An unconditionally stable linearized CCD-ADI method for generalized nonlinear Schrodinger equations with variable coefficients in two and three dimensions

被引:30
作者
He, Dongdong [1 ]
Pan, Kejia [2 ]
机构
[1] Tongji Univ, Sch Aerosp Engn & Appl Mech, Shanghai 200092, Peoples R China
[2] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
基金
中国国家自然科学基金;
关键词
Three-level linearly method; Schrodinger equation; CCD-ADI method; Unconditionally stable; Variable coefficients; DIRECTION IMPLICIT METHOD; COMPACT DIFFERENCE SCHEME; BOUNDARY-CONDITIONS; NUMERICAL-SOLUTION; DIFFUSION EQUATIONS; SOLITON-SOLUTIONS; QUANTUM DYNAMICS; QUANTIZED VORTEX; COLLOCATION; SIMULATION;
D O I
10.1016/j.camwa.2017.04.009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we propose a three-level linearly implicit combined compact difference method (CCD) together with alternating direction implicit method (ADI) for solving the generalized nonlinear Schrodinger equation (NLSE) with variable coefficients in two and three dimensions. The method is sixth-order accurate in space variable and second-order accurate in time variable. Fourier analysis shows that the method is unconditionally stable. Comparing to the nonlinear CCD-PRADI scheme for solving the 2D cubic NLSE with constant coefficients (Li et al., 2015), current method is a linear scheme which generally requires much less computational cost. Moreover, current method can handle 3D problems with variable coefficients naturally. Finally, numerical results for both 2D and 3D cases are presented to illustrate the advantages of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2360 / 2374
页数:15
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