New conservative schemes with discrete variational derivatives for nonlinear wave equations
New conservative schemes with discrete variational derivatives for nonlinear wave equations
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DOI：
10.1016/j.cam.2006.03.009
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发表时间：
2007-06
影响因子：
2.4
通讯作者：
Takayasu Matsuo
中科院分区：
文献类型：
--
作者：
Takayasu Matsuo
对一类非线性波动方程提出了新的守恒差分格式。其中的关键工具是“离散变分导数”，它实现了离散守恒性。Furihata最近提出了一种用于目标方程的类似方法，但本文探索了一种不同的方法，其中目标方程首先被转换为等效系统表示，这是更自然的形式，以查看守恒性质。非线性Klein-Gordon方程和所谓的“好”Boussinesq方程的应用。数值算例表明了新格式的良好性能。
New conservative finite difference schemes for certain classes of nonlinear wave equations are proposed. The key tool there is “discrete variational derivative”, by which discrete conservation property is realized. A similar approach for the target equations was recently proposed by Furihata, but in this paper a different approach is explored, where the target equations are first transformed to the equivalent system representations which are more natural forms to see conservation properties. Applications for the nonlinear Klein–Gordon equation and the so-called “good” Boussinesq equation are presented. Numerical examples reveal the good performance of the new schemes.