The decomposition method, proposed by \textit{G. Adomian} [J. Math. Anal. Appl. 102, 420--434 (1984; Zbl 0554.60065)], used initially to solve partial differential equations, has been extended to solve a wide class of problems: linear and nonlinear deterministic and stochastic problems, from physics, biology and chemical reactions. The key of this method is to decompose the nonlinear term in the equations into a series of polynomials (Adomian polynomials). In this paper, the authors develop a reliable technique for calculating Adomian polynomials for a nonlinear operator. The algorithm can be easily programmed in Maple and can be applied for solving nonlinear differential equations (initial value problems and boundary value problems).