A difference scheme for the time-fractional diffusion equation on a metric star graph

In this paper, we propose an unconditionally stable numerical scheme based on finite difference for the approximation of time-fractional diffusion equation on a metric star graph. The fractional derivative is considered in Caputo sense and the so-called L1 method is used for the discrete approximation of Caputo fractional derivative. The convergence and stability of the difference scheme has been proved by means of energy method. Test examples are illustrated in order to verify the feasibility of the proposed scheme. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.