On Solving Coullet System by Differential Transformation Method

Year 2011, Volume: 8 Issue: 1, - , 01.05.2011

Mehmet Merdan , Ahmet Gökdoğan Vedat Suat Ertürk

Abstract

The differential transformation method is employed to solve a system of nonlinear
differential equations, namely Coullet system. Numerical results are compared to
those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and
effectiveness of the proposed method. It is shown that the proposed method is robust,
accurate and easy to apply. 

Keywords

Coullet system, differential transformation, Runge-Kutta, numerical method

References

• [1] J. K. Zhou, Differential Transformation and its Applications for Electrical Circuits (In Chinese), Huazhong University Press, Wuhan, China 1986.
• [2] V. S. Ert¨urk, Differential transformation method for solving differential equations of LaneEmden type, Mathematical and Computational Applications 12 (2007), 135–139.
• [3] V. S. Ert¨urk, Solution of linear twelfth-order boundary value problems by using differential transform method, International Journal of Applied Mathematics & Statistics 13(M08) (2008), 57–63.
• [4] S.-H. Chang and I.-L. Chang, A new algorithm for calculating one-dimensional differential transform of nonlinear functions, Applied Mathematics and Computation 195 (2008), 799–808.
• [5] H. Demir and ˙I. C¸ . S¨ung¨u, Numerical solution of a class of nonlinear Emden-Fowler equations by using differential transform method, C¸ ankaya Universitesi Journal of Arts and Sciences ¨ 12 (2009), 75–81.
• [6] M. Merdan and A. G¨okdo˘gan, Solution of nonlinear oscillators with fractional nonlinearities by using the modified differential transformation method, Mathematical and Computational Applications 16 (2011), 761–772.
• [7] I. Hashim, M. S. M. Noorani, R. Ahmad, S. A. Bakar, E. S. Ismail and A. M. Zakaria, Accuracy of the Adomian decomposition method applied to the Lorenz system, Chaos, Solitons & Fractals 28 (2006), 1149–1158.
• [8] A. Arneodo, P. Coullet and C. Tresser, Possible new strange attractors with spiral structure, Communications in Mathematical Physics 79 (1981), 573–579.
• [9] P. Coullet, C. Tresser and A. Arneodo, Transition to stochasticity for a class of forced oscillators, Physics Letters A 72 (1979), 268–270.
• [10] J.-B. Hu, Y. Han and L.-D. Zhao, Synchronization in the Genesio Tesi and Coullet systems using the backstepping approach, Journal of Physics: Conference Series 96 (2008), 012150.
• [11] X. Shi and Z. Wang, Adaptive synchronization of Coullet systems with mismatched parameters based on feedback controllers, International Journal of Nonlinear Science 8 (2009), 201–205.
• [12] J. Ghasemi, A. Ranjbar N. and A. Afzalian, Synchronization in the Genesio-Tesi and Coullet systems using the sliding mode control, International Journal of Engineering 4 (2010), 60–65.
• [13] L. Yang-Zheng and F. Shu-Min, Synchronization in the Genesio-Tesi and Coullet systems with nonlinear feedback controlling, Acta Physica Sinica (Chinese Edition) 54 (2005), 3490–3495.