一种线性隐式守恒差分格式用于广义Rosenau-Kawahara-RLW方程
A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation
AI总结：
本文提出了一种线性隐式差分格式，用于求解广义Rosenau-Kawahara-RLW方程，证明了该格式在时间与空间上的二阶精度及无条件稳定性，并通过数值实验验证了能量守恒性和长期模拟的有效性。
摘要：
本文研究了通过耦合广义Rosenau-RLW方程和广义Rosenau-Kawahara方程得到的广义Rosenau-Kawahara-RLW方程的数值解法。首先推导了该方程的能量守恒定律，然后开发了一种三阶线性隐式差分格式用于求解该方程。证明了所提出格式在时间与空间变量上均具有二阶精度，且无条件稳定且能量守恒。最后通过数值实验验证了该格式的能量守恒性、收敛性和长期模拟的有效性。
英文摘要：
This paper concerns the numerical study for the generalized Rosenau-Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLW equation and the generalized Rosenau-Kawahara equation. We first derive the energy conservation law of the equation, and then develop a three-level linearly implicit difference scheme for solving the equation. We prove that the proposed scheme is energy-conserved, unconditionally stable and second-order accurate both in time and space variables. Finally, numerical experiments are carried out to confirm the energy conservation, the convergence rates of the scheme and effectiveness for long-time simulation.
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