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3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：

The numerical solution for an initial - boundary value problem of Benjamin - Bona - Mahony equation was considered. A pseudo - compact finite difference of three levels was proposed. The existence and uniqueness of solution are studied. It is proved that the finite difference scheme is convergent with the convergence order 2 and stable by the discrete functional analysis. And the results are demonstrated by the numerical examples.