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Asymptotic Behavior of an Adapted Implicit Discretization of Slowly Damped Second Order Dynamical Systems

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Abstract

In the context of damped second order linear dynamical systems, we study the asymptotic behavior of a time discretization of a slowly damped differential equation. We prove that this discretization can be constructed by means of a variable time step that gives rise to the same asymptotic behaviour as for the system in continuous time.

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Author notes

  1. Thierry Horsin and Mohamed Ali Jendoubi contributed equally to this work.

Authors and Affiliations

  1. Laboratoire M2N, EA7340, CNAM, 2 rue Conté, Paris, 75003, France

    Thierry Horsin

  2. Institut Préparatoire aux Etudes Scientifiques et Techniques, Université de Carthage, B.P. 51, La Marsa, 2070, Tunisia

    Mohamed Ali Jendoubi

  3. Laboratoire Équations aux Dérivés Partielles, LR03ES04, Faculté des sciences de Tunis, Université Tunis El Manar, Tunis, 2092, Tunisia

    Mohamed Ali Jendoubi

Authors
  1. Thierry Horsin
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  2. Mohamed Ali Jendoubi
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Horsin, T., Jendoubi, M.A. Asymptotic Behavior of an Adapted Implicit Discretization of Slowly Damped Second Order Dynamical Systems. Appl Math Optim 88, 64 (2023). https://doi.org/10.1007/s00245-023-10027-z

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