Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities

Thierry Horsin (1) , Mohamed Ali Jendoubi (2, 3)

1 M2N - Modélisation mathématique et numérique
2 IPEST - Institut préparatoire aux études scientifiques et techniques [La Marsa]
3 LEDP - Laboratoire Equations aux Dérivées Partielles

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

Keywords: Discretization; Angle condition; Lojasiewicz's inequality; single limit-point convergence; stability; convergence rates

Domains: Mathematics [math]

Thierry Horsin, Mohamed Ali Jendoubi. Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities. Communications on Pure & Applied Analysis, 2022, 21 (3), pp.999. ⟨10.3934/cpaa.2022007⟩. ⟨hal-03622761⟩