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Volume 19, Issue 4
Long-Time Behavior of Finite Difference Solutions of a Nonlinear Schrödinger Equation with Weakly Damped

Fa-Yong Zhang & Shu-Juan Lu

J. Comp. Math., 19 (2001), pp. 393-406.

Published online: 2001-08

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  • Abstract

A weakly damped Schrödinger equation possessing a global attractor are considered. The dynamical properties of a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case.  

  • Keywords

Global attractor, Nonlinear Schrödinger equation, Finite difference method, Stability and convergence.

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COPYRIGHT: © Global Science Press

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@Article{JCM-19-393, author = {Zhang , Fa-Yong and Lu , Shu-Juan}, title = {Long-Time Behavior of Finite Difference Solutions of a Nonlinear Schrödinger Equation with Weakly Damped}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {4}, pages = {393--406}, abstract = {

A weakly damped Schrödinger equation possessing a global attractor are considered. The dynamical properties of a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8992.html} }
TY - JOUR T1 - Long-Time Behavior of Finite Difference Solutions of a Nonlinear Schrödinger Equation with Weakly Damped AU - Zhang , Fa-Yong AU - Lu , Shu-Juan JO - Journal of Computational Mathematics VL - 4 SP - 393 EP - 406 PY - 2001 DA - 2001/08 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8992.html KW - Global attractor, Nonlinear Schrödinger equation, Finite difference method, Stability and convergence. AB -

A weakly damped Schrödinger equation possessing a global attractor are considered. The dynamical properties of a class of finite difference scheme are analysed. The existence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case.  

Zhang , Fa-Yong and Lu , Shu-Juan. (2001). Long-Time Behavior of Finite Difference Solutions of a Nonlinear Schrödinger Equation with Weakly Damped. Journal of Computational Mathematics. 19 (4). 393-406. doi:
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