Asymptotics for some discretizations of dynamical systems, application to second order systems with nonlocal nonlinearities

Thierry Horsin (1) , Mohamed Ali Jendoubi (2)

1 M2N - Modélisation mathématique et numérique
2 UTM - Université de Tunis El Manar

In the present paper we study the asymptotic behavior of discretized finite dimen- sional dynamical systems. We prove that under some discrete angle condition and under a Lojasiewicz’s inequality condition, the solutions to an implicit scheme con- verge to equilibria points. We also present some numerical simulations suggesting that our results may be extended under weaker assumptions or to infinite dimensional dynamical systems.

Mots clés: Discretization; Angle condition; Lojasiewicz’s inequality; single limit-point con- vergence; stability; convergence rates.

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Thierry Horsin, Mohamed Ali Jendoubi. Asymptotics for some discretizations of dynamical systems, application to second order systems with nonlocal nonlinearities. 2021. ⟨hal-03278131v2⟩