Department
Departement of Physics
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Recent Publications
Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme
SIR model for epidemics. We broadened the model to include
vaccination, treatment, and incidence rate. The vaccination rate is
a testament to the alternatives made by individuals when it comes
to receiving vaccinations and merging with the community of the
recovered. The treatment rate measures how often people who
have contracted a disease are able to transition into the recovered
category. The continuous Galerkin-Petrov method, specifically the
cGP(2)-method, is employed to calculate the numerical solutions of
the models. The cGP(2)-method imperative to analyse two
unknowns over every time interval. The unknowns can be determined by solving a block system of size (2 × 2). This approach
demonstrates a strong level of precision throughout the entire
time interval, with an impressive rate of convergence at the discrete
time points. In addition, the article investigates the concept of the
basic reproduction number (R0) and explores the intricacies of
conducting sensitivity analysis of the developed system
Citation
M. MAHDI Khaled, (2024-10-16), "Computational approaches on integrating vaccination and treatment strategies in the SIR model using Galerkin time discretization scheme", [national] Mathematical and Computer Modelling of Dynamical Systems , Taylor and Francis Ltd
Numerical study and optimization of a conical autoclave receiver
designed to prepare steam to meet the sterilization needs of medical instruments. A conical concentrator coupled
to an autoclave in cylindrical form is placed in the conical reflector axis. We present a mathematical model
explaining the thermal behaviour of water in a medical autoclave. The validation of the model was well done
with the literature results. Our results indicate that the system produces saturated steam and takes 20 to 30 min,
depending on climatic conditions and autoclave dimensions. The sufficient time to reach a temperature of more
than 121 ◦C where no organism reproduces after being kept in an autoclave at 126 ◦C for 6 min or at 121 ◦C for at
least 20 min. The simulation results encourage us to optimize the concentrator device to obtain a useful solar
sterilizer, using the theoretical model as a safe guide to achieve this.
Citation
M. MAHDI Khaled, (2024-03-12), "Numerical study and optimization of a conical autoclave receiver", [national] Partial Differential Equations in Applied Mathematics , Elsevier
On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up
dynamic boundary condition. Given convenient initial data, we obtained the local
existence of a weak solution. Local existence results of solutions are obtained using
the Faedo-Galerkin method and the Schauder fixed-point theorem. Additionally,
under suitable assumptions on initial data, the lower bound time of the blow-up
result is investigated.
Citation
M. MAHDI Khaled, (2023-12-19), "On a logarithmic wave equation with nonlinear dynamical boundary conditions: local existence and blow-up", [national] Journal of Inequalities and Applications , Springer International Publishing