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On the inverse Cauchy problem for linear ordinary differential equations

Abstract : The Cauchy problem characterizes the solutions of a linear ordinary differential equation that satisfies initial conditions. In this paper, we investigate the converse problem, namely, given a function that is known to satisfy a linear ordinary differential equation of a fixed order, determine the coefficients of the ordinary differential equation and the initial conditions. The techniques used to investigate the inverse Cauchy problem come from the algebraic estimation problem introduced by Fliess and Sira-Ramírez. From the perfect observation of the solution, i.e., without external perturbation and noise corrupting it, the initial value problem can be explicitly reconstructed using only iterative indefinite integrals of the solution.
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Contributor : Alban Quadrat Connect in order to contact the contributor
Submitted on : Monday, January 17, 2022 - 6:19:43 PM
Last modification on : Thursday, April 7, 2022 - 1:58:27 PM
Long-term archiving on: : Monday, April 18, 2022 - 9:33:57 PM

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Maya Chartouny, Thomas Cluzeau, Alban Quadrat. On the inverse Cauchy problem for linear ordinary differential equations. GAMM 2021 - 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Mar 2021, Kassel, Germany. ⟨10.1002/pamm.202100214⟩. ⟨hal-03530281⟩

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