  This paper proposes a numerical method based on the Adomian decomposition
approach for the time discretization, applied to Euler equations. A recursive
property is demonstrated that allows to formulate the method in an appropriate
and efficient way. To obtain a fully numerical scheme, the space discretization
is achieved using the classical DG techniques. The efficiency of the obtained
numerical scheme is demonstrated through numerical tests by comparison to exact
solution and the popular Runge-Kutta DG method results.
