Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Schrodinger equation

In this paper we present and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional Schrodinger equation, where the fractional derivative is described in the Caputo sense. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. A stability and error analysis is performed on the numerical methods. Numerical results confirm the expected convergence rates and illustrate the effectiveness of the method. Crown Copyright (C) 2012 Published by Elsevier BY. All rights reserved.