Numerical solution of two and three dimensional time fractional damped nonlinear Klein-Gordon equation using ADI spectral element method
Numerical solution of two and three dimensional time fractional damped nonlinear Klein-Gordon equation using ADI spectral element method
复制标题
DOI：
10.1016/j.amc.2021.126182
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
M. Saffarian;A. Mohebbi
中科院分区：
文献类型：
--
作者：
M. Saffarian;A. Mohebbi
本文提出了一种新的数值方法求解二维和三维时间分数阶非线性阻尼Klein-Gordon方程。为此，我们采用Legendre谱元方法在空间方向上离散方程，在时间步长上采用基于O（τ 2）阶格式的交替方向隐式（ADI）方法。我们证明了所提出的方法是无条件稳定的，并得到了全离散格式的误差估计。数值实验表明，所提出的ADI谱元方法具有良好的精度和效率。
At the present work, we propose a new numerical scheme for the solution of two and three dimensional time fractional nonlinear damped Klein–Gordon equation (DKGE). To this end, we use the Legendre spectral element method to discretize the equation in the spatial directions and for the time stepping, an alternating direction implicit (ADI) method based on a scheme of order O (τ 2) is considered. We prove that the presented method is unconditionally stable and obtain an error estimate for the fully discrete scheme. The presented numerical experiments demonstrate the good accuracy and efficiency of the proposed ADI spectral element method.