities are transformed into a noncoercive elliptic quasi-variational inequalities. A new iterative discrete algorithm is proposed to show the existence and uniqueness, and a simple proof to asymptotic behavior in uniform norm is also given using the theta time scheme combined with a finite element spatial approximation. The proposed approach stands on a discrete L∞-stability property with respect to the right-hand side and obstacle defined as an impulse control problem.

MOHAMED HAIOUR & SALAH BOULAARAS . (2011), Overlapping domain decomposition methods for elliptic quasi-variational inequalities related to impulse control problem with mixed boundary conditions. Proceedings-Mathematical Sciences : springer., https://link.springer.com/article/10.1007/s12044-011-0042-7

Résumé: Abstract. In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for quasi-variational inequalities related to impulse control problem with mixed boundary conditions. We provide that the discretization on every sub-domain converges in uniform norm. Furthermore, a result of approximation in uniform norm is given.

2009
M. Haiour and E. Hadidi. (2009), Uniform Convergence of Schwarz Method for Noncoercive Variational Inequalities. Int. J. Contemp. Math. Sciences : hikari, https://www.m-hikari.com/ijcms-password2009/29-32-2009/hadidiIJCMS29-32-2009.pdf

Résumé: Abstract In this paper we study noncoercive variational inequalities studied by Courty-Dumont, using the Schwarz method. The main idea of this method consists in decomposing the domain in two subdomains. We demonstrate that the discretisation on every subdomain converges in uniform norm and we give a result of approximation for the method in uniform norm.

2001
M. Boulbrachene, M. Haiour. (2001), The finite element approximation of Hamilton-Jacobi-Bellman equations. Computers & Mathematics with Applications : sciencedirect, https://www.sciencedirect.com/science/article/pii/S0898122100003345

Résumé: Abstract This paper deals with the finite element approximation of Hamilton-Jacobi-Bellman equations. We establish a convergence and a quasi-optimal L∞-error estimate, involving a weakly coupled systems of quasi-variational inequalities for the solution of which an interative scheme of monotone kind is introduced and analyzed.