中文摘要：

作者对广义正则长波方程的初边值问题进行了数值研究，提出了两层隐式拟紧致差分格式，该格式很好地模拟了问题的守恒性质，得到了差分解的存在唯一性，并分析了该格式的二阶收敛性与无条件稳定性．数值算例表明，该格式是可行的，且相对于一般的二阶格式，计算精度有明显提高．

英文摘要：

The numerical solution for an initial-boundary value problem of generalized regularized long wave equation is considered. An implicit pseudo-compact finite difference 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. The numerical examples show this scheme is feasible and its accuracy is better than usual difference scheme of two levels.