About this Journal Submit a Manuscript Table of Contents 
International Journal of Differential Equations
Volume 2011 (2011), Article ID 649748, 7 pages
doi:10.1155/2011/649748
Research Article

Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity

Najeeb Alam Khan,1 Muhammad Jamil,2,3 and Asmat Ara1

1Department of Mathematics, University of Karachi, Karachi 75270, Pakistan
2Abdul Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
3Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan

Received 28 May 2011; Accepted 14 June 2011

Academic Editor: Leonid Berezansky

Copyright © 2011 Najeeb Alam Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Rafei, D. D. Ganji, H. Daniali, and H. Pashaei, “The variational iteration method for nonlinear oscillators with discontinuities,” Journal of Sound and Vibration, vol. 305, no. 4-5, pp. 614–620, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  2. L.-N. Zhang and J.-H. He, “Resonance in Sirospun yarn spinning using a variational iteration method,” Computers & Mathematics with Applications, vol. 54, no. 7-8, pp. 1064–1066, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. T. Öziş and A. Yıldırım, “A study of nonlinear oscillators with u1/3 force by He's variational iteration method,” Journal of Sound and Vibration, vol. 306, no. 1-2, pp. 372–376, 2007. View at Publisher · View at Google Scholar
  4. A. Beléndez, C. Pascual, M. Ortuño, T. Beléndez, and S. Gallego, “Application of a modified He's homotopy perturbation method to obtain higher-order approximations to a nonlinear oscillator with discontinuities,” Nonlinear Analysis: Real World Applications, vol. 10, no. 2, pp. 601–610, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Beléndez, C. Pascual, S. Gallego, M. Ortuño, and C. Neipp, “Application of a modified He's homotopy perturbation method to obtain higher-order approximations of an x1/3 force nonlinear oscillator,” Physics Letters A, vol. 371, no. 5-6, pp. 421–426, 2007. View at Publisher · View at Google Scholar
  6. J.-H. He, “The homotopy perturbation method nonlinear oscillators with discontinuities,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 287–292, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. Beléndez, A. Hernández, T. Beléndez, E. Fernández, M. L. Álvarez, and C. Neipp, “Application of He's homotopy perturbation method to the Duffin-harmonic oscillator,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 1, pp. 79–88, 2007.
  8. H.-M. Liu, “Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt-Poincare method,” Chaos, Solitons and Fractals, vol. 23, no. 2, pp. 577–579, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. J.-H. He, “Variational approach for nonlinear oscillators,” Chaos, Solitons and Fractals, vol. 34, no. 5, pp. 1430–1439, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. D.-H. Shou, “Variational approach to the nonlinear oscillator of a mass attached to a stretched wire,” Physica Scripta, vol. 77, no. 4, Article ID 045006, 2008. View at Publisher · View at Google Scholar
  11. F. Ö. Zengin, M. O. Kaya, and S. A. Demirbağ, “Application of parameter-expansion method to nonlinear oscillators with discontinuities,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 3, pp. 267–270, 2008.
  12. J.-H. He, “Max-min approach to nonlinear oscillators,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 9, no. 2, pp. 207–210, 2008.
  13. Z. Guo and A. Y. T. Leung, “The iterative homotopy harmonic balance method for conservative Helmholtz-Duffing oscillators,” Applied Mathematics and Computation, vol. 215, no. 9, pp. 3163–3169, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. J.-H. He, “Hamiltonian approach to nonlinear oscillators,” Physics Letters. A, vol. 374, no. 23, pp. 2312–2314, 2010. View at Publisher · View at Google Scholar
  15. Z.-F. Ren and J.-H. He, “A simple approach to nonlinear oscillators,” Physics Letters. A, vol. 373, no. 41, pp. 3749–3752, 2009. View at Publisher · View at Google Scholar