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

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  • Le Mézo, Thomas
  • Jaulin, Luc
  • Zerr, Benoît

Abstract

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.

Suggested Citation

  • Le Mézo, Thomas & Jaulin, Luc & Zerr, Benoît, 2018. "Bracketing the solutions of an ordinary differential equation with uncertain initial conditions," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 70-79.
    • Handle: RePEc:eee:apmaco:v:318:y:2018:i:c:p:70-79
    DOI: 10.1016/j.amc.2017.07.036
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    References listed on IDEAS

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    1. Walawska, Irmina & Wilczak, Daniel, 2016. "An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 303-322.
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    Cited by:

    1. Auguste Bourgois & Simon Rohou & Luc Jaulin & Andreas Rauh, 2022. "Proving Feasibility of a Docking Mission: A Contractor Programming Approach," Mathematics, MDPI, vol. 10(7), pages 1-20, April.

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