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A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation |
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| Authors: | Zhang Rong-Pei Yu Xi-Jun and Zhao Guo-Zhong |
| Institution: | Graduate School of China Academy of Engineering Physics, Beijing 100088, China;Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;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 Schrö dinger equation three-level finite difference convergence and stability analysis |
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