中文摘要：

作者对Rosenau-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，讨论了差分解的存在唯一性，并分析了该格式的二阶收敛性与稳定性，数值试验验证了该方法的有效性．

英文摘要：

A three level average implicit finite difference scheme for the numerical solution of the initial- boundary value problem of Rosenau-Burgers equation is presented. Existence and uniqueness of numerical solutions are discussd. It is proved that the finite difference scheme is convergent in the order of o（r2 ＋ h2） and stable. Numerical simulations show that the method is efficient.