Improved Adomian decomposition method (solving nonlinear non-homogenous initial value problem)

The Adomian decomposition method (ADM) cannot deal generally with the non-homogenous differential equations. The method still needs improvements. This paper introduces a qualitative improvement in the method. The improved method is called the improved Adomian decomposition method (IADM). A comparison between ADM and IADM shows that the ADM gives results that is not accepted in some examples and cannot solve the other examples while IADM solves the problems effectively and efficiently.