Year: 2017
Author: Jialing Wang, Yushun Wang
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 3 : pp. 289–318
Abstract
In this paper, based on the concatenating method, we present a unified framework to construct a series of local structure-preserving algorithms for the Korteweg-de Vries (KdV) equation, including eight multi-symplectic algorithms, eight local energy-conserving algorithms and eight local momentum-conserving algorithms. Among these algorithms, some have been discussed and widely used while the most are new. The outstanding advantage of these proposed algorithms is that they conserve the local structures in any time-space region exactly. Therefore, the local structure-preserving algorithms overcome the restriction of global structure-preserving algorithms on the boundary conditions. Numerical experiments are conducted to show the performance of the proposed methods. Moreover, the unified framework can be easily applied to many other equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1605-m2015-0343
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 3 : pp. 289–318
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Korteweg-de Vries (KdV) equation structure-preserving algorithms concatenating method multi-symplectic conservation law.
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