On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations

Hassan Ibrahim (1) , Regis Monneau (1)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique

In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations. We provide a quantitative error estimate between the solutions of a first-order ordinary differential equation with rapidly oscillating coefficients and the limiting homogenized solution. As an application of our result, we obtain an error estimate for the solution of some particular linear transport equations.

Mots clés: Homogenization of ODEs; error estimates; transport equations

Domaines: Equations aux dérivées partielles [math.AP]

Hassan Ibrahim, Regis Monneau. On the rate of convergence in periodic homogenization of scalar first-order ordinary differential equations. SIAM Journal on Mathematical Analysis, 2010, 42 (5), pp.2155-2176. ⟨10.1137/080738830⟩. ⟨hal-00332835⟩