Restarted Adomian method for nonlinear differential equations

The Adomian method is a strong tool for solving partial and ordinary differential equations [Cherruault, Y. and N'Dour, M. (1997). The decomposition method applied to a diffusion model, Kybernetes , 26 , No. 8, 921-935; Wazwaz, A. M. (1998). A comparison between Adomian decomposion method and Taylor series method in the series solutions, Appl. Math. Comput. 97 , 37-44.] In this paper, we apply a new algorithm named the restarted Adomian method used for solving algebraic equations and nonlinear integral equations [Babolian, E. and Javadi, Sh. (2003). Restarted Adomian method for algebraic equations, Appl. Math. Comput. , 146 , 533-541; Babolian, E., Javadi, Sh. and Sadeghi, H. Restarted Adomian method for nolinear integral equations, Appl. Math. Comput. , 153 , 353-359.]. By some examples and comparing results in both the methods (restarted and standard Adomian method) with exact solution, we show that the new method gives better numerical results.