We develop a one step matrix method in order to obtain approximate
solutions of first order non-linear systems and non-linear ordinary
differential equations, reducible to first order systems. We find a
sequence of such solutions that converge to the exact solution. We apply
the method to different well known examples and check its precision, in
terms of local error, comparing it with the error produced by other
methods. The advantage of the method over others widely used lies on the
great simplicity of its implementation.