Email this article A Class of Momentum-Preserving Finite Difference Schemes for the Korteweg-de Vries Equation
- Authors: Yan J.1,2, Zheng L.3
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Affiliations:
- Department of Mathematics and Computer, Wuyi University
- Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University
- Department of Information and Computer Technology, No.1 middle school of Nanping
- Issue: Vol 59, No 10 (2019)
- Pages: 1582-1596
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/180826
- DOI: https://doi.org/10.1134/S0965542519100154
- ID: 180826
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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.
About the authors
Jin-Liang Yan
Department of Mathematics and Computer, Wuyi University; Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University
Author for correspondence.
Email: yanjinliang3333@163.com
China, Wu Yi Shan, 354300; Jiangsu, 210023
Liang-Hong Zheng
Department of Information and Computer Technology, No.1 middle school of Nanping
Email: yanjinliang3333@163.com
China, Fujian, 353000
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