Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions
Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions
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DOI：
10.1007/s11075-023-01634-6
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发表时间：
2023-08
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影响因子：
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通讯作者：
Dongdong Hu;L. Kong;Wenjun Cai;Yushun Wang
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作者：
Dongdong Hu;L. Kong;Wenjun Cai;Yushun Wang
在本文中，我们打算利用最近的论文(Ju等人，SIAM J.Numer)提出的广义标量辅助变量(GSAV)方法。Anal.，60,1905-1931)对非局部耦合Sine-Gordon方程构造了一类完全解耦的、线性的、二阶精确的能量守恒格式。严格讨论了该格式的无条件唯一可解性和离散能量守恒律，并用数学归纳法证明了该格式的无条件收敛。特别地，由于相应的非线性项直接满足全局Lipschitz连续性，因此该格式的收敛分析涵盖了多维情况。最后，对具有不同非局部参数的控制方程的动力学行为的时间演化进行了观察，大量的数值比较表明，该格式在长时间计算中表现出了较高的效率。
In this paper, we intend to utilize the generalized scalar auxiliary variable (GSAV) approach proposed in recent paper (Ju et al., SIAM J. Numer. Anal., 60 , 1905–1931) for the nonlocal coupled sine-Gordon equation to construct a class of fully decoupled, linear, and second-order accurate energy-preserving scheme. The unconditional unique solvability and discrete energy conservation law of the proposed scheme are rigorously discussed, and the unconditional convergence is then proved by the mathematical induction. Particularly, the convergence analysis covers the proposed scheme in multiple dimensions due to the corresponding nonlinear terms satisfy the global Lipschitz continuity straightforwardly. Finally, time evolution of dynamical behavior of the governing equation with different nonlocal parameters are observed, and ample numerical comparisons demonstrate that the proposed scheme manifests high efficiency in long-time computations.