Asymptotic behavior of an adapted implicit discretization of slowly damped second order dynamical systems

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

1 M2N - Modélisation mathématique et numérique
2 University of Tunis El Manar

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 behavior as for the system in continuous time.

Keywords: 40A05 descent methods; real analytic functions; Lojasiewicz gradient inequality; single limit-point convergence; stability; asymptotically small dissipation; convergence rates; variable time-step discretization; implicit scheme; Mathematics Subject Classification 2010 (MSC2010): 65K05 65L20 90C26 37N40 26E05 40A05 descent methods real analytic functions Lojasiewicz gradient inequality single limit-point convergence stability asymptotically small dissipation convergence rates variable time-step discretization implicit scheme; Mathematics Subject Classification 2010 (MSC2010): 65K05; 65L20; 90C26; 37N40; 26E05

Domains: Mathematics [math]; Mathematics [math]; Dynamical Systems [math.DS]; Mathematics [math]; Numerical Analysis [math.NA]

Thierry Horsin, Mohamed Ali Jendoubi. Asymptotic behavior of an adapted implicit discretization of slowly damped second order dynamical systems. 2023. ⟨hal-03976691⟩