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Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation

Part of: Optics, electromagnetic theory - General

Published online by Cambridge University Press:  11 July 2017

Qi Hong ,
Yushun Wang  and
Qikui Du
Qi Hong*
Affiliation:
Graduate School of China Academy of Engineering Physics, Beijing 100088, China Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu 210023, China
Yushun Wang*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu 210023, China
Qikui Du*
Affiliation:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu 210023, China
*
*Corresponding author. Email:hq1162377655@163.com (Q.Hong), wangyushun@njnu.edu.cn (Y. S.Wang), 05270@njnu.edu.cn (Q. K. Du)
*Corresponding author. Email:hq1162377655@163.com (Q.Hong), wangyushun@njnu.edu.cn (Y. S.Wang), 05270@njnu.edu.cn (Q. K. Du)
*Corresponding author. Email:hq1162377655@163.com (Q.Hong), wangyushun@njnu.edu.cn (Y. S.Wang), 05270@njnu.edu.cn (Q. K. Du)
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Abstract

In this paper, based on the multi-symplectic formulations of the generalized fifth-order KdV equation and the averaged vector field method, two new energy-preserving methods are proposed, including a new local energy-preserving algorithm which is independent of the boundary conditions and a new global energy-preserving method. We prove that the proposed methods preserve the energy conservation laws exactly. Numerical experiments are carried out, which demonstrate that the numerical methods proposed in the paper preserve energy well.

Keywords

Generalized fifth-order KdV equationlocal energy-preservingglobal energy-preservingaverage vector fieldFourier pseudospectral

MSC classification

Secondary: 78A48: Composite media; random media
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1206 - 1224
Copyright
Copyright © Global-Science Press 2017 

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