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

被引：170

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 50 条

[41] A compact ADI Crank-Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation
Li, Mingzhu
Ma, Qiang
Ding, Xiaohua
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (12) : 2525 - 2538
[42] RICHARDSON EXTRAPOLATION OF THE CRANK-NICOLSON SCHEME FOR BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS
Xu, Yafei
Zhao, Weidong
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2024, 21 (02) : 268 - 294
[43] The approximation of a Crank-Nicolson scheme for the stochastic Navier-Stokes equations
Yang, Xiaoyuan
Wang, Wei
Duan, Yuanyuan
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 225 (01) : 31 - 43
[44] Unconditional Superconvergence Analysis of a Crank-Nicolson Galerkin FEM for Nonlinear Schrodinger Equation
Shi, Dongyang
Wang, Junjun
JOURNAL OF SCIENTIFIC COMPUTING, 2017, 72 (03) : 1093 - 1118
[45] The Splitting Crank-Nicolson Scheme with Intrinsic Parallelism for Solving Parabolic Equations
Xue, Guanyu
Gong, Yunjie
Feng, Hui
JOURNAL OF FUNCTION SPACES, 2020, 2020
[46] Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations
Wei Qu
Yong Liang
Advances in Difference Equations, 2017
[47] Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations
Qu, Wei
Liang, Yong
ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[48] Superconvergence analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrodinger equation
Zhang, Houchao
Wang, Junjun
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (02) : 799 - 820
[49] Nonlinear Galerkin method and Crank-Nicolson approximation for the Navier Stokes equations
He, Yinnian
Huang, Qinghuai
Hsi-An Chiao Tung Ta Hsueh/Journal of Xi'an Jiaotong University, 1995, 29 (02): : 97 - 106
[50] CRANK-NICOLSON ALTERNATIVE DIRECTION IMPLICIT METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NONSEPARABLE COEFFICIENTS
Lin, Xue-Lei
Ng, Michael K.
Sun, Hai-Wei
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (03) : 997 - 1019

← 1 2 3 4 5 →