Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrödinger equations

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• 作者：Tingchun Wang^a ; ^{wangtingchun@nuaa.edu.cn"" rel=""nofollow} ; ^{wangtingchun2010@gmail.com"" rel=""nofollow}
• 关键词：Coupled nonlinear Schr&#xf6 ; dinger equations ; Finite difference scheme ; Convergence in maximum norm
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2011
• 出版时间：15 May 2011
• 年：2011
• 卷：235
• 期：14
• 页码：4237-4250
• 全文大小：1302 K

文摘

In this article, a linearized conservative difference scheme for a coupled nonlinear Schrödinger equations is studied. The discrete energy method and an useful technique are used to analyze the difference scheme. It is shown that the difference solution unconditionally converges to the exact solution with second order in the maximum norm. Numerical experiments are presented to support the theoretical results.