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

TL;DR

This paper investigates how quickly solutions of scalar first-order ODEs with oscillating coefficients approach their homogenized limits, providing quantitative error estimates and applying these results to specific linear transport equations.

Contribution

It introduces a new quantitative error estimate for the convergence rate in periodic homogenization of scalar ODEs, enhancing understanding of the approximation accuracy.

Findings

Derived explicit error bounds for homogenization convergence

Applied results to linear transport equations

Quantified the rate of convergence in specific cases

Abstract

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.