中文摘要：

对广义BBM-Burgers方程的初边值问题进行了数值研究,提出了一个三层平均隐式差分格式,得到了差分解的先验估计;利用能量方法分析了该格式的二阶收敛性与无条件稳定性,并利用数值算例进行验证。

英文摘要：

The numerical solution to an initial-boundary value problem of the generalized BBM-Burgers equation is considered.An implicit finite difference scheme of three levels is proposed.The prior estimate of the solution is obtained.It is proved that the finite difference scheme is convergent with the convergence order 2 and stable by the discrete functional analysis.Numerical examples demonstrate the theoretical results.