The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional non-linear Schrodinger equation

被引：109
|
作者：
Dehghan, Mehdi [1 ]
Mirzaei, Davoud [1 ]
机构：
[1] Amirkabir Univ Technol, Dept Appl Math, Fac Math & Comp Sci, Tehran 15914, Iran
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2008年 / 32卷 / 09期
关键词：
non-linear Schrodinger equation; meshless local Petrov-Galerkin (MLPG) method; unit heaviside test function; moving least square (MLS) approximation;
D O I：
10.1016/j.enganabound.2007.11.005
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper the meshless local Petrov-Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional nonlinear Schrodinger equation. The method is based on the local weak form and the moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time stepping method is employed for the time derivative. To deal with the non-linearity, we use a predictor-corrector method. A very simple and efficient method is presented for evaluation the local domain integrals. Finally numerical results are presented for some examples to demonstrate the accuracy, efficiency and high rate of convergence of this method. (c) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：747 / 756
页数：10
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