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Generalized differential transform method to differential-difference equation |
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| Authors: | Li Zou Zhen Wang Zhi Zong |
| Institution: | a School of Aeronautics and Astronautics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116085, China b Centre for ACES, Department of Mechanical Engineering, National University of Singapore, Singapore 117574, Singapore c Department of Applied Mathematics, Dalian University of Technology, Dalian 116085, China d School of Naval Architecture Engineering, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116085, China |
| Abstract: | In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation. |
| Keywords: | 02 30 Jr 02 60 Cb 02 60 Lj |
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