An explicit structure-preserving algorithm for the nonlinear fractional Hamiltonian wave equation
An explicit structure-preserving algorithm for the nonlinear fractional Hamiltonian wave equation
复制标题
非线性分数哈密顿波动方程的显式保结构算法
DOI：
10.1016/j.aml.2019.106123
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发表时间：
2020
影响因子：
3.7
通讯作者：
Wang Yushun
中科院分区：
文献类型：
--
作者：
Fu Yayun;Cai Wenjun;Wang Yushun
本文提出了一种新的构造非线性分数阶波动方程显式保结构格式的方法。首先，我们将方程重新表述为正则哈密顿系统。然后，利用四阶分数中心差分公式在空间方向上对方程进行离散，得到一个保守的半离散系统。随后，我们开发了一个显式的全离散能量保持计划的方程，通过使用所提出的方法。最后通过数值算例验证了理论分析的正确性.
In this paper, we propose a new approach to construct an explicit structure-preserving scheme for the nonlinear fractional wave equation. First, we reformulate the equation as a canonical Hamiltonian system. Then, we utilize the fourth-order fractional centered difference formula to discretize the equation in space direction, and obtain a conservative semi-discrete system. Subsequently, we develop an explicit fully-discrete energy-preserving scheme for the equation by using the proposed approach. Numerical examples are provided to confirm our theoretical analysis in long time computations at last.