Local discontinuous Galerkin methods for nonlinear Schrodinger equations

被引：230
作者：
Xu, Y
Shu, CW
机构：
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
[2] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2005年 / 205卷 / 01期
基金：
美国国家科学基金会;
关键词：
local discontinuous Galerkin method; nonlinear schrodinger equation;
D O I：
10.1016/j.jcp.2004.11.001
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
In this paper we develop a local discontinuous Galerkin method to solve the generalized nonlinear Schrodinger equation and the coupled nonlinear Schrodinger equation. L-2 stability of the schemes are obtained for both of these nonlinear equations. Numerical examples are shown to demonstrate the accuracy and capability of these methods. (c) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：72 / 97
页数：26
相关论文
共 34 条
[1]   A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations [J].
Bassi, F ;
Rebay, S .
JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 131 (02) :267-279
[2]   PROPAGATION OF NONLINEAR WAVE ENVELOPES [J].
BENNEY, DJ ;
NEWELL, AC .
JOURNAL OF MATHEMATICS AND PHYSICS, 1967, 46 (02) :133-&
[3]   GAUSSONS - SOLITONS OF THE LOGARITHMIC SCHRODINGER EQUATION [J].
BIALYNICKIBIRULA, I ;
MYCIELSKI, J .
PHYSICA SCRIPTA, 1979, 20 (3-4) :539-544
[4]   SOLITONS IN LASER PHYSICS [J].
BULLOUGH, RK ;
JACK, PM ;
KITCHENSIDE, PW ;
SAUNDERS, R .
PHYSICA SCRIPTA, 1979, 20 (3-4) :364-381
[5]   Difference schemes for solving the generalized nonlinear Schrodinger equation [J].
Chang, QS ;
Jia, EH ;
Sun, W .
JOURNAL OF COMPUTATIONAL PHYSICS, 1999, 148 (02) :397-415
[6]  
Ciarlet P, 1975, FINITE ELEMENT METHO
[7]   The local discontinuous Galerkin method for time-dependent convection-diffusion systems [J].
Cockburn, B ;
Shu, CW .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (06) :2440-2463
[8]   Runge-Kutta discontinuous Galerkin methods for convection-dominated problems [J].
Cockburn, Bernardo ;
Shu, Chi-Wang .
Journal of Scientific Computing, 2001, 16 (03) :173-261
[9]   The Runge-Kutta discontinuous Galerkin method for conservation laws V - Multidimensional systems [J].
Cockburn, B ;
Shu, CW .
JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 141 (02) :199-224
[10]   TVB RUNGE-KUTTA LOCAL PROJECTION DISCONTINUOUS GALERKIN FINITE-ELEMENT METHOD FOR CONSERVATION-LAWS .2. GENERAL FRAMEWORK [J].
COCKBURN, B ;
SHU, CW .
MATHEMATICS OF COMPUTATION, 1989, 52 (186) :411-435
1234