Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2008.1962.1966JaradatOmar K.102008810In this study, we implement a relatively new analytical technique, the Adomian Decomposition Method (ADM), for solving Abelian differential equations. The analytical and numerical results of the equations have been obtained in terms of convergent series with easily computable components. The method is applied to solve two problems. The current results are compared with these derived from the established Runge-Kutta method in order to verify the accuracy of the ADM. It is shown that there is excellent agreement between the two sets of results. This finding confirms that the ADM is powerful and efficient tool for solving Abelian differential equations.]]>Abbaoui, K. and Y. Cherruault,1996Adomian, G.,1988Adomian, G.,1990Adomian, G.,1990Adomian, G., R.C. Rach and R.E. Meyers,1991Adomian, G.,1994Bulut, H. and D.J. Evans,2002Cherruault, Y.,1989Cherruault, Y. and G. Adomian,1993El-Tawil, M.A., A.A. Bahnasawi and A. Abdel-Naby,2004Guellal, S. and Y. Cherruault,1995Momani, S.,2006Momani, S. and N. Shawagfeh,2006Momani, S. and R. Qaralleh,2007Seng, V., K. Abbaoui and Y. Cherruault,1996Zill, D.G.,1997