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Numerical Algorithms

, Volume 74, Issue 3, pp 659–674 | Cite as

A new high-order energy-preserving scheme for the modified Korteweg-de Vries equation

  • Jin-Liang Yan
  • Qian Zhang
  • Zhi-Yue Zhang
  • Dong Liang
Original Paper

Abstract

In this paper, a new high-order energy-preserving scheme is proposed for the modified Korteweg-de Vries equation. The proposed scheme is constructed by using the Hamiltonian boundary value methods in time, and Fourier pseudospectral method in space. Exploiting this method, we get second-order and fourth-order energy-preserving integrators. The proposed schemes not only have high accuracy, but also exactly conserve the total mass and energy in the discrete level. Finally, single solitary wave and the interaction of two solitary waves are presented to illustrate the effectiveness of the proposed schemes.

Keywords

Mass Momentum Energy Hamiltonian boundary value methods Fourier pseudospectral method mKdV equation 

Mathematics Subject Classification (2010)

65M99 70H06 74J35 74S99 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Jin-Liang Yan
    • 1
    • 2
  • Qian Zhang
    • 1
  • Zhi-Yue Zhang
    • 1
  • Dong Liang
    • 3
  1. 1.Jiangsu Key Laboratory for NSLSCS, School of Mathematical SciencesNanjing Normal UniversityJiangsuChina
  2. 2.Department of Mathematics and ComputerWuyi UniversityWu Yi ShanChina
  3. 3.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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