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Solving the inverse problem for an ordinary differential equation using conjugation. (English) Zbl 1453.34024

The authors consider the inverse problem of recovering an ordinary differential equation \(x'(t) = v(x)\) from a set of data points \(P = \{(t_i, x_i), i = 1,\dots, N\}\), such that \(x_i\approx x(t_i)\) as closely as possible. The key to the proposed method is to find approximations of the recursive or discrete propagation function \(D(x)\) from the given data set. The field \(v(x)\) is determined using the conjugate map defined by Schröder’s equation and the solution of a related Julia’s equation. Numerical algorithms are presented at the end.

MSC:

34A55 Inverse problems involving ordinary differential equations
65L09 Numerical solution of inverse problems involving ordinary differential equations
65Q20 Numerical methods for functional equations

Software:

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References:

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