Work

Quantitative homogenization of first-order ODEs

Year: 2025

Type: preprint

Abstract: This paper investigates the quantitative homogenization of first-order ODEs. For single-scale scalar ODEs, we obtain a sharp $O(\varepsilon)$ convergence rate and characterize the effective constant. In the multi-scale setting, our results match those of \cite{IM} for long times but improve the short-time error to $O(\varepsilon)$. We also obtain what appears to be the first uniform $O(\varepsilon)$ homogenization estimate for scalar ODEs with quasi-periodic fast dependence on the state variable. The scalar framework is further extended to higher dimensions under a bounded-mean-motion-type assumption. For weakly coupled systems with fast switching rates, we derive an explicit $O(\varepsilon)$ convergence rate that captures the initial layer. These results have applications to linear transport equations and broader connections to PDEs and gradient systems.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2508.17628

Author: Ni, Panrui

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Japan Society for the Promotion of Science

Awards: Quantitative homogenization theory for Hamilton–Jacobi equations, G4526851097

OpenAlex ID: W7077937967

Cites:

Cited by:

Related to: