A new definition of the Adomian polynomials

Purpose – To provide a new proof of convergence of the Adomian decomposition series for solving nonlinear ordinary and partial differential equations based upon a thorough examination of the historical milieu preceding the Adomian decomposition method.Design/methodology/approach – Develops a theoretical background of the Adomian decomposition method under the auspices of the Cauchy‐Kovalevskaya theorem of existence and uniqueness for solution of differential equations. Beginning from the concepts of a parametrized Taylor expansion series as previously introduced in the Murray‐Miller theorem based on analytic parameters, and the Banach‐space analog of the Taylor expansion series about a function instead of a constant as briefly discussed by Cherruault et al., the Adomian decompositions series and the series of Adomian polynomials are found to be a uniformly convergent series of analytic functions for the solution u and the nonlinear composite function f(u). To derive the unifying formula for the family of ...

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