Rosenau-KdV-RLW方程的一个两层线性化差分方法

A Two-Level Linearized Difference Scheme for Rosenau-KdV-RLW Equation

对带有齐次边界条件的Rosenau-KdV-RLW方程的初边值问题进行了数值研究,提出了一个具有二阶理论精度的两层线性化差分格式,该格式合理地模拟了原问题的一个守恒性质,证明了差分解的存在唯一性,在不能得到其差分解的最大模估计的情况下,综合运用数学归纳法和离散泛函分析方法,直接证明了该格式的收敛性和稳定性.数值实验表明该方法是可靠的.

In this paper, the numerical solution of initial-boundary value problem for Rosenau-KdV-RLW equation with homogeneous boundary has been considered. A two-level linearized difference scheme with the second order has been proposed. The difference scheme simulates the conservation property of the problem quite well. The existence and uniqueness of the difference solutions have also beenproved. In the case that the maximum mold estimator of the difference solutions cannot be obtained, it is proved that the difference scheme is convergent and stable by mathematical induction and the discrete function analysis.And the results are demonstrated by the numerical examples.