Rosenau方程的一个新的守恒差分格式

A New Conservative Difference Scheme for Rosenau Equation

对Rosenau方程的初边值问题进行了数值研究,提出了一个三层隐式差分格式,讨论了差分解的先验估计,并利用离散泛函分析方法分析了该格式的二阶收敛性与稳定性,最后利用数值实验进行了验证.

The numerical solution for an initial-boundary value problem of Rosenau equation is considered.An implicit finite difference of three levels is proposed.This scheme simulates the conservation properties of the problem well.And the prior estimate of the solution is obtained.It is proved that the finite difference scheme is convergent with order 2and stable by the discrete functional analysis.Numerical examples demonstrate the theoretical results.