Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2007, Article ID 10120, 11 pages
http://dx.doi.org/10.1155/2007/10120
Research Article

Variational Problems with Moving Boundaries Using Decomposition Method

Department of Mathematics, Faculty of Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran

Received 12 December 2006; Revised 23 April 2007; Accepted 25 July 2007

Academic Editor: T. Zolezzi

Copyright © 2007 Reza Memarbashi. 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. U. Brechtken-Manderschied, Introduction to the Calculus of Variations, Translated from the German by P. G. Engstrom, Chapman and Hall Mathematics Series, Chapman & Hall, London, UK, 1991. View at Zentralblatt MATH · View at MathSciNet
  2. H. Sagan, “Introduction to the Calculus of Variations,” Dover, New York, NY, USA, 1992. View at MathSciNet
  3. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, vol. 60 of Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994. View at Zentralblatt MATH · View at MathSciNet
  4. G. Adomian, “A review of the decompositiom method in applied methematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501–544, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. Cherruault, “Convergence of Adomian's method,” Mathematical and Computer Modelling, vol. 14, pp. 83–86, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. Y. Cherruault, G. Saccomandi, and B. Some, “New results for convergence of Adomian's method applied to integral equations,” Mathematical and Computer Modelling, vol. 16, no. 2, pp. 85–93, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Dehghan, “The use of adomian decomposition method for solving the one-dimensional parabolic equation with non-local boundary specifications,” International Journal of Computer Mathematics, vol. 81, no. 1, pp. 25–34, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Dehghan, “Application of the Adomian decomposition method for two-dimensional parabolic equation subject to nonstandard boundary specifications,” Applied Mathematics and Computation, vol. 157, no. 2, pp. 549–560, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Dehghan and M. Tatari, “The use of Adomian decomposition method for solving problems in calculus of variations,” Mathematical Problems in Engineering, vol. 2006, Article ID 65379, 12 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. M. A. El-Sayed and M. Gaber, “The Adomian decomposition method for solving partial differential equations of fractal order in finite domains,” Physics Letters A, vol. 359, no. 3, pp. 175–182, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  11. I. Hashim, M. S. M. Noorani, and M. R. Said Al-Hadidi, “Solving the generalized Burgers-Huxley equation using the Adomian decomposition method,” Mathematical and Computer Modelling, vol. 43, no. 11-12, pp. 1404–1411, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. D. Kaya and S. M. El-Sayed, “Numerical soliton-like solutions of the potential Kadomtsev-Petviashvili equation by the decomposition method,” Physics Letters A, vol. 320, no. 2-3, pp. 192–199, 2003. View at Zentralblatt MATH · View at MathSciNet
  13. D. Lesnic, “The decomposition method for Cauchy advection-diffusion problems,” Computers & Mathematics with Applications, vol. 49, no. 4, pp. 525–537, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. Lesnic, “The decomposition method for linear, one-dimensional, time-dependent partial differential equations,” International Journal of Mathematics and Mathematical Sciences, vol. 2006, Article ID 42389, 29 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. R. Memarbashi, “Numerical solution of the Laplace equation in annulus by Adomian decomposition method,” to appear in Chaos, Solitons and Fractals (2006), doi:10.1016/j.chaos.2006.06.016. View at Publisher · View at Google Scholar · View at MathSciNet
  16. S. Momani and Z. Odibat, “Analytical approach to linear fractional partial differential equations arising in fluid mechanics,” Physics Letters A, vol. 355, no. 4-5, pp. 271–279, 2006. View at Publisher · View at Google Scholar
  17. S. Saha Ray and R. K. Bera, “Analytical solution of a fractional diffusion equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 174, no. 1, pp. 329–336, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. S. Saha Ray and R. K. Bera, “Approximate solution of a nonlinear fractional diffusion equation by Adomian decomposition method,” Applied Mathematics and Computation, vol. 167, pp. 561–571, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  19. 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
  20. M. Tatari, M. Dehghan, and M. Razzaghi, “Application of the Adomian decomposition method for the Fokker-Planck equation,” Mathematical and Computer Modelling, vol. 45, no. 5-6, pp. 639–650, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  21. A.-M. Wazwaz, “A reliable modification of Adomian decomposition method,” Applied Mathematics and Computation, vol. 102, no. 1, pp. 77–86, 1999. View at Zentralblatt MATH · View at MathSciNet
  22. 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 · View at MathSciNet
  23. 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 Zentralblatt MATH · View at MathSciNet
  24. A.-M. Wazwaz, “A comparison between the variational iteration method and Adomian decomposition method,” Journal of Computational and Applied Mathematics, vol. 207, no. 1, pp. 129–136, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet