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Journal of Applied Mathematics
Volume 2012, Article ID 490342, 14 pages
http://dx.doi.org/10.1155/2012/490342
Research Article

Rational Homotopy Perturbation Method

Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, Mexico

Received 28 June 2012; Accepted 16 August 2012

Academic Editor: Turgut Öziş

Copyright © 2012 Héctor Vázquez-Leal. 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. Biazar and H. Aminikhah, “Study of convergence of homotopy perturbation method for systems of partial differential equations,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2221–2230, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. J. Biazar and H. Ghazvini, “Convergence of the homotopy perturbation method for partial differential equations,” Nonlinear Analysis, vol. 10, no. 5, pp. 2633–2640, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. A. Barari, M. Omidvar, A. R. Ghotbi, and D. D. Ganji, “Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations,” Acta Applicandae Mathematicae, vol. 104, no. 2, pp. 161–171, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. H. Vazquez-Leal, R. Castaneda-Sheissa, U. Filobello-Nino, A. Sarmiento-Reyes, and J. Sanchez-Orea, “High accurate simple approximation of normal distribution related integrals,” Mathematical Problems in Engineering, vol. 2012, Article ID 124029, 22 pages, 2012. View at Publisher · View at Google Scholar
  5. H. Vazquez-Leal and U. Filobello-Nino, “Modified hpms inspired by homotopy continuation methods,” Mathematical Problems in Engineering, vol. 2012, Article ID 309123, 19 pages, 2012. View at Publisher · View at Google Scholar
  6. J.-H. He, “Comparison of homotopy perturbation method and homotopy analysis method,” Applied Mathematics and Computation, vol. 156, no. 2, pp. 527–539, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. J.-H. He, “An elementary introduction to the homotopy perturbation method,” Computers & Mathematics with Applications, vol. 57, no. 3, pp. 410–412, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. 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
  10. J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar
  12. J.-H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005. View at Google Scholar
  13. J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. Y. Khan, H. Vazquez-Leal, and Q. Wu, “An efficient iterated method for mathematical biology model,” Neural Computing and Applications. In press. View at Publisher · View at Google Scholar
  15. Y. Khan, Q. Wu, N. Faraz, A. Yildirim, and M. Madani, “A new fractional analytical approach via a modified riemannliouville derivative,” Applied Mathematics Letters, vol. 25, no. 10, pp. 1340–1346, 2012. View at Google Scholar
  16. N. Faraz and Y. Khan, “Analytical solution of electrically conducted rotating flow of a second grade fluid over a shrinking surface,” Ain Shams Engineering Journal, vol. 2, no. 34, pp. 221–226, 201. View at Google Scholar
  17. Y. Khan, Q. Wu, N. Faraz, and A. Yildirim, “The effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet,” Computers & Mathematics with Applications, vol. 61, no. 11, pp. 3391–3399, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. Y. Khan, H. Vázquez-Leal, and L. Hernandez-Martínez, “Removal of noise oscillation term appearingin the nonlinear equation solution,” Journal of Applied Mathematics, vol. 2012, Article ID 387365, 9 pages, 2012. View at Publisher · View at Google Scholar
  19. H. Aminikhah, “The combined laplace transform and new homotopy perturbation methods for stiff systems of odes,” Applied Mathematical Modelling, vol. 36, no. 8, pp. 3638–3644, 2012. View at Google Scholar
  20. F. I. Compean, D. Olvera, F. J. Campa, L. N. Lopez de Lacalle, A. Elias-Zuniga, and C. A. Rodriguez, “Characterization and stability analysis of a multivariable milling tool by the enhanced multistage homotopy perturbation method,” International Journal of Machine Tools and Manufacture, vol. 57, pp. 27–33, 2012. View at Google Scholar
  21. J. Biazar and B. Ghanbari, “The homotopy perturbation method for solving neutral functional-differential equations with proportional delays,” Journal of King Saud University—Science, vol. 24, no. 1, pp. 33–37, 2012. View at Google Scholar
  22. A. M. A. El-Sayed, A. Elsaid, I. L. El-Kalla, and D. Hammad, “A homotopy perturbation technique for solving partial differential equations of fractional order in finite domains,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8329–8340, 2012. View at Google Scholar
  23. S. T. Mohyud-Din, A. Yildirim, and Mustafa Inc, “Coupling of homotopy perturbation and modified lindstedtpoincar methods for traveling wave solutions of the nonlinear kleingordon equation,” Journal of King Saud University—Science, vol. 24, no. 2, pp. 187–191, 2012. View at Google Scholar
  24. J. Biazar and M. Eslami, “A new homotopy perturbation method for solving systems of partial differential equations,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 225–234, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. U. Filobello-Nino, H. Vazquez-Leal, Y. Khan et al., “Hpm applied to solve nonlinear circuits: a study case,” Applied Mathematical Sciences, vol. 6, no. 85–88, pp. 4331–4344, 2012. View at Google Scholar
  26. U. Filobello-Nino, H. Vazquez-Leal, R. Castaneda-Sheissa et al., “An approximate solution of blasius equation by using hpm method,” Asian Journal of Mathematics and Statistics, vol. 5, pp. 50–59, 2012. View at Google Scholar
  27. Y.-G. Wang, W.-H. Lin, and N. Liu, “A homotopy perturbation-based method for large deflection of a cantilever beam under a terminal follower force,” International Journal for Computational Methods in Engineering Science and Mechanics, vol. 13, pp. 197–201, 2012. View at Google Scholar
  28. M. Madani, M. Fathizadeh, Y. Khan, and A. Yildirim, “On the coupling of the homotopy perturbation method and Laplace transformation,” Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 1937–1945, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. S. H. Behiry, H. Hashish, I. L. El-Kalla, and A. Elsaid, “A new algorithm for the decomposition solution of nonlinear differential equations,” Computers & Mathematics with Applications, vol. 54, no. 4, pp. 459–466, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. S. Momani, G. H. Erjaee, and M. H. Alnasr, “The modified homotopy perturbation method for solving strongly nonlinear oscillators,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2209–2220, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  31. H. Bararnia, E. Ghasemi, S. Soleimani, R. Abdoul Ghotbi, and D. D. Ganji, “Solution of the falkner-skan wedge flow by hpm-pade’ method,” Advances in Engineering Software, vol. 43, no. 1, pp. 44–52, 2012. View at Google Scholar