A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

doi:10.1088/1674-1056/20/3/030204

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30204-030204.doi: 10.1088/1674-1056/20/3/030204

A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

张荣培¹, 蔚喜军², 赵国忠²

(1)Graduate School of China Academy of Engineering Physics, Beijing 100088, China; (2)Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2010-03-11 修回日期:2010-10-22 出版日期:2011-03-15 发布日期:2011-03-15

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

Received:2010-03-11 Revised:2010-10-22 Online:2011-03-15 Published:2011-03-15

摘要/Abstract

摘要： 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.

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.

Key words: dissipative cubic nonlinear Schrödinger equation, three-level finite difference, convergence and stability analysis

中图分类号: (Numerical approximation and analysis)

02.60.-x

张荣培, 蔚喜军, 赵国忠. A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation[J]. 中国物理B, 2011, 20(3): 30204-030204.

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[J]. Chin. Phys. B, 2011, 20(3): 30204-030204.

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A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

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