求解BBM方程的一个两层线性化差分格式

A linear two-level difference scheme for solving BBM equation

摘要:

本文对一类带有齐次边界条件的Benjamin-Bona-Mahony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为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.本文证明了该格式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，本文还综合运用数学归纳法和离散泛函分析方法直接证明了该差分格式的收敛性和稳定性.数值实验表明该方法是可靠的.

Abstract:

In this paper, the numerical solution of initial-boundary value problem for Benjamin-Bona-Mahony equation with homogeneous boundary is considered. A two-level linearized difference scheme with second order is proposed. The difference scheme simulates the conservation property of the problem quite well. Then the existence, uniqueness, convergence and stability of the difference solutions are also proved. The results are demonstrated by a numerical example.