On Solving Coullet System by Differential Transformation Method

Mehmet Merdan [1] , Ahmet Gökdoğan [2] , Vedat Suat Ertürk [3]

41 2288

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. 

Coullet system, differential transformation, Runge-Kutta, numerical method
  • [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.
Konular
Dergi Bölümü Makaleler
Yazarlar

Yazar: Mehmet Merdan

Yazar: Ahmet Gökdoğan

Yazar: Vedat Suat Ertürk

Bibtex @araştırma makalesi { cankujse369884, journal = {Çankaya Üniversitesi Bilim ve Mühendislik Dergisi}, issn = {1309-6788}, eissn = {2564-7954}, address = {Çankaya Üniversitesi}, year = {}, volume = {8}, pages = { - }, doi = {}, title = {On Solving Coullet System by Differential Transformation Method}, key = {cite}, author = {Ertürk, Vedat Suat and Merdan, Mehmet and Gökdoğan, Ahmet} }
APA Merdan, M , Gökdoğan, A , Ertürk, V . (). On Solving Coullet System by Differential Transformation Method. Çankaya Üniversitesi Bilim ve Mühendislik Dergisi, 8 (1), . Retrieved from http://dergipark.gov.tr/cankujse/issue/33205/369884
MLA Merdan, M , Gökdoğan, A , Ertürk, V . "On Solving Coullet System by Differential Transformation Method". Çankaya Üniversitesi Bilim ve Mühendislik Dergisi 8 (): <http://dergipark.gov.tr/cankujse/issue/33205/369884>
Chicago Merdan, M , Gökdoğan, A , Ertürk, V . "On Solving Coullet System by Differential Transformation Method". Çankaya Üniversitesi Bilim ve Mühendislik Dergisi 8 ():
RIS TY - JOUR T1 - On Solving Coullet System by Differential Transformation Method AU - Mehmet Merdan , Ahmet Gökdoğan , Vedat Suat Ertürk Y1 - 2019 PY - 2019 N1 - DO - T2 - Çankaya Üniversitesi Bilim ve Mühendislik Dergisi JF - Journal JO - JOR SP - EP - VL - 8 IS - 1 SN - 1309-6788-2564-7954 M3 - UR - Y2 - 2019 ER -
EndNote %0 Çankaya Üniversitesi Bilim ve Mühendislik Dergisi On Solving Coullet System by Differential Transformation Method %A Mehmet Merdan , Ahmet Gökdoğan , Vedat Suat Ertürk %T On Solving Coullet System by Differential Transformation Method %D 2019 %J Çankaya Üniversitesi Bilim ve Mühendislik Dergisi %P 1309-6788-2564-7954 %V 8 %N 1 %R %U
ISNAD Merdan, Mehmet , Gökdoğan, Ahmet , Ertürk, Vedat Suat . "On Solving Coullet System by Differential Transformation Method". Çankaya Üniversitesi Bilim ve Mühendislik Dergisi 8 / 1 -.