| In this paper,we first propose a Differential Equation Based Scatter Data Fitting Theory which could be considered as a generalization of the classic nonlinear approximating theory of Prony.After short discussion of the Prony Method,we show the details of our theory.The main idea of it is to assume that the function implied by the Scatter Data observes a general physical model,which we refer to as the Differential Equation. And our object is to find out this general model behind the Data so that it could be used to construct the base functions fitting the Scatter Data.In addition,in the first part we discussed some basic theory problems involved,including how to determine the order of the Differential Equation and for which functions our method could be applied to. Answer to the first problem is given from two aspects that are calculation and estimation. As for the second problem,analytic functions are proved to be satisfied with the requirement of our theory.The second part of this paper apply the theory to the simplification of the UNESCO Equation of State for Sea Water.The result is given which is not only simple in form but also possessing a high accuracy of about 2×10-3kg/m3 in average.
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