`Mathematical Problems in EngineeringVolume 2011, Article ID 724927, 19 pageshttp://dx.doi.org/10.1155/2011/724927`
Research Article

## On the Solutions of Nonlinear Higher-Order Boundary Value Problems by Using Differential Transformation Method and Adomian Decomposition Method

Department of Mathematics, University Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

Received 8 November 2010; Accepted 7 February 2011

Copyright © 2011 Che Haziqah Che Hussin and Adem Kiliçman. 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. A.-M. Wazwaz, “A reliable modification of Adomian decomposition method,” Applied Mathematics and Computation, vol. 102, no. 1, pp. 77–86, 1999.
2. A.-M. Wazwaz, “Approximate solutions to boundary value problems of higher order by the modified decomposition method,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 679–691, 2000.
3. A.-M. Wazwaz, “The numerical solution of fifth-order boundary value problems by the decomposition method,” Journal of Computational and Applied Mathematics, vol. 136, no. 1-2, pp. 259–270, 2001.
4. A.-M. Wazwaz, “The numerical solution of sixth-order boundary value problems by the modified decomposition method,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 311–325, 2001.
5. M. Meštrović, “The modified decomposition method for eighth-order boundary value problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1437–1444, 2007.
6. M. M. Hosseini and M. Jafari, “A note on the use of Adomian decomposition method for highorder and system of nonlinear differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, pp. 1952–1957, 2009.
7. M. Dehghan and F. Shakeri, “The numerical solution of the second Painlevé equation,” Numerical Methods for Partial Differential Equations, vol. 25, no. 5, pp. 1238–1259, 2009.
8. 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, 9 pages, 2006.
9. M. Dehghan and R. Salehi, “A seminumeric approach for solution of the eikonal partial differential equation and its applications,” Numerical Methods for Partial Differential Equations, vol. 26, no. 3, pp. 702–722, 2010.
10. M. Dehghan, J. M. Heris, and A. Saadatmandi, “Application of semi-analytic methods for the Fitzhugh-Nagumo equation, which models the transmission of nerve impulses,” Mathematical Methods in the Applied Sciences, vol. 33, no. 11, pp. 1384–1398, 2010.
11. M. Dehghan, M. Shakourifar, and A. Hamidi, “The solution of linear and nonlinear systems of Volterra functional equations using Adomian-Pade technique,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2509–2521, 2009.
12. M. Dehghan, A. Hamidi, and M. Shakourifar, “The solution of coupled Burgers' equations using Adomian-Pade technique,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1034–1047, 2007.
13. M. Dehghan and R. Salehi, “Solution of a nonlinear time-delay model in biology via semi-analytical approaches,” Computer Physics Communications, vol. 181, no. 7, pp. 1255–1265, 2010.
14. F. Shakeri and M. Dehghan, “Application of the decomposition method of adomian for solving the pantograph equation of order m,” Zeitschrift fur Naturforschung, vol. 65, no. 5, pp. 453–460, 2010.
15. M. Dehghan, “The solution of a nonclassic problem for one-dimensional hyperbolic equation using the decomposition procedure,” International Journal of Computer Mathematics, vol. 81, no. 8, pp. 979–989, 2004.
16. S. S. 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.
17. F. Ayaz, “On the two-dimensional differential transform method,” Applied Mathematics and Computation, vol. 143, no. 2-3, pp. 361–374, 2003.
18. F. Ayaz, “Solutions of the system of differential equations by differential transform method,” Applied Mathematics and Computation, vol. 147, no. 2, pp. 547–567, 2004.
19. V. S. Ertürk and S. Momani, “Comparing numerical methods for solving fourth-order boundary value problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1963–1968, 2007.
20. A. Arikoglu and I. Ozkol, “Solution of fractional differential equations by using differential transform method,” Chaos, Solitons and Fractals, vol. 34, no. 5, pp. 1473–1481, 2007.
21. I. H. Abdel-Halim Hassan and V. S. Ertürk, “Solutions of different types of the linear and non-linear higher-order boundary value problems by differential transformation method,” European Journal of Pure and Applied Mathematics, vol. 2, no. 3, pp. 426–447, 2009.