Rosenau-RLW 方程的加权守恒差分格式

Conservative Weighted Finite Difference Scheme for the Rosenau-RLW Equation

摘要:

本文对Rosenau-RLW方程初边值问题的数值解法进行了研究，提出了一个三层的加权差分格式，该格式较好地模拟了方程的守恒性质.讨论了差分解的存在唯一性，给出了差分解的先验估计和误差估计，利用能量方法分析了该格式的二阶收敛性、无条件稳定性.数值算例验证了格式的可靠性，并且适当调整加权系数，可以提高计算精度.

Abstract:

In this paper a numerical method for an initial-boundary problem of the Rosenau-RLW equation is considered. A three-layer weighted conservative difference scheme is proposed. The scheme simulates the conservation property of the equations. The existence of discrete solution is discussed. The priori and error estimates of the discrete solution are derived, and the second order convergence and unconditional stability of the discrete solution are analyzed by the discrete energy method. Numerical examples verify the reliability of the scheme, and that the accuracy of the calculation can be improved by adjusting weighted coefficient properly.