In this article we use Adomian decomposition method, which is a well-known
method for solving functional equations now-a-days, to solve systems of differential
equations of the first order and an ordinary differential equation of any order by converting
it into a system of differential of the order one. Theoretical considerations are
being discussed, and convergence of the method for theses systems is addressed. Some
examples are presented to show the ability of the method for linear and non-linear
systems of differential equations.
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