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Article Dans Une Revue Applied Mathematics and Computation Année : 2018

Bracketing the solutions of an ordinary differential equation with uncertain initial conditions

Luc Jaulin
Benoit Zerr
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Résumé

In this paper, we present a new method for bracketing (i.e., characterizing from inside and from outside) all solutions of an ordinary differential equation in the case where the initial time is inside an interval and the initial state is inside a box. The principle of the approach is to cast the problem into bracketing the largest positive invariant set which is included inside a given set X. Although there exists an efficient algorithm to solve this problem when X is bounded, we need to adapt it to deal with cases where X is unbounded.
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Dates et versions

hal-01574711 , version 1 (16-08-2017)

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Thomas Le Mézo, Luc Jaulin, Benoit Zerr. Bracketing the solutions of an ordinary differential equation with uncertain initial conditions. Applied Mathematics and Computation, 2018, 318 (1), pp.70-79. ⟨10.1016/j.amc.2017.07.036⟩. ⟨hal-01574711⟩
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