Document Type : Research Paper


Department of Mathematics, University of Bonab, Bonab, Iran.


The work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on Homotopy analysis method  and Adomian decomposition method for solving  differential equations of integer and fractional orders.


[1] G.C. Wu, Y.G. Shi, K.T. Wu, Adomian decomposition method and non-analytical solutions of fractional di erential equations, Romanian J. Phys. 56 (2011) 873880.
[2] M. Ganjiani, Solution of nonlinear fractional di erential equations using homotopy analysis method, Applied Mathematical Modelling 34(2010)16341641.
[3] S.J. Liao, Beyond perturbation: introduction to homotopy analysis method, Boca Raton. FL, Chapman and Hall, 2004.
[4] S. J. Liao, The proposed homotipy analysis method technique for the solution of non-linear problems, PhD dissertation, Shanghai Jiao Tong University(1992).
[5] G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl. 135, 501544 (1988)
[6] H.R. Marasi, M. Nikbakht, Adomian decompositiom method for boundary value problems, Aus. J. Basic. Appl. Sci. 5, 2106-2111(2011)
[7] H.R. Marasi, S. Karimi, Convergence of variational iteration method for solving fractional Klein-Gordon equation (accepted).
[8] Jun-Sheng Duan , Temuer Chaolu, Randolph Rach , Lei Lu,The Adomian decomposition method with convergence acceleration techniques for nonlinear fractional di erential equation.Comput.Math. Appl.66 (2013) 728-736
[9] F. Abidi, K. Omrani, The homotopy analysis method for solving the FornbergWhitham equation and com- parison with Adomians decomposition method, Comput. Math. Appl. 59 (2010) 27432750.