Benjamin-Bona-Mahony方程的一个高精度线性差分格式

High precise linearized difference scheme for Benjamin-Bona-Mahony equation

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,提出了一个理论精度为O(τ~2+h^4)的三层线性差分格式,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.

In this paper,numerical solution for the initial-boundary value problem of 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 energy method.Numerical experiments indicate the reliability of this method.