A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrödinger system
Articles > Article · 2012
Authors: Leilei WEI, Xindong ZHANG, Sunil KUMAR, Ahmet YILDIRIM
Computers & Mathematics with Applications, Journal Indexed in SCI Expanded, International, WoS, 2012, vol 64, pp 2603-2615
DOI: 10.1016/j.camwa.2012.07.004
Summary
In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LOG) 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) + (Delta t)(2) + (Delta t)(alpha/2) h(k+1/2)) for the linear case. Extensive numerical results are provided to demonstrate the efficiency and accuracy of the scheme. (C) 2012 Elsevier Ltd. All rights reserved.