The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations
The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations
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线性修正保能有限差分法求解二维非线性耦合波动方程的研究
DOI：
10.1007/s11075-021-01099-5
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发表时间：
2021-04
影响因子：
2.1
通讯作者：
Qiang Wu
中科院分区：
文献类型：
--
作者：
Dingwen Deng;Qiang Wu
利用不变能量二次化方法（IEQM），设计了求解二维非线性耦合sine-Gordon方程（CSGE）和耦合Klein-Gordon方程（CKGE）的四种线性能量保持有限差分方法（EP-FDM）.首先引入两个辅助函数将原问题改写为只包含一阶时间导数的新系统，然后分别采用Crank-Nicolson（C-N）方法和二阶中心差分方法离散时间导数和空间导数。第二EP-FDM是直接基于使用二阶中心差分方法来近似二阶时间和空间导数而设计的。第一和第二EP-FDM需要在每个时间水平上具有变系数矩阵的代数系统的数值解。通过修改第二EP-FDM，第三EP-FDM，这是通过计算的代数方程组的常系数矩阵在每个时间水平上，实现开发。最后，将交替方向隐式（ADI）有限差分法与第三代EP-FDM相结合，建立了能量保持的交替方向隐式（ADI）有限差分法（EP-ADI-FDM）。利用离散能量方法，证明了它们都是唯一可解的，并且它们的解具有H ~ 1-范数收敛速度，满足离散守恒律。数值结果表明了它们的有效性和准确性。
In this paper, four linearly energy-preserving finite difference methods (EP-FDMs) are designed for two-dimensional (2D) nonlinear coupled sine-Gordon equations (CSGEs) and coupled Klein-Gordon equations (CKGEs) using the invariant energy quadratization method (IEQM). The 1st EP-FDM is designed by first introducing two auxiliary functions to rewrite the original problems into the new system only including the 1st-order temporal derivatives, and then applying Crank-Nicolson (C-N) method and 2nd-order centered difference methods for the discretizations of temporal and spatial derivatives, respectively. The 2nd EP-FDM is directly devised based on the uses of 2nd-order centered difference methods to approximate 2nd-order temporal and spatial derivatives. The 1st and 2nd EP-FDMs need numerical solutions of the algebraic system with variable coefficient matrices at each time level. By modifying the 2nd EP-FDM, the 3rd EP-FDM, which is implemented by computing the system of algebraic equations with constant coefficient matrices at each time level, is developed. Finally, an energy-preserving alternating direction implicit (ADI) finite difference method (EP-ADI-FDM) is established by a combination of ADI method with the 3rd EP-FDM. By using the discrete energy method, it is shown that they are all uniquely solvable, and their solutions have a convergent rate ofinH1-norm and satisfy the discrete conservative laws. Numerical results show the efficiency and accuracy of them.
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影响因子：
4.1
作者：
Cai Wenjun;Li Haochen;Wang Yushun
通讯作者：
Wang Yushun
岩溶含水层系统微可压缩Forchheimer裂缝简化耦合模型的有限差分近似
影响因子：
2.1
作者：
Liu Wei;Cui Jintao;Wang Zhifeng
通讯作者：
Wang Zhifeng
影响因子：
2.6
作者：
Shikuo Liu;Zuntao Fu;Shi-da Liu;Zhanggui Wang
通讯作者：
Shikuo Liu;Zuntao Fu;Shi-da Liu;Zhanggui Wang
DOI：
10.1016/j.cpc.2015.12.013
发表时间：
2016-04
期刊：
Comput. Phys. Commun.
影响因子：
--
作者：
Jinliang Yan;Zhiyue Zhang
通讯作者：
Jinliang Yan;Zhiyue Zhang
DOI：
10.1016/j.amc.2012.10.005
发表时间：
2012-12
期刊：
Appl. Math. Comput.
影响因子：
--
作者：
Weiliang Xiao;Yan Ping
通讯作者：
Weiliang Xiao;Yan Ping