广义Rosenau-RLW方程的一个守恒差分逼近

A conservative difference approximation of generalized Rosenau - RLW equation

摘要:

本文对广义Rosenau-RLW方程的初边值问题进行了数值研究，提出了一个两层的非线性有限差分格式，格式合理地模拟了问题的守恒性质,得到了差分解的先验估计和存在唯一性，利用能量方法分析了格式的二阶收敛性与无条件稳定性，并利用数值算例进行验证。

Abstract:

The numerical solution for an initial-boundary conditions of generalized Rosenau - RLW equation is considered.A nonlinear two-level difference scheme is designed.The difference scheme simulates the conservation properties of the problem well.The prior estimate, existence and uniqueness of the finite difference solution are also obtained. It is proved that the finite difference scheme is convergent with second-order and unconditionally stable by discrete functional analysis method.The results attained form numerical experiments.