中文摘要：

对Benjamin—Bona—Mahony（BBM）方程的初边值问题进行了数值研究，提出了一个两层拟紧致隐式差分格式，讨论了差分解的存在唯一性，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，并利用数值实验进行了验证．

英文摘要：

In this paper, a finite difference method for a initial-boundary value problem of Benjamin-Bona- Mahony equation was considered. A pseudo-compact finite difference of two levels was proposed. Existence and uniqueness of numerical solutions are derived. It is proved that the finite difference scheme is convergent in order o（τ2 ＋h2） and stable. Numerical experiments show that this method is efficient.