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International Journal of Differential Equations
Volume 2018, Article ID 8725014, 11 pages
https://doi.org/10.1155/2018/8725014
Research Article

Application of Optimal Homotopy Asymptotic Method to Some Well-Known Linear and Nonlinear Two-Point Boundary Value Problems

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, University of Peshawar, Pakistan

Correspondence should be addressed to Muhammad Asim Khan; moc.liamg@gfa.misa

Received 20 May 2018; Accepted 21 October 2018; Published 3 December 2018

Guest Editor: Dongfang Li

Copyright © 2018 Muhammad Asim 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. C. Chun and R. Sakthivel, “Homotopy perturbation technique for solving two-point boundary value problems---comparison with other methods,” Computer Physics Communications, vol. 181, no. 6, pp. 1021–1024, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  2. H. B. Keller, Numerical Methods for Two-Point Boundary-Value Problems, Courier Dover Publications, 2018.
  3. G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. Tatari and M. Dehghan, “The use of the Adomian decomposition method for solving multipoint boundary value problems,” Physica Scripta, vol. 73, no. 6, pp. 672–676, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Inc and D. J. Evans, “The decomposition method for solving of a class of singular two-point boundary value problems,” International Journal of Computer Mathematics, vol. 80, no. 7, pp. 869–882, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. B. Jang, “Exact solutions to one dimensional non-homogeneous parabolic problems by the homogeneous Adomian decomposition method,” Applied Mathematics and Computation, vol. 186, no. 2, pp. 969–979, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. M. Wazwaz, “A reliable algorithm for obtaining positive solutions for nonlinear boundary value problems,” Computers & Mathematics with Applications, vol. 41, pp. 1237–1244, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  8. B. Jang, “Two-point boundary value problems by the extended Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 219, no. 1, pp. 253–262, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. H. Yaghoobi and M. Torabi, “The application of differential transformation method to nonlinear equations arising in heat transfer,” International Communications in Heat and Mass Transfer, vol. 38, no. 6, pp. 815–820, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. D. D. Ganji, G. A. Afrouzi, and R. A. Talarposhti, “Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations,” Physics Letters Section A: General, Atomic and Solid State Physics, vol. 368, no. 6, pp. 450–457, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. A. H. Nayfeh, Introduction to Perturbation Techniques, John Wiley & Sons, New York, NY, USA, 1981. View at MathSciNet
  12. A. H. Nayfeh, Perturbation Methods, John Wiley & Sons, New York, NY, USA, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. Rafiq, M. Y. Malik, and T. Abbasi, “Solution of nonlinear pull-in behavior in electrostatic micro-actuators by using He's homotopy perturbation method,” Computers & Mathematics with Applications. An International Journal, vol. 59, no. 8, pp. 2723–2733, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. V. Marinca and N. Herişanu, “Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer,” International Communications in Heat and Mass Transfer, vol. 35, no. 6, pp. 710–715, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Javidi and A. Golbabai, “A new domain decomposition algorithm for generalized Burger's-Huxley equation based on Chebyshev polynomials and preconditioning,” Chaos, Solitons & Fractals, vol. 39, no. 2, pp. 849–857, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Wang, D. Li, C. Zhang, and Y. Tang, “Long time behavior of solutions of gKdV equations,” Journal of Mathematical Analysis and Applications, vol. 390, no. 1, pp. 136–150, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Acosta, P. García, H. Leiva, and A. Merlitti, “Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling,” International Journal of Differential Equations, vol. 2017, Article ID 1946304, 7 pages, 2017. View at Google Scholar · View at Scopus
  18. D. Li and J. Zhang, “Efficient implementation to numerically solve the nonlinear time fractional parabolic problems on unbounded spatial domain,” Journal of Computational Physics, vol. 322, pp. 415–428, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. D. Li, J. Zhang, and Z. Zhang, “Unconditionally optimal error estimates of a linearized galerkin method for nonlinear time fractional reaction–subdiffusion equations,” Journal of Scientific Computing, pp. 1–19, 2018. View at Google Scholar · View at Scopus
  20. A. J. Khattak, “A computational meshless method for the generalized Burger's-Huxley equation,” Applied Mathematical Modelling, vol. 33, no. 9, pp. 3718–3729, 2009. View at Publisher · View at Google Scholar · View at Scopus