Solving the inverse problem for an ordinary differential equation using conjugation
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We consider the following inverse problem for an ordinary differential equations (ODE): given a set of data points (t_i,x_i), i=1,...,N, find an ODE x^'(t) = v (x(t)) that admits a solution x(t) such that x_i = x(t_i). To determine the field v(x), we use the conjugate map defined by Schröder equation and the solution of a related Julia equation. We also study existence, uniqueness, stability and other properties of this solution. Finally, we present several numerical methods for the approximation of the field v(x) and provide some illustrative examples of the application of these methods.
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