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High Order Energy-Preserving Method of the “Good” Boussinesq Equation

Part of: Numerical approximation and computational geometry

Published online by Cambridge University Press:  15 February 2016

Chaolong Jiang ,
Jianqiang Sun ,
Xunfeng He  and
Lanlan Zhou
Chaolong Jiang
Affiliation:
Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China
Jianqiang Sun*
Affiliation:
Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China
Xunfeng He
Affiliation:
Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China
Lanlan Zhou
Affiliation:
Department of Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China
*
*Corresponding author. Email addresses: [email protected] (C.-L. Jiang), [email protected] (J.-Q. Sun), [email protected] (X.-F. He), [email protected] (L.-L. Zhou)
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Abstract

The fourth order average vector field (AVF) method is applied to solve the “Good” Boussinesq equation. The semi-discrete system of the “good” Boussinesq equation obtained by the pseudo-spectral method in spatial variable, which is a classical finite dimensional Hamiltonian system, is discretizated by the fourth order average vector field method. Thus, a new high order energy conservation scheme of the “good” Boussinesq equation is obtained. Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the “good” Boussinesq equation exactly and simulate evolution of different solitary waves well.

Keywords

“Good” Boussinesq equationaverage vector field methodsolitary wavesconservation law

MSC classification

Secondary: 65D17: Computer aided design (modeling of curves and surfaces)
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 9 , Issue 1 , February 2016 , pp. 111 - 122
Copyright
Copyright © Global-Science Press 2016 

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