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Bracketing the solutions of an ordinary differential equation with uncertain initial conditions. (English) Zbl 1426.93022
Summary: 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 \(\mathbb{X} \). Although there exists an efficient algorithm to solve this problem when \(\mathbb{X}\) is bounded, we need to adapt it to deal with cases where \(\mathbb{X}\) is unbounded.

93B03 Attainable sets, reachability
34A34 Nonlinear ordinary differential equations and systems
34C45 Invariant manifolds for ordinary differential equations
Full Text: DOI
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