中文摘要：

作者对一类广义对称正则长波（GSRLW）方程的初边值问题进行了数值研究，提出了一个两层有限差分格式，该格式合理地模拟了初边值问题的守恒性质，得到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无条件稳定性．数值结果表明，本文作者所提供的格式是可信的．

英文摘要：

The numerical solution for an initial-boundary value problem of generalized symmetrical regularized long wave equation （GSRLW） is considered. A finite difference scheme of two levels is proposed. This scheme simulates the conservation properties of the problem well. And the existence and uniqueness of the solution are also obtained. It is proved that the finite difference scheme is convergent with order 2 and stable without condition by discrete functional analysis method. The nemerieal examples show this scheme is feasible.