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math.GM2024
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…
math.GM2023
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…
math.GM2023
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…