On Adomian's decomposition method and some comparisons with Picard's iterative scheme

We consider the general mathematical framework of Adomian's decomposition method (G. Adomian, “Stochastic Systems,” Academic Press, New York, 1983) for a large class of nonlinear operator equations. Picard's iterative scheme is considered for the same class for equations and compared with the decomposition method. The paper identifies carefully all substantial differences between the two methods and shows that various advantages exist for the decomposition method.