Convergence to equilibrium for solutions of some forced discretized second-order gradient-like systems
Haythem Cheikh · Mathematical Control and Related Fields · 2023
In this paper we prove that the solutions of an implicit scheme converge to equilibrium points under certain conditions on the potential function $ F $ and the forcing term $ g $. For this purpose, we use a Lojasiewicz inequality and introduce a discretized energy and a Lyapunov function. In addition, we provide some numerical simulations that support our findings.