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 Schrödinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 749–766, 2011