Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 704184, 6 pages
http://dx.doi.org/10.5402/2012/704184
Research Article

A Comparative Study on the Stability of Laplace-Adomian Algorithm and Numerical Methods in Generalized Pantograph Equations

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Department of Mathematics, Sinnar University, Singa 107, Sudan

Received 31 May 2012; Accepted 29 July 2012

Academic Editors: T. Allahviranloo and K. T. Miura

Copyright © 2012 Sabir Widatalla. 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. G. Aiello, H. I. Freedman, and J. Wu, “Analysis of a model representing stage-structured population growth with state-dependent time delay,” SIAM Journal on Applied Mathematics, vol. 52, no. 3, pp. 855–869, 1992. View at Publisher · View at Google Scholar
  2. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic, New York, NY, USA, 1993.
  3. P. Brunovský, A. Erdélyi, and H.-O. Walther, “On a model of a currency exchange rate—local stability and periodic solutions,” Journal of Dynamics and Differential Equations, vol. 16, no. 2, pp. 393–432, 2004. View at Publisher · View at Google Scholar
  4. R. V. Culshaw and S. Ruan, “A delay-differential equation model of HIV infection of CD4+ T-cells,” Mathematical Biosciences, vol. 165, no. 1, pp. 27–39, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. A. De Gaetano and O. Arino, “Mathematical modelling of the intravenous glucose tolerance test,” Journal of Mathematical Biology, vol. 40, no. 2, pp. 136–168, 2000. View at Google Scholar · View at Scopus
  6. H. O. Walther, “On a model for soft landing with state-dependent delay,” Journal of Dynamics and Differential Equations, vol. 19, no. 3, pp. 593–622, 2007. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Iserles and Y. K. Liu, “On pantograph integro-differential equations,” Journal of Integral Equations and Applications, vol. 6, no. 2, pp. 213–237, 1994. View at Publisher · View at Google Scholar
  8. M. Gülsu and M. Sezer, “A taylor collocation method for solving high-order linear pantograph equations with linear functional argument,” Numerical Methods for Partial Differential Equations, vol. 27, no. 6, pp. 1628–1638, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. O. R. Işik, Z. Güney, and M. Sezer, “Bernstein series solutions of pantograph equations using polynomial interpolation,” Journal of Difference Equations and Applications, vol. 18, no. 3, pp. 357–374, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. A. El-Safty and S. M. Abo-Hasha, “On the application of spline functions to initial value problems with retarded argument,” International Journal of Computer Mathematics, vol. 32, pp. 173–179, 1990. View at Google Scholar
  11. M. Shadia, Numerical solution of delay differential and neutral differential equations using spline methods [Ph.D. thesis], Assuit University, Assuit, Egypt, 1992.
  12. M. Z. Liu and D. Li, “Properties of analytic solution and numerical solution of multi-pantograph equation,” Applied Mathematics and Computation, vol. 155, no. 3, pp. 853–871, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. D. J. Evans and K. R. Raslan, “The Adomian decomposition method for solving delay differential equation,” International Journal of Computer Mathematics, vol. 82, no. 1, pp. 49–54, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. S. A. Khuri, “A Laplace decomposition algorithm applied to a class of nonlinear differential equations,” Journal of Applied Mathematics, vol. 1, no. 4, pp. 141–155, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Khan, M. Hussain, H. Jafari, and Y. Khan, “Application of Laplace decomposition method to solve nonlinear coupled partial differential equations,” World Applied Sciences Journal, vol. 9, Special Issue of Applied Math, pp. 13–19, 2010. View at Google Scholar
  16. S. A. Khuri, “A new approach to Bratu's problem,” Applied Mathematics and Computation, vol. 147, no. 1, pp. 131–136, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. M. Y. Ongun, “The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4+T cells,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 597–603, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. 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 Scopus
  19. Y. Khan and N. Faraz, “Application of modified Laplace decomposition method for solving boundary layer equation,” Journal of King Saud University, vol. 23, no. 1, pp. 115–119, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. E. Yusufoglu, “Numerical solution of Duffing equation by the Laplace decomposition algorithm,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 572–580, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, Mass, USA, 1994.
  22. 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 Google Scholar · View at Scopus
  23. Y. Muroya, E. Ishiwata, and H. Brunner, “On the attainable order of collocation methods for pantograph integro-differential equations,” Journal of Computational and Applied Mathematics, vol. 152, no. 1-2, pp. 347–366, 2003. View at Publisher · View at Google Scholar · View at Scopus