• Views 569
• Citations 0
• ePub 20
• PDF 459
`Journal of Applied MathematicsVolume 2013 (2013), Article ID 286529, 7 pageshttp://dx.doi.org/10.1155/2013/286529`
Research Article

## New Iterative Method Based on Laplace Decomposition Algorithm

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

Received 26 November 2012; Revised 28 January 2013; Accepted 29 January 2013

Academic Editor: Srinivasan Natesan

Copyright © 2013 Sabir Widatalla and M. Z. Liu. 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.

1. S. Widatalla, Iterative methods for solving nonlinear pantograph equations [Ph.D. thesis], Harbin Institute of Technology, 2013.
2. 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.
3. H. K. Mishra and A. K. Nagar, “He-Laplace method for linear and nonlinear partial differential equations,” Journal of Applied Mathematics, vol. 2012, Article ID 180315, 16 pages, 2012.
4. A. Saadatmandi and M. Dehghan, “Variational iteration method for solving a generalized pantograph equation,” Computers & Mathematics with Applications, vol. 58, no. 11-12, pp. 2190–2196, 2009.
5. A. Ghorbani, “Beyond Adomian polynomials: he polynomials,” Chaos, Solitons and Fractals, vol. 39, no. 3, pp. 1486–1492, 2009.
6. M. Y. Ongun, “The Laplace Adomian Decomposition Method for solving a model for HIV infection of $CD{4}^{+}T$ cells,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 597–603, 2011.
7. M. Khan and M. A. Gondal, “A reliable treatment of Abel's second kind singular integral equations,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1666–1670, 2012.
8. Y. Khan, “An effective modification of the Laplace decomposition method for nonlinear equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, pp. 1373–1376, 2009.
9. Y. Khan and N. Faraz, “Application of modified Laplace decomposition method for solving boundary layer equation,” Journal of King Saud University, vol. 23, pp. 115–119, 2011.
10. M. Hussain and M. Khan, “Modified Laplace decomposition method,” Applied Mathematical Sciences, vol. 4, no. 33-36, pp. 1769–1783, 2010.
11. S. Widatalla and M. A. Koroma, “Approximation algorithm for a system of pantograph equations,” Journal of Applied Mathematics, vol. 2012, Article ID 714681, 9 pages, 2012.
12. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, Mass, USA, 1994.
13. A. Iserles, “On nonlinear delay differential equations,” Transactions of the American Mathematical Society, vol. 344, no. 1, pp. 441–477, 1994.