A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrödinger system

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schrödinger system. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. Through analysis we show that our scheme is unconditionally stable, and the L 2 error estimate has the convergence rate O(hk+ 1+(? t 2+( ?t)?2hk+ 12) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme. © 2012 Elsevier Ltd. All rights reserved