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

摘要

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for solving the time-fractional coupled Schrodinger 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(h~(k+1) + (△t)~2 + (△t)2/a h~(k+2/1)) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.