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This is a study of iteractive procedures which can be used as discrete aproximations of differential equations. Rather than'the accuracy of the methods in bounded intervals, in which is mostly concerned the numerical analysts, we are interested in asymptotic properties of solutions which are preserved in the discrete scheme. Several examples are given. In chapter I we study the concept of first order endomorphism. In chapter II we show how a differential equation can be reduced to a difference equation. We give some examples where is possible to see when the stability properties are preserved. The Study of a differential-difference equation is also presented. In chapter III, a modified method of RouthHurwitz is applied in order to state conditions-for the roots of certain characteristic polinomials have modulus less than one.