文章基本信息

标题：Nonstandard finite difference variational integrators for nonlinear Schrödinger equation with variable coefficients
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作者：Cuicui Liao ; Xiaohua Ding
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：12
DOI：10.1186/1687-1847-2013-12
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, the idea of nonstandard finite difference discretization is employed to develop two variational integrators for the nonlinear Schrödinger equation with variable coefficients. These integrators are naturally multi-symplectic, and their multi-symplectic structures are presented by the multi-symplectic form formulas. Local truncation errors and convergences of the integrators are briefly discussed. The effectiveness and efficiency of the proposed schemes, such as the convergence order, numerical stability, and the capability in preserving the norm conservation, are verified in the numerical experiments.
关键词：variational integrators ; nonstandard finite difference ; multi-symplectic ; Schrödinger equation