Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM

Current Applied Physics

Volumn 11, Issue 4, 2011, Pages 965-971

  Ghafoori, S ^a   Motevalli, M ^b   Nejad, M G ^a   Shakeri, F ^a   Ganji, D D ^a   Jalaal, M ^c  

^a BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Differential transform method (DTM); Homotopy perturbation method (HPM); Nonlinear oscillation; Series based solution; Variation iteration method (VIM)

Indexed keywords

DIFFERENTIAL TRANSFORM METHOD; HOMOTOPY PERTURBATION METHOD (HPM); NONLINEAR OSCILLATION; SERIES-BASED SOLUTION; VARIATION ITERATION METHOD (VIM);

BEAMS AND GIRDERS; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; NUMERICAL METHODS; OSCILLATORS (MECHANICAL); PERTURBATION TECHNIQUES;

ITERATIVE METHODS;

EID: 79957574864     PISSN: 15671739     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cap.2010.12.018     Document Type: Article

References (34)

1. A.H. Nayef Problems in Perturbation 1985 John Wiley New York
2. D.D. Ganji, and A. Sadighi Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations Int. J. Nonlinear Sci. Numer. Simul. 7 4 2006 411 418 (Pubitemid 44433692)
3. I. Mehdipour, D.D. Ganji, and M. Mozaffari Application of the energy balance method to nonlinear vibrating equations Curr. Appl. Phys. 10 2010 104 112
4. M. Shaban, D.D. Ganji, and M.M. Alipour Nonlinear fluctuation, frequency and stability analyses in free vibration of circular sector oscillation systems Curr. Appl. Phys. 10 2010 1267 1285
5. S.S. Ganji, D.D. Ganji, A.G. Davodi, and S. Karimpour Analytical solution to nonlinear oscillation system of the motion of a rigid rod rocking back using max-min approach Appl. Math. Model. 34 2010 2676 2684
6. D.D. Ganji, M. Rafei, A. Sadighi, and Z.Z. Ganji A comparative comparison of He's method with perturbation and numerical methods for nonlinear vibrations equations Int. J. Nonlinear Dyn. Eng. Sci. 1 1 2009 1 20
7. M. Jalaal, M.G. Nejad, P. Jalili, M. Esmaeilpour, H. Bararnia, E. Ghasemi, Soheil Soleimani, D.D. Ganji, S.M. Moghimi, Homotopy perturbation method for motion of a spherical solid particle, Comput. Math. Appl., doi:10.1016/j.camwa.2010.09.042.
8. M. Jalaal, H. Bararnia, G. Domairry, A series exact solution for one-dimensional non-linear particle equation of motion, Powder Technol., doi:10.1016/j.powtec.2010.10.025.
9. A.A. Joneidi, D.D. Ganji, and M. Babaelahi Micropolar flow in a porous channel with high mass transfer Int. Commun. Heat and Mass Trans. 36 10 2009 1082 1088
10. M. Babaelahi, D.D. Ganji, and A.A. Joneidi Analysis of velocity equation of steady flow of a viscous Incompressible fluid in channel with porous walls Int. J. Numer. Methods Fluids 63 9 2010 1048 1059
11. A.A. Joneidi, G. Domairry, M. Babaelahi, and M. Mozaffari Analytical treatment on Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching hollow cylinder Int. J. Numer. Methods Fluids 63 5 2010 548 563
12. N. Jamshidi, and D.D. Ganji Application of energy balance method and variational iteration method to an oscillation of a mass attached to a stretched elastic wire Curr. Appl. Phys. 10 2 2010 484 486
13. M. Jalaal, D.D. Ganji, and G. Ahmadi Analytical investigation on acceleration motion of a vertically falling spherical particle in incompressible Newtonian media Adv. Powder Technol. 21 3 2010 298 304
14. M. Jalaal, D.D. Ganji, On unsteady rolling motion of spheres in inclined tubes filled with incompressible Newtonian fluids, Adv. Powder Technol., doi:10.1016/j.apt.2010.03.011.
15. M. Jalaal, and D.D. Ganj An analytical study on motion of a sphere rolling down an inclined plane submerged in a Newtonian fluid Powder Technol. 198 1 2010 82 92
16. J.K. Zhou Differential Transformation and Its Applications for Electrical Circuits 1986 Huarjung University Press Wuuhahn, China (in Chinese)
17. J.S. Chiou, and J.R. Tzeng Application of the Taylor transform to nonlinear vibration problems Trans. Am. Soc. Mech. Eng., J. Vib. Acoust. 118 1996 83 87 (Pubitemid 126767060)
18. M.J. Jang, C.L. Chen, and Y.C. Liu Two-dimensional differential transform for partial differential equations Appl. Math. Comput. 121 2001 261 270
19. I.H. Abdel-Halim Hassan On solving some eigenvalue-problems by using a differential transformation Appl. Math. Comput. 127 2002 1 22 (Pubitemid 34116067)
20. C.K. Chen, and S.P. Ju Application of differential transformation to transient advective-dispersive transport equation Appl. Math. Comput. 155 2004 25 38
21. C.K. Chen, and S.S. Chen Application of the differential transformation method to a non-linear conservative system Appl. Math. Comput. 154 2004 431 441
22. A.A. Joneidi, G. Domairry, and M. Babaelahi Three analytical methods applied to Jeffery-Hamel flow Commun. Nonlinear Sci. Numer. Simul. 2010 10.1016/j.cnsns.2009.12.023
23. A.A. Joneidi, G. Domairry, and M. Babaelahi Analytical treatment of MHD free convective flow and mass transfer over a stretching sheet with chemical reaction J. Taiwan Inst. Chem. Eng. 41 1 January 2010 35 43
24. A.A. Joneidi, D.D. Ganji, and M. Babaelahi Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity Int. Commun. Heat Mass Transfer 36 2009 757 762
25. M. Jalaal, S. Ghafoori, M. Motevalli, M.G. Nejad, and D.D. Ganji One-dimensional single rising bubble at low Reynolds numbers: solution of equation of motion by differential transformation method Asia-Pac. J. Chem. Eng 2010 10.1002/apj.530
26. Kuo Bor-Lih, and Lo Cheng-Ying Application of the differential transformation method to the solution of a damped system with high nonlinearity Nonlinear Anal. 70 2009 1732 1737
27. Zaid Odibat, Shaher Momani, and Vedat Suat Erturk Generalized differential transform method: application to differential equations of fractional order Appl. Math. Comput. 197 2008 467 477 (Pubitemid 351273764)
28. Shih-Shin Chen, and Cha'o-Kuang Chen Application of the differential transformation method to the free vibrations of strongly non-linear oscillators Nonlinear Anal. Real World Appl. 10 2009 881 888
29. A. Fidlin Nonlinear Oscillations in Mechanical Engineering 2006 Springer-Verlag Berlin Heidelberg
30. A.D. Dimarogonas, and S. Haddad Vibration for Engineers 1992 Prentice-Hall Englewood Cliffs, New Jersey
31. A.H. Nayfeh, and D.T. Mook Nonlinear Oscillations 1979 Wiley New York
32. Stephen T. Thornton, and Jerry B. Marion Classical Dynamics of Particles and Systems fifth ed. 2004 Brook/Cole Belmont CA 0534408966 (chapter 10)
33. Federal Aviation Administration Pilot's Encyclopedia of Aeronautical Knowledge 2007 Skyhorse Publishing Inc Oklahoma City OK 1602390347 Figure 3-21
34. David Halliday, Robert Resnick, and Jearl Walker Fundamentals of Physics fifth ed. 1997 John Wiley & Sons New York 0471148547 pp. 381