Abstract: 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.

Key words: Rosenau-Burgers equation, Crank-Nicolson method, modified local Crank-Nicolson scheme