By imposing some conditions on the discrete dynamical system generated by p-steps discretization methods, we find two classes of difference equations of order p which are suitable for solving ordinary differential equations.These generate in particular two non linear methods wich turn out to be A-stable according to the current definitions; the first of them is a two steps methods of the second order, the second one is a three steps method of the third order. Both are particularly suitable in the case of stiff differential equations and whenever the interval of integration is very large.

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