广义Rosenau-Kawahara方程的一个非线性守恒差分逼近

A conservative nonlinear difference approximation of generalized Rosenau - Kawahara equation

摘要:

本文对一类带有齐次边界条件的广义Rosenau-Kawahara方程进行了数值研究，提出了一个两层非线性Crank-Nicolson差分格式，格式合理地模拟了问题的一个守恒性质，得到了差分解的先验估计和存在唯一性，并利用离散泛函分析方法分析了差分格式的二阶收敛性与无条件稳定性，数值试验表明，我们的方法是可信的。

Abstract:

The numerical solution for an homogeneous boundary conditions of generalized Rosenau - Kawahara equation is considered.A nonlinear two-level Crank-Nicolson 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 numerical example show this scheme is feasible.