Discrete Schrödinger equations and dissipative dynamical systems
Mostafa Abounouh - Universite Cadi Ayyad, Faculte des Sciences et Techniques, Avenue Abdelkrim Khattabi, BP 549, Marrakech, Morocco (email)
Abstract: We introduce a Crank-Nicolson scheme to study numerically the long-time behavior of solutions to a one dimensional damped forced nonlinear Schrödinger equation. We prove the existence of a smooth global attractor for these discretized equations. We also provide some numerical evidences of this asymptotical smoothing effect.
Keywords: Finite differences, stability, multilevel decomposition.
Received: February 2007; Revised: July 2007; Published: December 2007.
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