A. Abdelrazec and D. Pelinovsky

Convergence of the Adomian decomposition method for initial-value problems

Numerical Methods for PDEs 27 (2011), 749-766

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 Schr\"{o}dinger equation.

Adomian method, Cauchy-Kowalevskaya theorem, nonlinear Schrodinger equation.