About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 424510, 10 pages
http://dx.doi.org/10.1155/2013/424510
Research Article

On the Convergence of the Homotopy Analysis Method for Inner-Resonance of Tangent Nonlinear Cushioning Packaging System with Critical Components

1School of Mathematical Science, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, Gomal University, 29050 Dera Ismail Khan, Pakistan

Received 13 January 2013; Accepted 12 August 2013

Academic Editor: Douglas Anderson

Copyright © 2013 Mohammad Ghoreishi 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. J. Wang, Y. Khan, R. H. Yang, L. X. Lu, Z. W. Wang, and N. Faraz, “A mathematical modelling of inner-resonance of tangent nonlinear cushioning packaging system with critical components,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 2573–2576, 2011.
  2. J. Wang, R. H. Yang, and Z. B. Li, “Inner-resonance in a cushioning packaging system,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 11, pp. 351–352, 2010.
  3. J. Wang, Z. Wang, L. X. Lu, Y. Zhu, and Y. G. Wang, “Three-dimensional shock spectrum of critical component for nonlinear packaging system,” Shock and Vibration, vol. 18, no. 3, pp. 437–445, 2011.
  4. J. Wang, J. H. Jiang, L. X. Lua, and Z. W. Wang, “Dropping damage evaluation for a tangent nonlinear system with a critical component,” Computers and Mathematics with Applications, vol. 61, pp. 1979–1982, 2011.
  5. J. Wang and Z. Wang, “Damage boundary surface of a tangent nonlinear packaging system with critical components,” Journal of Vibration and Shock, vol. 27, no. 2, pp. 166–167, 2008.
  6. M. M. Rashidi, S. A. M. pour, and S. Abbasbandy, “Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, pp. 1874–1889, 2011.
  7. A. K. Alomari, M. S. M. Noorani, R. Nazar, and C. P. Li, “Homotopy analysis method for solving fractional Lorenz system,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, pp. 1864–1872, 2010.
  8. A. S. Bataineh, M. S. M. Noorani, and I. Hashim, “Modified homotopy analysis method for solving systems of second-order BVPs,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 430–442, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Ghoreishi, A. I. B. Md. Ismail, and A. Rashid, “Solution of a strongly coupled reaction-diffusion system by the homotopy analysis method,” Bulletin of the Belgian Mathematical Society, vol. 18, no. 3, pp. 471–481, 2011. View at Zentralblatt MATH · View at MathSciNet
  10. A. K. Alomari, M. S. M. Noorani, and R. Nazar, “Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrodinger-KdV equation,” Journal of Applied Mathematics and Computing, vol. 31, no. 1-2, pp. 1–12, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. K. Alomari, M. S. M. Noorani, and R. Nazar, “The homotopy analysis method for the exact solutions of the K(2,2), Burgers and coupled Burgers equations,” Applied Mathematical Sciences, vol. 2, no. 40, pp. 1963–1977, 2008. View at MathSciNet
  12. M. Ghoreishi, A. I. B. Md. Ismail, and A. K. Alomari, “Application of the homotopy analysis method for solving a model for HIV infection of CD4+ T-cells,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 3007–3015, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. M. Ghoreishi, A. I. B. Md. Ismail, and A. K. Alomari, “Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth-order integro-differential equation,” Mathematical Methods in the Applied Sciences, vol. 34, no. 15, pp. 1833–1842, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Ghoreishi, A. I. B. Md. Ismail, A. K. Alomari, and A. S. Bataineh, “The comparison between homotopy analysis method and optimal homotopy asymptotic method for nonlinear age-structured population models,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 3, pp. 1163–1177, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. Ghoreishi, A. I. B. Md. Ismail, and A. Rashid, “The solution of coupled modified KdV system by the homotopy analysis method,” TWMS Journal of Pure and Applied Mathematics, vol. 3, no. 1, pp. 122–134, 2012. View at Zentralblatt MATH · View at MathSciNet
  16. K. Hosseini, B. Daneshian, N. Amanifard, and R. Ansari, “Homotopy analysis method for a fin with temperature dependent internal heat generation and thermal conductivity,” International Journal of Nonlinear Science, vol. 14, no. 2, pp. 201–210, 2012. View at Zentralblatt MATH · View at MathSciNet
  17. S. J. Liao, Beyond Perturbation: Introduction to the homotopy Analysis Method, Chapman and Hall/CRC Press, Boca Raton, Fla, USA, 2003.
  18. S. J. Liao, “Comparison between the homotopy analysis method and homotopy perturbation method,” Applied Mathematics and Computation, vol. 169, no. 2, pp. 1186–1194, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. S. J. Liao, “An optimal homotopy-analysis approach for strongly nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2003–2016, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Z. Niu and C. Wang, “A one-step optimal homotopy analysis method for nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2026–2036, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet