Structure-preserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions
Structure-preserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions
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DOI：
10.1016/j.apnum.2021.08.009
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
A. Umeda;Yuta Wakasugi;S. Yoshikawa
中科院分区：
文献类型：
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作者：
A. Umeda;Yuta Wakasugi;S. Yoshikawa
本文讨论一维非线性波动方程动力边界条件的有限差分格式的数值分析。从离散变分导数方法的观点出发，推导出了该问题的能量守恒差分格式，它尽可能广泛地覆盖了各种方程。其次，我们将注意力集中在半线性波动方程上，利用继承的能量结构证明了该格式解的存在唯一性和误差估计。
In this article, we discuss the numerical analysis for the finite difference scheme of the one-dimensional nonlinear wave equations with dynamic boundary conditions. From the viewpoint of the discrete variational derivative method we propose the derivation of the energy-conserving finite difference schemes of the problem, which covers a variety of equations as widely as possible. Next, we focus our attention on the semilinear wave equation, and show the existence and uniqueness of the solution for the scheme and error estimates with the help of the inherited energy structure.