Crank-Nicolson difference scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative
In this paper, the Crank-Nicolson (CN) difference scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative is studied. The existence of this difference solution is proved by the Brouwer fixed point theorem. The stability and convergence of the CN scheme are discussed in the L-2 norm. When the fractional order is two, all those results are in accord with the difference scheme developed for the classical non-fractional coupled nonlinear Schrodinger equations. Some numerical examples are also presented. (C) 2013 Elsevier Inc. All rights reserved.
fractional schrodinger equation crank-nicolson scheme fractional centered difference