In this study, homotopy perturbation method and parameterexpanding
method are applied to the motion equations of two nonlinear oscillators. Our
results show that both the (HPM) and (PEM) yield the same results for the
nonlinear problems. In comparison with the exact solution, the results show
that these methods are very convenient for solving nonlinear equations and also
can be used for strong nonlinear oscillators.
References
[1]
J. H. He, European Journal of Physics, Vol. 29, 2008, pp. 19-22. http://dx.doi.org/10.1088/0143-0807/29/4/L02
[2]
J. H. He, International Journal of Nonlinear Science and Numerical Simulation, Vol. 9, 2008, pp. 211-212. http://dx.doi.org/10.1515/IJNSNS.2008.9.2.211
[3]
A. G. Davodi, D. D. Gangi, R. Azami and H. Babazadeh, Modern Physics Letters B, Vol. 23, 2009, pp. 3427-3436. http://dx.doi.org/10.1142/S0217984909021466
[4]
I. Mehdipour, D. D. Ganji and M. Mozaffari, Current Applied Physics, Vol. 10, 2010, pp. 104-112. http://dx.doi.org/10.1016/j.cap.2009.05.016
[5]
D. Younesian, H. Askari, Z. Saadatnia and M. Kalami Yazdi, Computers and Mathematics with Applications, Vol. 59, 2010, pp. 3222-3228. http://dx.doi.org/10.1016/j.camwa.2010.03.013
[6]
H. Askari, M. Kalami Yazdi and Z. Saadatnia, Nonlinear Science Letters A, Vol. 1, 2010, pp. 425-430.
[7]
J. H. He, G. C. Wu and F. Austin, Nonlinear Science Letters A, Vol. 1, 2010, pp. 1-30.
[8]
N. Herisanu and V. Marinca, Nonlinear Science Letters A, Vol. 1, 2010, pp. 183-192.
[9]
J. H. He, International Journal of Modern Physics B, Vol. 20, 2006, pp. 2561-2568. http://dx.doi.org/10.1142/S0217979206034819
[10]
J. H. He, International Journal of Non-Linear Mechanics, Vol. 35, 2000, pp. 37-43.
[11]
J. H. He, Chaos, Solitons and Fractals, Vol. 26, 2005, pp. 695-700. http://dx.doi.org/10.1016/j.chaos.2005.03.006
[12]
D. D. Ganji, Physics Letters A, Vol. 355, 2006, pp. 337-341. http://dx.doi.org/10.1016/j.physleta.2006.02.056
[13]
J. H. He, International Journal of Modern Physics B, Vol. 20, 2006, pp. 1141-1199. http://dx.doi.org/10.1142/S0217979206033796
[14]
L. Xu, Journal of Computational and Applied Mathematics, Vol. 207, 2007, pp. 148-154. http://dx.doi.org/10.1016/j.cam.2006.07.020
[15]
L. Xu, Journal of Sound and Vibration, Vol. 302, 2007, pp. 178-184. http://dx.doi.org/10.1016/j.jsv.2006.11.011
[16]
J. H. He, Computer Methods in Applied Mechanics and Engineering, Vol. 178, 1999, pp. 257-262. http://dx.doi.org/10.1016/S0045-7825(99)00018-3
[17]
J. H. H Journal of Sound and Vibration, Vol. 229, 2000, pp. 1257-1263. http://dx.doi.org/10.1006/jsvi.1999.2509
[18]
J. H. He, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 2, 2001, pp. 257-264. http://dx.doi.org/10.1515/IJNSNS.2001.2.3.257
[19]
R. E. Mickens, Journal of Sound and Vibration, Vol. 292, 2006, pp. 964-968. http://dx.doi.org/10.1016/j.jsv.2005.08.020
[20]
T. Ozis and A. Yildirm, Journal of Sound and Vibration, Vol. 306, 2007, pp. 372-376. http://dx.doi.org/10.1016/j.jsv.2007.05.021
[21]
D. D. Ganji, M. Esmaeilpour and S. Soleimani, International Journal of Computer Mathematics, Vol. 9, 2010, pp. 2014-2023.
[22]
I. S. Gradshteyn and I. S. Ryzhik, “Table of Integrals, Series and Products,” Academic Press, New York, 1980.
[23]
C. W. Lim and S. K. Lai, International Journal of Mechanical Sciences, Vol. 48, 2006, pp. 483-892. http://dx.doi.org/10.1016/j.ijmecsci.2005.12.009
[24]
J. J. Stoker, “Nonlinear Vibrations in Mechanical and Electrical Systems,” Wiley, New York, 1992.
[25]
D. W. Jordan and P. Smith, “Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems,” Oxford University Press, New York, 1999.
