本文给出了 Rosenau-Burgers 方程的两种修正局部 Crank-Nicolson 格式．首先，求解原有的偏微分方程对空间方向进行有限差分离散而得到的常微分方程．其次，利用矩阵分裂技术对这个方程的指数系数矩阵分别按行和元素进行逼近．最后，利用修正局部 Crank-Nicolson 方法得到了两种格式．讨论了格式的稳定性、收敛性和先验误差估计．数值实验结果表明了理论证明的正确性及格式的有效性．该格式具有结构简单、精度高的优点．

Two class of modified local Crank-Nicolson schemes for Rosenau-Burgers equation are proposed. Firstly, we obtain the exact solution of the ODE which reached from the original PDE by using central finite difference discretization in space direction. Next, the exponential coefficient matrix of this equation is approximated by using matrix splitting technique by line and element. Finally, two types of methods are achieved by using modified local Crank-Nicolson scheme. The stability, convergence and priori error estimation of two schemes are discussed. The accuracy of theoretical proof and efficiency of both schemes are demonstrated by numerical results. The proposed methods possess the advantages of simple structure and high accuracy.