Crank-Nicolson difference scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative

被引：175

作者：

Wang, Dongling ^{[1
]}

Xiao, Aiguo ^{[1
]}

Yang, Wei ^{[1
]}

机构：

[1] Xiangtan Univ, Key Lab Intelligent Comp & Informat Proc, Minist Educ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2013年 / 242卷

关键词：

Fractional Schrodinger equation; Crank-Nicolson scheme; Fractional centered difference; DIFFUSION EQUATION; NUMERICAL-METHODS; CONVERGENCE;

D O I：

10.1016/j.jcp.2013.02.037

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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.

引用

页码：670 / 681

页数：12

共 32 条

[1] Collocation method for fractional quantum mechanics [J].