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Nonstandard finite difference variational integrators for nonlinear Schrödinger equation with variable coefficients

Liao, Cuicui, Ding, Xiaohua·2013·Advances in Difference Equations
DOI 10.1186/1687-1847-2013-12
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Abstract

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.

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Cited by 11

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Metadata

Authors
Liao, C., & Ding, X.
Venue
Advances in Difference Equations
Publisher
Springer Science and Business Media LLC
Published
2013-01-16
Volume
2013
Issue
1
ISSN
1687-1847
DOI
10.1186/1687-1847-2013-12
Cited by
11
Language
en
Licence
creativecommons.org/licenses/by/2.0 (tdm)

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Liao, C., & Ding, X. (2013). Nonstandard finite difference variational integrators for nonlinear Schrödinger equation with variable coefficients. Advances in Difference Equations. https://doi.org/10.1186/1687-1847-2013-12

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