A high-order nodal discontinuous Galerkin method for nonlinear fractional Schrodinger type equations

摘要

We propose a nodal discontinuous Galerkin method for solving the nonlinear Riesz space fractional Schrdinger equation and the strongly coupled nonlinear Riesz space fractional Schrdinger equations. These problems have been expressed as a system of low order dif-ferential/ integral equations. Moreover, we prove, for both problems, L-2 stability and optimal order of convergence O(h(N+1)), where h is space step size and N is polynomial degree. Finally, the performed numerical experiments confirm the optimal order of convergence. (C) 2017 Elsevier B. V. All rights reserved.