Inverse Cauchy Theorem for Constructing Differential Equation
by
Valko G. Petrov
Bulgarian Academy of Sciences

In many cases, a dynamical system single component, measured as a discrete time series, is approximated in a form of an analytic function. We consider this function presents an informational source for possible determining the order of an ordinary differential equation, solved with respect to the highest derivative and having the given analytic function for a solution. Concerning that, sufficient conditions for existence, constrained uniqueness and analyticity of the unknown right hand side can be formulated and proved. These conditions present the content of a such named inverse Cauchy theorem we introduce first time. In view of that it is reasonably to search the right hand side of the unknown equation in the form of a specific interpolation polynomial. This purpose can be achieved by a corresponding interpolation method using the given analytic function and its time-derivatives.

Date received: March 16, 1999