6 citations · 10 across the 8 of their papers we have counts for
9 papers
Error estimation for numerical approximations of ODEs via composition techniques. Part II: BDF methods
Ahmad Deeb, Denys Dutykh, Maryam Al Zohbi
Integration of Ordinary Differential Equations (ODEs) using Backward Difference formula (BDF) methods with p backward steps achieves order p accuracy if specific conditions are met…
From Time Series Expansion to Proper Generalized Decomposition via Graph-Theoretical Connection: Stabilized Simulation of Fluids Flow
Ahmad Deeb, Vladimir Parezanovic, Denys Dutykh
In this paper, we employ graph theory to establish a connection between the Time Series Expansion (TSE) and Proper Generalized Decomposition (PGD) methods. Using the concept of a d…
Numerical Integration of Navier-Stokes Equations by Time Series Expansion and Stabilized FEM
Ahmad Deeb, Denys Dutykh
This manuscript introduces an advanced numerical approach for the integration of incompressible Navier-Stokes (NS) equations using a Time Series Expansion (TSE) method within a Fin…
Error estimation for numerical approximations of ODEs via composition techniques. Part I: One-step methods
Ahmad Deeb, Denys Dutykh
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition technique…
Stabilized Time Series Expansions for High-Order Finite Element Solutions of Partial Differential Equations
Ahmad Deeb, Denys Dutykh
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transi…
Numerical Approach Based on the Composition of One-Step Time-Integration Schemes For Highly Deformable Interfaces
Aymen Laadhari, Ahmad Deeb
In this work, we propose a numerical approach for simulations of large deformations of interfaces in a level set framework. To obtain a fast and viable numerical solution in both t…
A Finite Element Approach For Modeling Biomembranes In Incompressible Power-Law Flow
Aymen Laadhari, Ahmad Deeb
We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculat…
Performance of Borel-Padé-Laplace integrator for the resolution of stiff and non-stiff problems
Ahmad Deeb, Aziz Hamdouni, Dina Razafindralandy
A stability analysis of the Borel-Laplace series summation technique, used as explicit time integrator, is carried out. Its numerical performance on stiff and non-stiff problems is…
Some robust integrators for large time dynamics
Dina Razafindralandy, Vladimir Salnikov, Aziz Hamdouni +1
This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. T…