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 - <p style="text-align: justify;">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.&nbsp;&nbsp;</p>