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Chin. Phys. B, 2011, Vol. 20(3): 030204    DOI: 10.1088/1674-1056/20/3/030204
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A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

Zhang Rong-Pei(张荣培)a),Yu Xi-Jun(蔚喜军)b),and Zhao Guo-Zhong(赵国忠) b)
a Graduate School of China Academy of Engineering Physics, Beijing 100088, China; b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract  This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.
Keywords:  dissipative cubic nonlinear Schrödinger equation      three-level finite difference      convergence and stability analysis  
Received:  11 March 2010      Revised:  22 October 2010      Accepted manuscript online: 
PACS:  02.60.-x (Numerical approximation and analysis)  

Cite this article: 

Zhang Rong-Pei(张荣培),Yu Xi-Jun(蔚喜军),and Zhao Guo-Zhong(赵国忠) A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation 2011 Chin. Phys. B 20 030204

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