Convergence of the Adomian decomposition method for initial‐value problems

We prove convergence of the Adomian decomposition method for an abstract initial-value problem using the method of majorants from the Cauchy-Kowalevskaya theorem for differential equations with analytic vector fields. Convergence rates of the Adomian method are investigated in the context of the nonlinear Schrodinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 749–766, 2011