In this paper a new treatment for the Adomian decomposition method (ADM) is introduced.
The new treatment is called the improved Adomian decomposition method (IADM)
which improves the results obtained from the known Adomian decomposition method.
The improved Adomian decomposition method is applied for the analytic treatment of
nonlinear initial value problems. The improved method accelerates the convergence of the
series solution, and provides the exact power series solution. It solves the drawbacks in the
standard Adomian decomposition method.