LOCAL STRUCTURE-PRESERVING ALGORITHMS FOR THE KDV EQUATION
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 algo- rithms and eight local momentum-c...
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| Published in | Journal of computational mathematics Vol. 35; no. 3; pp. 289 - 318 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chinese Academy of Mathematices and Systems Science (AMSS) Chinese Academy of Sciences
01.05.2017
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| Online Access | Get full text |
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| Summary: | 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 algo- rithms 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 re- gion 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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| Bibliography: | 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 algo- rithms 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 re- gion 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. Korteweg-de Vries （KdV） equation, Structure-preserving algorithms, Concate-nating method, Multi-symplectic conservation law. 11-2126/O1 |
| ISSN: | 0254-9409 1991-7139 |
| DOI: | 10.4208/jcm.1605-m2015-0343 |