A. Abdelrazec and D. Pelinovsky
Convergence of the Adomian decomposition method for initial-value problems
Numerical Methods for PDEs 27 (2011), 749-766
Abstract:
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.
Keywords:
Adomian method, Cauchy-Kowalevskaya theorem,
nonlinear Schrodinger equation.