Abstract

In this work, we adapted another time the Adomian decomposition method for solving nonlinear and non-autonomous ODEs systems. Therefore, our expressions of the Adomian polynomials are determined for a several-variable differential operators. The solution series is shown that it stay coincide with the Taylor series. Thus new conditions of convergence have been established, some systemes has been solved by ADM using Maple 2020. keywords Adomian decomposition method, Adomian polynomials, ODEs systems, initial value problems, several-variables differential operators. Classification 26B12, 34L30, 47E05, 65B10, 65L05, 65L80