A new finite difference scheme for a dissipative cubic nonlinear Schrdinger equation

作者：Zhang Rong Pei a) Yu Xi Jun b) and Zhao Guo Zhong b) a) Graduate School of China Academy of Engineering Physics Beijing China b) Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

来源：Chinese Physics B, 2011, (03): 31-36.

• dissipative cubic nonlinear Schr&uml
• odinger equation
• three-level finite difference
• convergence and stability analysis

This paper considers the one-dimensional dissipative cubic nonlinear Schrdinger 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.