中文摘要：

对一类广义Rosenau‐Kawahara方程的初边值问题进行数值研究，提出了一个两层非线性有限差分格式，合理模拟了问题的两个守恒性质，得到了差分解的先验估计和存在唯一性；利用能量方法分析了差分格式的二阶收敛性与无条件稳定性；最后，利用数值算例验证了差分格式的有效性。

英文摘要：

The numerical solution of the initial‐boundary value problem for generalized Rosenau‐Kawahara equation is considered , and a nonlinear two‐level finite difference scheme is designed . The difference schemes simulate two conservative quantities of the problem well . The prior estimate , existence and uniqueness of the finite difference solution are also obtained . It is show n that the finite difference scheme is second‐order convergence and unconditionally stable by discrete functional analysis method . Numerical experiments verify the theoretical results .