Adomian decomposition and Padé approximate for solving differential-difference equation

In this paper, we apply the Adomian decomposition method and Padé-approximate to solving the differential-difference equations (DDEs) for the first time. A simple but typical example is used to illustrate the validity and the great potential of the Adomian decomposition method (ADM) in solving DDEs. Comparisons are made between the results of the proposed method and exact solutions. The results show that ADM is an attractive method in solving the differential-difference equations.