New energy-preserving schemes using Hamiltonian Boundary Value and Fourier pseudospectral methods for the numerical solution of the "good" Boussinesq equation
New energy-preserving schemes using Hamiltonian Boundary Value and Fourier pseudospectral methods for the numerical solution of the "good" Boussinesq equation
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DOI：
10.1016/j.cpc.2015.12.013
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发表时间：
2016-04
期刊：
影响因子：
--
通讯作者：
Jinliang Yan;Zhiyue Zhang
中科院分区：
文献类型：
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作者：
Jinliang Yan;Zhiyue Zhang
利用Hamiltonian边值方法和Fourier拟谱方法，对“好的”Boussinesq（GBq）方程提出了两种能量守恒格式.方程在空间上用Fourier拟谱方法离散，在时间上用Hamilton边值方法离散。所提出的方案的突出优点是，他们可以精确地保持整体质量和能量，并提供高精度的结果。通过单个孤立波、两个孤立波的相互作用以及孤立波的产生来验证所提出格式的精度和守恒性。此外，我们还比较了我们的数值结果与其他已知的研究方法的数值精度和守恒性质。
Two energy-preserving schemes are proposed for the “good” Boussinesq (GBq) equation using the Hamiltonian Boundary Value and Fourier pseudospectral methods. The equation is discretized in space by Fourier pseudospectral method and in time by Hamiltonian Boundary Value methods (HBVMs). The outstanding advantages of the proposed schemes are that they can precisely conserve the global mass and energy, and provide highly accurate results. The single solitary wave, the interaction of two solitary waves and the birth of solitary waves are presented to validate the accuracy and conservation properties of the proposed schemes. In addition, we also compare our numerical results with other known studied methods in terms of numerical accuracy and conservation properties.