Table of Contents
International Journal of Partial Differential Equations
Volume 2014 (2014), Article ID 607259, 6 pages
http://dx.doi.org/10.1155/2014/607259
Research Article

Improvement of the Modified Decomposition Method for Handling Third-Order Singular Nonlinear Partial Differential Equations with Applications in Physics

Department of Mechanical Engineering, Salmas Branch, Islamic Azad University, Salmas, Iran

Received 4 June 2014; Accepted 9 October 2014; Published 6 November 2014

Academic Editor: Athanasios N. Yannacopoulos

Copyright © 2014 Nemat Dalir. 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. W. F. Ames, Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, NY, USA, 1972. View at MathSciNet
  2. L. Debnath, Nonlinear Partial Differential Equations for Scientists and Engineers, Birkhäuser, Berlin , Germany, 1997. View at MathSciNet
  3. A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman and Hall, New York, NY, USA, 2003. View at MathSciNet
  4. F. C. Cirstea, Nonlinear methods in the study of singular partial differential equations [Ph.D. thesis], Victoria University of Technology, Victoria, Australia, 2004.
  5. A. M. Wazwaz, Partial Differential Equations and Solitary Wave Theory, Springer, New York, NY, USA, 2009. View at MathSciNet
  6. A. M. Wazwaz, “Construction of soliton solutions and periodic solutions of the Boussinesq equation by the modified decomposition method,” Chaos, Solitons and Fractals, vol. 12, no. 8, pp. 1549–1556, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A.-M. Wazwaz, “The modified decomposition method and Padé approximants for a boundary layer equation in unbounded domain,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 737–744, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. A.-M. Wazwaz, “The modified decomposition method for analytic treatment of differential equations,” Applied Mathematics and Computation, vol. 173, no. 1, pp. 165–176, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. S. A. Kechil and I. Hashim, “Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method,” Physics Letters A: General, Atomic and Solid State Physics, vol. 363, no. 1-2, pp. 110–114, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. Y. Q. Hasan and L. M. Zhu, “Modified adomian decomposition method for singular initial value problems in the second order ordinary differential equations,” Surveys in Mathematics and its Applications, vol. 3, pp. 183–193, 2008. View at Google Scholar · View at MathSciNet
  11. A.-M. Wazwaz, “The combined Laplace transform-Adomian decomposition method for handling nonlinear Volterra integro-differential equations,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1304–1309, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A.-M. Wazwaz and M. S. Mehanna, “The combined Laplace-Adomian method for handling singular integral equation of heat transfer,” International Journal of Nonlinear Science, vol. 10, no. 2, pp. 248–252, 2010. View at Google Scholar · View at MathSciNet
  13. T. R. Sivakumar and S. Baiju, “Shooting type Laplace-Adomian decomposition algorithm for nonlinear differential equations with boundary conditions at infinity,” Applied Mathematics Letters, vol. 24, no. 10, pp. 1702–1708, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. A. Noghrehabadi, M. Ghalambaz, and A. Ghanbarzadeh, “A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique,” Computers & Mathematics with Applications, vol. 64, no. 9, pp. 2806–2815, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J.-S. Duan and R. Rach, “Higher-order numeric Wazwaz-El-Sayed modified Adomian decomposition algorithms,” Computers & Mathematics with Applications, vol. 63, no. 11, pp. 1557–1568, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. Y. Lin, Y. Liu, and Z. Li, “Symbolic computation of analytic approximate solutions for nonlinear fractional differential equations,” Computer Physics Communications, vol. 184, no. 1, pp. 130–141, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. M. M. Kermani and M. Dehestani, “Solving the nonlinear equations for one-dimensional nano-sized model including Rydberg and Varshni potentials and Casimir force using the decomposition method,” Applied Mathematical Modelling, vol. 37, no. 5, pp. 3399–3406, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. L. Song and W. Wang, “A new improved Adomian decomposition method and its application to fractional differential equations,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 1590–1598, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus