Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 586454, 18 pages
http://dx.doi.org/10.1155/2012/586454
Research Article

A New Efficient Method for Nonlinear Fisher-Type Equations

Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 41335-1914, Rasht, Iran

Received 16 December 2011; Revised 31 March 2012; Accepted 9 April 2012

Academic Editor: B. V. Rathish Kumar

Copyright © 2012 Hossein Aminikhah 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.-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
  2. 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
  3. J. H. He, “New interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. J.-H. He, “Recent development of the homotopy perturbation method,” Topological Methods in Nonlinear Analysis, vol. 31, no. 2, pp. 205–209, 2008. View at Google Scholar · View at Zentralblatt MATH
  5. 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
  6. X. Y. Wang, “Exact and explicit solitary wave solutions for the generalised Fisher equation,” Physics Letters A, vol. 131, no. 4-5, pp. 277–279, 1988. View at Publisher · View at Google Scholar
  7. 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 Publisher · View at Google Scholar · View at Scopus
  8. J. H. He, “Limit cycle and bifurcation of nonlinear problems,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 827–833, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Rajabi, D. D. Ganji, and H. Taherian, “Application of homotopy perturbation method in nonlinear heat conduction and convection equations,” Physics Letters A, vol. 360, no. 4-5, pp. 570–573, 2007. View at Publisher · View at Google Scholar
  10. D. D. Ganji and A. Sadighi, “Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 24–34, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. D. D. Ganji, “The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer,” Physics Letters A, vol. 355, no. 4-5, pp. 337–341, 2006. View at Publisher · View at Google Scholar
  12. S. Abbasbandy, “A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 257–260, 2007. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Biazar and H. Ghazvini, “Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method,” Physics Letters. A, vol. 366, no. 1-2, pp. 79–84, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. S. Abbasbandy, “Numerical solutions of the integral equations: homotopy perturbation method and Adomian's decomposition method,” Applied Mathematics and Computation, vol. 173, no. 1, pp. 493–500, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. 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
  16. Q. Wang, “Homotopy perturbation method for fractional KdV-Burgers equation,” Chaos, Solitons and Fractals, vol. 35, no. 5, pp. 843–850, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. E. Yusufoǧlu, “Homotopy perturbation method for solving a nonlinear system of second order boundary value problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 3, pp. 353–358, 2007. View at Google Scholar · View at Scopus
  18. Y. Khan, N. Faraz, A. Yildirim, and Q. Wu, “A series solution of the long porous slider,” Tribology Transactions, vol. 54, no. 2, pp. 187–191, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Khan, Q. Wu, N. Faraz, A. Yildirim, and S. T. Mohyud Din, “Three-dimensional flow arising in the long porous slider: an analytic solution,” Zeitschrift für Naturforschung, vol. 66, no. 8-9, pp. 507–511, 2011. View at Google Scholar
  20. H. Moosaei, M. Mirzazadeh, and A. Yildirim, “Exact solutions to the perturbed nonlinear Schrodingers equation with Kerr law nonlinearity by using the first integral method,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 3, pp. 332–339, 2011. View at Google Scholar
  21. T. Kawahara and M. Tanaka, “Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation,” Physics Letters A, vol. 97, no. 8, pp. 311–314, 1983. View at Publisher · View at Google Scholar
  22. J. A. Sherratt, “On the transition from initial data to travelling waves in the Fisher-KPP equation,” Dynamics and Stability of Systems, vol. 13, no. 2, pp. 167–174, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. P. K. Brazhnik and J. J. Tyson, “On traveling wave solutions of Fisher's equation in two spatial dimensions,” SIAM Journal on Applied Mathematics, vol. 60, no. 2, pp. 371–391, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  24. W. Malfliet, “Solitary wave solutions of nonlinear wave equations,” American Journal of Physics, vol. 60, no. 7, pp. 650–654, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. M. J. Ablowitz and A. Zeppetella, “Explicit solutions of Fisher's equation for a special wave speed,” Bulletin of Mathematical Biology, vol. 41, no. 6, pp. 835–840, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. D. S. Jones and B. D. Sleeman, Differential Equations and Mathematical Biology, Chapman & Hall/CRC, New York, NY, USA, 2003.
  27. A.-M. Wazwaz and A. Gorguis, “An analytic study of Fisher's equation by using Adomian decomposition method,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 609–620, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. H. Aminikhah and M. Hemmatnezhad, “An efficient method for quadratic Riccati differential equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 4, pp. 835–839, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. D. Ağırseven and T. Öziş, “An analytical study for Fisher type equations by using homotopy perturbation method,” Computers & Mathematics with Applications, vol. 60, no. 3, pp. 602–609, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH