Application of a New Algorithm to a Generalized Nonlinear Oscillator


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


In this paper, our new algorithm is applied to obtain an approximate periodic solution of a generalized nonlinear oscillator. The method is extremely simple but remarkably effective. Comparison of the obtained solution with the exact one is given, showing high accuracy of the approximate solutions.
Copyright © 2019 Praise Worthy Prize - All rights reserved.

Keywords


Amplitude-Frequency Formulation; Nonlinear Oscillator; Energy Balance

Full Text:

PDF


References


S. Q . Wang, J . H. He. Nonlinear oscillator with discontinuity by parameter expansion method. Chaos, Solitons & Fractals, 35, 688 (2008).

F. O. Zengin, M.O. Kaya, SA. Demirbag. Application of parameter- expansion method to nonlinear oscillators with discontinuities. Int. J Nonlin Sci NumSimul , 9,267 (2008).

D. H. Shou, J.H. He. Application of parameter-expanding method to strongly nonlinear oscillators. Int. J Nonlin Sci Num Simul ,8, 121 (2007).

H. M. Liu. Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt–Poincare method. Chaos, Solitons & Fractals, 23, 2, 577 (2005).

J. H. He. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput , 151, 287 (2004).

J. H. He. Homotopy perturbation method for solving boundary value problems. Phys Lett. A , 350, 87 (2006).

J. H. He. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J Nonlin Sci Num Simul , 6, 207 (2005).

J. H. He. Limit cycle and bifurcation of nonlinear problems. Chaos, Solitons & Fractals , 26, 827 (2005).

X. C. Cai, W. Y. Wu, M.S. Li. Approximate period solution for a kind of nonlinear oscillator by He’ s perturbation method. Int. J Nonlin Sci Num Simul , 7, 109 (2006).

P. D. Ariel, T. Hayat, S. Asghar. Homotopy perturbation method and axisymmetric flow over a stretching sheet. Int. J Nonlin Sci Num Simul , 7, 399 (2006).

D. D. Ganji, A. Sadighi. Application of He’ s homotopy-perturbation method to nonlinear coupled systems of reaction– diffusion equations. Int. J Nonlin SciNum Simul , 7, 411 (2006).

L. Cveticanin. Homotopy-perturbation method for pure nonlinear differential equation. Chaos, Solitons & Fractals , 30, 1221 (2006).

H. Ozer. Application of the variational iteration method to the boundary value problems with jump discontinuities arising in solid mechanics. Int. J Nonlin Sci. Num Simul , 8, 513 (2007).

S. S. Ganji, D.D. Ganji, S. Karimpour. He’s energy balance and He’s variational methods for nonlinear oscillations in engineering. Int. J Mod Phys B, 23, 3, 461 (2009).

J. H. He. Preliminary report on the energy balance for nonlinear oscillations. Mech Res Commun , 29, 107 (2002).

J. H. He. Variational approach for nonlinear oscillators. Chaos, Solitons & Fractals , 34, 430 (2007).

S. M. Varedi, D. D. Ganji. Rajabi M. Analytical approaches for system of nonlinear equations arising in melting of a finite slab. Int. J Mod Phys B , 23, 209 (2009).

J. H. He . An improved amplitude–frequency formulation for nonlinear oscillators. Int. J Nonlin Sci Num Simul , 9, 211 (2008).

J. H. He. Some asymptotic methods for strongly nonlinear equations. Int. J Mod Phys B , 20, 1141 (2006).

J. H. He. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J Mod Phys B, 22, 21, 3487 (2008).


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize