Anouar Ben Mabrouk

Malika Jallouli, Wafa Bel Hadj Khalifa, Anouar Ben Mabrouk et al.

3D image processing constitutes nowadays a challenging topic in many scientific fields such as medicine, computational physics and informatics. Therefore, development of suitable tools that guaranty a best treatment is a necessity. Spherical shapes are a big class of 3D images whom processing necessitates adoptable tools. This encourages researchers to develop spherical wavelets and spherical harmonics as special mathematical bases able for 3D spherical shapes. The present work lies in the whole topic of 3D image processing with the special spherical harmonics bases. A spherical harmonics based approach is proposed for the reconstruction of images provided with spherical harmonics Shannon-type entropy to evaluate the order/disorder of the reconstructed image. Efficiency and accuracy of the approach is demonstrated by a simulation study on several spherical models.

Abdelhamid Bezia, Anouar Ben Mabrouk, Kamel Betina

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating Lyapunov-Sylvester operators. Some numerical implementations are provided at the end of the paper to validate the theoretical results.

Abdurahman F. Aljohani, Anouar Ben Mabrouk

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea consists in transforming the continuous system into an algebraic quasi linear dynamical discrete one leading to generalized semi-linear operators. Next, the discrete algebraic system is studied for solvability, stability, convergence and stability. At the final step, numerical examples are provided to illustrate the efficiency of the theoretical results.

Riadh Chteoui, Anouar Ben Mabrouk, Hichem Ounaies

In the present paper a numerical method is developed to approximate the solution of two-dimensional NLS equation in the presence of a singular potential. The method leads to Lyapunov-Syslvester algebraic operators that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and stable using the based on Lyapunov criterion, lax equivalence theorem and the properties of the Lyapunov-Syslvester operators.

Abdelhamid Bezia, Anouar Ben Mabrouk

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Kuramoto-Sivashinsky equation. It consists of an order reduction method and a finite difference discretization which is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

Anouar Ben Mabrouk, Riadh Chteoui

A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.

Malika Jallouli, Makerem Zemni, Anouar Ben Mabrouk et al.

Biosignals are nowadays important subjects for scientific researches from both theory and applications especially with the appearance of new pandemics threatening humanity such as the new Coronavirus. One aim in the present work is to prove that Wavelets may be successful machinery to understand such phenomena by applying a step forward extension of wavelets to multiwavelets. We proposed in a first step to improve the multiwavelet notion by constructing more general families using independent components for multi-scaling and multiwavelet mother functions. A special multiwavelet is then introduced, continuous and discrete multiwavelet transforms are associated, as well as new filters and algorithms of decomposition and reconstruction. The constructed multiwavelet framework is applied for some experimentations showing fast algorithms, ECG signal, and a strain of Coronavirus processing.