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The aim of this paper is the construction of a measure of the rate of convergence or the rate that a function converges to a limit value, in the category of real functions. The potential convergence, as it will be defined later on, constitutes the measure of the rate of convergence, while its calculation is done through a suitable algorithm. This theory applies in the field of ordinary differential equations suggesting methods of tracking down and finding particular solutions on the class of non linear D.E.

Part I: Theory of potential of convergence Part II: Applications in the field of ordinary differential equations