On the Rate of Convergence in Periodic Homogenization of Scalar First-Order Ordinary Differential Equations
Hassan Ibrahim, Régis Monneau · SIAM Journal on Mathematical Analysis · 2010
In this paper, we study the rate of convergence in periodic homogenization of scalar ordinary differential equations (ODEs). We provide a quantitative error estimate between the solutions of a first-order ODE with rapidly oscillating coefficients and the solution of the limiting homogenized equation. As an application of our result, we obtain an error estimate for the solution of some particular linear transport equations.