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

Abstract

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 L2 error estimate has the convergence rate O(hk+1+(Δt)2+(Δt)α2hk+12) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme.