Volume 9, Issue 1
High Order Energy-Preserving Method of the "Good" Boussinesq Equation

Chaolong Jiang, Jianqiang Sun, Xunfeng He & Lanlan Zhou

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 111-122.

Published online: 2016-09

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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 discretized 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.

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@Article{NMTMA-9-111, author = {}, title = {High Order Energy-Preserving Method of the "Good" Boussinesq Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {1}, pages = {111--122}, 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 discretized 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.m1420}, url = {http://global-sci.org/intro/article_detail/nmtma/12369.html} }
TY - JOUR T1 - High Order Energy-Preserving Method of the "Good" Boussinesq Equation JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 111 EP - 122 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2015.m1420 UR - https://global-sci.org/intro/article_detail/nmtma/12369.html KW - AB -

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 discretized 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.

Chaolong Jiang, Jianqiang Sun, Xunfeng He & Lanlan Zhou. (2020). High Order Energy-Preserving Method of the "Good" Boussinesq Equation. Numerical Mathematics: Theory, Methods and Applications. 9 (1). 111-122. doi:10.4208/nmtma.2015.m1420
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