Application of the modified differential transform method to fractional oscillators

Kybernetes

Volumn 40, Issue 5, 2011, Pages 751-761

  Abu Gurra, Sana ^a   Ertürk, Vedat Suat ^b   Momani, Shaher ^c  

^a MUTAH UNIVERSITY   (Jordan)

^b ONDOKUZ MAYIS UNIVERSITY   (Turkey)

^c UNIVERSITY OF JORDAN   (Jordan)

Author keywords

Approximation theory; Cybernetics; Laplace transforms

Indexed keywords

APPROXIMATION THEORY; CYBERNETICS; FLOW MEASUREMENT; LAPLACE TRANSFORMS; OSCILLATORS (MECHANICAL);

ANALYTIC SOLUTION; APPROXIMATE ANALYTICAL SOLUTIONS; APPROXIMATE SOLUTION; DESIGN/METHODOLOGY/APPROACH; DIFFERENTIAL TRANSFORM METHOD; FOURTH ORDER RUNGE-KUTTA METHODS; FRACTIONAL OSCILLATORS; OSCILLATORY SYSTEM;

RUNGE KUTTA METHODS;

EID: 79961044548     PISSN: 0368492X     EISSN: None     Source Type: Journal    
DOI: 10.1108/03684921111142296     Document Type: Review

References (21)

1. Arikoglu, A. and Ozkol, I. (2005), "Solution of boundary value problems for integro-differential equations by using differential transform method" in Applied Mathematics and Computation, Vol. 168, No. 2, pp. 1145-58.
2. Ayaz, F. (2004), "Solutions of the system of differential equations by differential transform method" in Applied Mathematics and Computation, Vol. 147, No. 2, pp. 547-67.
3. Baker, G.A. (1975), Essentials of Padé Approximants, Academic Press, London.
4. Bildik, N., Konuralp, A., Bek, F. and Kucukarslan, S. (2006), "Solution of different type of the partial differential equation by differential transform method and Adomian decomposition method" in Applied Mathematics and Computation, Vol. 172, No. 1, pp. 551-67.
5. Brogliato, R. (1998), Nonsmooth Mechanics, Springer, Berlin.
6. Chen, C.K. and Ho, S.H. (1999), "Solving partial differential equations by two-dimensional differential transform method" in Applied Mathematics and Computation, Vol. 106, Nos 2/3, pp. 171-9.
7. Ertürk, V.S. and Momani, S. (2007), "Comparing numerical methods for solving fourth-order boundary value problems" in Applied Mathematics and Computation, Vol. 188, No. 2, pp. 1963-8.
8. Hassan, I.H.A.H. (2004), "Differential transformation technique for solving higher-order initial value problems" in Applied Mathematics and Computation, Vol. 154, No. 2, pp. 3299-311.
9. Hassan, I.H.A.H. (2006), "Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems" in Chaos, Solitons & Fractals, Vol. 36, No. 1, pp. 53-65.
10. Hogan, S.J. (2003), "Relaxation oscillations in a system with a piecewise smooth drag coefficient" in Journal of Sound and Vibration, Vol. 263, No. 2, pp. 467-71.
11. Jang, M.J., Chen, C.L. and Liu, Y.C. (2000), "On solving the initial-value problems using the differential transformation method" in Applied Mathematics and Computation, Vol. 115, Nos 2/3, pp. 145-60.
12. Jang, M.J., Chen, C.L. and Liu, Y.C. (2001), "Two-dimensional differential transform for partial differential equations" in Applied Mathematics and Computation, Vol. 121, Nos 2/3, pp. 261-70.
13. Jiao, Y.C., Yamamoto, Y., Dang, C. and Hao, Y. (2002), "An aftertreatment technique for improving the accuracy of Adomian's decomposition method" in Computers & Mathematics with Applications, Vol. 43, Nos 6/7, pp. 783-98.
14. Lim, C.W. and Wu, B.S. (2003), "Accurate higher-order approximations to frequencies of nonlinear oscillators with fractional powers" in Journal of Sound and Vibration, Vol. 281, Nos 3-5, pp. 1157-62.
15. Liu, H. and Song, Y. (2006), "Differential transform method applied to high index" in Applied Mathematics and Computation, Vol. 168, No. 2, pp. 748-53.
16. Mickens, R.E. (2003), "A combined equivalent linearization and averaging perturbation method for non-linear oscillator equations" in Journal of Sound and Vibration, Vol. 264, No. 5, pp. 1195-200.
17. Mickens, R.E., Oyedeji, K.O. and Rucker, S.A. (2003), "Analysis of the simple harmonic oscillator with fractional damping" in Journal of Sound and Vibration, Vol. 268, No. 4, pp. 839-42.
18. Momani, S. (2004), "Analytical approximate solutions of non-linear oscillators by the modified decomposition method" in International Journal of Modern Physics C, Vol. 15, No. 7, pp. 1-13.
19. Momani, S. and Ertürk, V.S. (2008), "Solutions of non-linear oscillators by the modified differential transform method" in Computers & Mathematics with Applications, Vol. 55, No. 4, pp. 833-42.
20. Oyedeji, K.O. (2005), "An analysis of a nonlinear elastic force van der Pol oscillator equation" in Journal of Sound and Vibration, Vol. 281, Nos 1/2, pp. 417-22.
21. Zhou, J.K. (1986), Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, (in Chinese).