Fourth-order compact and energy conservative difference schemes for the nonlinear Schr?dinger equation in two dimensions

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• 作者：Tingchun Wang^a ; ^{wangtingchun2010@gmail.com} ; Boling Guo^b ; Qiubin Xu^c
• 关键词：Nonlinear Schrö ; dinger equation ; Compact and conservative difference scheme ; A priori estimate ; Unconditional convergence
• 刊名：Journal of Computational Physics
• 出版年：2013
• 出版时间：15 June, 2013
• 年：2013
• 卷：243
• 期：Complete
• 页码：382-399
• 全文大小：2912 K

文摘

In this paper, a fourth-order compact and energy conservative difference scheme is proposed for solving the two-dimensional nonlinear Schr?dinger equation with periodic boundary condition and initial condition, and the optimal convergent rate, without any restriction on the grid ratio, at the order of in the discrete -norm with time step and mesh size h is obtained. Besides the standard techniques of the energy method, a new technique and some important lemmas are proposed to prove the high order convergence. In order to avoid the outer iteration in implementation, a linearized compact and energy conservative difference scheme is derived. Numerical examples are given to support the theoretical analysis.