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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 10, Page 1648
DOI: https://doi.org/10.1134/S0044466919100156 (Mi zvmmf10962) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A class of momentum-preserving finite difference schemes for the Korteweg–de Vries equation

Yan Jin-Liangab, Zheng Liang-Hongc

a Department of Mathematics and Computer, Wuyi University, Wu Yi Shan, China
b Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Wu Yi Shan, China
c Department of Information and Computer Technology, No. 1 middle school of Nanping, Fujian, China
Citations (1)
DOI: https://doi.org/10.1134/S0044466919100156
Abstract: To preserve some invariant properties of the original differential equation is an important criterion to judge the success of a numerical simulation. In this paper, we construct, analyze and numerically validate a class of momentum-preserving finite difference methods for the Korteweg–de Vries equation. The proposed schemes can conserve the discrete momentum to machine precision. Numerical experiments reveal that the phase and amplitude errors, after long time simulation, are well controlled due to the momentum-preserving property. Besides, the numerical results show that the numerical errors grow only linearly as a function of time.
Key words: momentum, bi-hamiltonian systems, finite difference methods, KdV equation.
Funding agency Grant number
National Natural Science Foundation of China 11471166
Natural Science Foundation of Jiangsu Province BK20141443
Education Foundation for Young Teachers of Fujian Province JA14319
PhD Start-up Fund of Wuyi University YJ201702
Priority Academic Program Development of Jiangsu Higher Education Institutions
This work is partially supported by the National Natural Science Foundation of China (grant no. 11471166), Natural Science Foundation of Jiangsu Province (grant no. BK20141443), Education Foundation for Young Teachers of Fujian Province (grant no. JA14319), PhD Start-up Fund of Wuyi University (grant no. YJ201702), and the Priority Academic Program Development of Jiangsu Higher Education Institutions.
Received: 10.01.2019
Revised: 21.02.2019
Accepted: 10.06.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 10, Pages 1582–1596
DOI: https://doi.org/10.1134/S0965542519100154
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: Yan Jin-Liang, Zheng Liang-Hong, “A class of momentum-preserving finite difference schemes for the Korteweg–de Vries equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:10 (2019), 1648; Comput. Math. Math. Phys., 59:10 (2019), 1582–1596
Citation in format AMSBIB
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\paper A class of momentum-preserving finite difference schemes for the Korteweg--de Vries equation
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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