Benjamin-Bona-Mahony方程的一个高精度线性差分格式

A high precise linearized difference scheme for Benjamin-Bona-Mahony 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，提出了一个三层线性差分格式,并利用能量方法分析了该格式的收敛性与稳定性.该格式合理地模拟了原问题的一个守恒性质.数值实验表明该方法是可靠的.

Abstract:

In this paper, numerical solution of the initial-boundary value problem for Benjamin-Bona-Mahony equation under homogeneous boundary is considered. A linearized three-level difference scheme is introduced. The difference scheme simulates a conservative quantity of the problem. Furthermore, convergence and stability of the difference scheme are proved by discrete energy method. Numerical experiments verify the reliability of this method.