7 papers
Error Profile for Discontinuous Galerkin Time Stepping of Parabolic PDEs
William McLean, Kassem Mustapha
We consider the time discretization of a linear parabolic problem by the discontinuous Galerkin (DG) method using piecewise polynomials of degree at most in , for …
A second-order accurate numerical scheme for a time-fractional Fokker-Planck equation
Kassem Mustapha, Omar M. Knio, Olivier P. Le Maître
A time-stepping scheme for solving a time fractional Fokker-Planck equation of order , with a general driving force, is investigated. A stability bound for the se…
Inverse source in two-parameter anomalous diffusion, numerical algorithms and simulations over graded time-meshes
Khaled M. Furati, Kassem Mustapha, Ibrahim O. Sarumi +1
We consider an inverse source two-parameter sub-diffusion model subject to a nonlocal initial condition. The problem models several physical processes, among them are the microwave…
An L1 approximation for a fractional reaction-diffusion equation, a second-order error analysis over time-graded meshes
Kassem Mustapha
A time-stepping L1 scheme for subdiffusion equation with a Riemann--Liouville time-fractional derivative is developed and analyzed. This is the first paper to show that the L1 sche…
Regularity theory for time-fractional advection-diffusion-reaction equations
William McLean, Kassem Mustapha, Raed Ali +1
We investigate the behavior of the time derivatives of the solution to a linear time-fractional, advection-diffusion-reaction equation, allowing space- and time-dependent coefficie…
Well-posedness of time-fractional, advection-diffusion-reaction equations
William McLean, Kassem Mustapha, Raed Ali +1
We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-depend…