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

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 fo...

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Bibliographic Details
Published in:Numerical algorithms 2017-03, Vol.74 (3), p.659-674
Main Authors: Yan, Jin-Liang, Zhang, Qian, Zhang, Zhi-Yue, Liang, Dong
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Energy
Korteweg-Devries equation
Mathematics
Methods
Numeric Computing
Numerical Analysis
Original Paper
Partial differential equations
Propagation
Simulation
Solitary waves
Spectral methods
Theory of Computation
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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-016-0166-z