About this Journal Submit a Manuscript Table of Contents
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 943232, 4 pages
http://dx.doi.org/10.1155/2013/943232
Research Article

A Comparison between Adomian’s Polynomials and He’s Polynomials for Nonlinear Functional Equations

1Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
2International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received 20 March 2013; Revised 11 May 2013; Accepted 2 June 2013

Academic Editor: Mufid Abudiab

Copyright © 2013 Hossein Jafari 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. T. Öziş and A. Yıldırım, “Comparison between Adomian's method and He's homotopy perturbation method,” Computers & Mathematics with Applications, vol. 56, no. 5, pp. 1216–1224, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. J.-L. Li, “Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 168–173, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Ghorbani, “Beyond Adomian polynomials: he polynomials,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1486–1492, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. N. Bellomo and R. A. Monaco, “Comparison between Adomian’s decomposition methods and perturbation techniques for onlinear random differential equations,” Journal of Mathematical Analysis and Applications, vol. 110, pp. 495–502, 1985.
  5. R. Rach, “On the Adomian (decomposition) method and comparisons with Picard's method,” Journal of Mathematical Analysis and Applications, vol. 128, no. 2, pp. 480–483, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Sadat, “Equivalence between the Adomian decomposition method and a perturbation method,” Physica Scripta, vol. 82, no. 4, Article ID 045004, 2010. View at Publisher · View at Google Scholar
  7. S. Liang and D. J. Jeffrey, “Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 12, pp. 4057–4064, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Sajid and T. Hayat, “Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations,” Nonlinear Analysis. Real World Applications, vol. 9, no. 5, pp. 2296–2301, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. Adomian, Y. Cherruault, and K. Abbaoui, “A nonperturbative analytical solution of immune response with time-delays and possible generalization,” Mathematical and Computer Modelling, vol. 24, no. 10, pp. 89–96, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. K. Abbaoui and Y. Cherruault, “Convergence of Adomian's method applied to differential equations,” Computers & Mathematics with Applications, vol. 28, no. 5, pp. 103–109, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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 · View at MathSciNet
  13. 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 MathSciNet
  14. S. J. Liao, “An approximate solution technique not depending on small parameters: a special example,” International Journal of Non-Linear Mechanics, vol. 30, no. 3, pp. 371–380, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, NY, USA, 1981. View at MathSciNet
  16. H. Jafari and S. Momani, “Solving fractional diffusion and wave equations by modified homotopy perturbation method,” Physics Letters A, vol. 370, no. 5-6, pp. 388–396, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H. Jafari, M. Alipour, and H. Tajadodi, “Convergence of homotopy perturbation method for solving integral equations,” Thai Journal of Mathematics, vol. 8, no. 3, pp. 511–520, 2010. View at Zentralblatt MATH · View at MathSciNet
  18. 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 · View at MathSciNet
  19. Y. Zhu, Q. Chang, and S. Wu, “A new algorithm for calculating Adomian polynomials,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 402–416, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. A.-M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Springer, 1st edition, 2011.