New conservative finite volume element schemes for the modified Korteweg–de Vries equation |
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| Authors: | Jinliang Yan Qian Zhang Zhiyue Zhang |
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| Affiliation: | 1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu, China;2. Department of Mathematics and Computer, Wuyi University, Wu Yi Shan, China |
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| Abstract: | In this paper, three conservative finite volume element schemes are proposed and compared for the modif ied Korteweg–de Vries equation, especially with regard to their accuracy and conservative properties. The schemes are constructed basing on the discrete variational derivative method and the finite volume element method to inherit the properties of the original equation. The theoretical analysis show that three schemes are conservative under suitable boundary conditions as well as unconditionally linear stability. Numerical experiments are given to confirm the theoretical results and the capacity of the proposed methods for capturing the solitary wave phenomena. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | conservative finite volume element method discrete variational derivative method KdV mKdV |
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