An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs

Irmina Walawska and Daniel Wilczak

Applied Mathematics and Computation, 2016, vol. 291, issue C, 303-322

Abstract: We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems literature. The method uses a high-order Taylor method as a predictor step and an implicit method based on the Hermite–Obreshkov interpolation as a corrector step. The proposed algorithm is an improvement of the C1-Lohner algorithm proposed by Zgliczyński and it provides sharper bounds.

Keywords: Validated numerics; Initial value problem; Variational equations; Uniform hyperbolicity; Chaos (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:291:y:2016:i:c:p:303-322

DOI: 10.1016/j.amc.2016.07.005

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