Rosenau-Burgers方程的一个新的差分方法

从动力学系统的实际问题出发，针对Rosenau-Burgers方程的初边值问题进行了数值研究，揭示了复杂离散动态系统理论中非线性波耗散问题. 在方程求解的时间和空间区域，采用网格化方法，提出了一个新的三层隐式差分格式，对差分解进行了先验估计，并给出了该格式的稳定性和收敛性的严格理论证明. 数值实验的结果表明，差分格式简单而有效、计算速度快、稳定性好，并且差分格式使用了加权方法，使其具有普遍意义和推广价值.

A New Finite Difference Method for Rosenau-Burgers Equation

From the study of the dynamic systems, this paper discussed the numerical method of the initial-boundary value problem of Rosenau-Burgers equation. It reveals the dissipation problems of nonlinear wave. By using the mesh method in time and space domain of the equation, a new implicit finite difference scheme of three levels was proposed. And the prior estimate of the solutions was obtained. It was proved that the finite difference scheme is convergent and stable. The numerical experiment indicates that the scheme is available and it is easy to implement, and computational time can be economized. The weighted difference scheme has universal significance and it is worth popularizing.