Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem - Gracia, José Luis; O’Riordan, Eugene; Stynes, Martin (Journal of computational methods in applied mathematics, 2018)
A standard finite difference method on a uniform mesh is used to solve a time-fractional convection-diffusion initial-boundary value problem. Such problems typically exhibit a mild singularity at the initial time . It is proved that the rate of convergence of the maximum nodal error on any subdomain that is bounded away from is higher than the rate obtained when the maximum nodal error is measured over the entire space-time domain. Numerical results are provided to illustrate the theoretical error bounds.