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 Schrodinger 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 classs of finite difference scheme also are analysed in the nonautonomous system case.

  • Keywords

Global attractor Nonlinear Schrodinger equation Finite difference method Stibility and convergence

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@Article{JCM-19-393, author = {}, 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 Schrodinger 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 classs 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 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 KW - Nonlinear Schrodinger equation KW - Finite difference method KW - Stibility and convergence AB - A weakly damped Schrodinger 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 classs of finite difference scheme also are analysed in the nonautonomous system case.
Fa Yong Zhang & Shu Juan Lu. (1970). 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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