# A stroboscopic averaging algorithm for highly oscillatory delay problems

## TL;DR

This paper introduces a multiscale numerical method called the stroboscopic averaging method (SAM) for efficiently solving highly oscillatory delay differential equations with fast periodic forcing, achieving high accuracy with reduced computational effort.

## Contribution

The paper presents a novel heterogenous multiscale method (SAM) that provides accurate approximations for delay differential equations under fast periodic forcing, with error bounds independent of the forcing frequency.

## Key findings

- Achieves (H^2+1/\u03a9^2) error bounds.
- Computational effort scales like H^{-1}, independent of forcing frequency.
- Uniform accuracy across a range of high-frequency forcings.

## Abstract

We propose and analyze a heterogenous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic forcing. The stroboscopic averaging method (SAM) suggested here may provide approximations with $\(\mathcal{O}(H^2+1/\Omega^2)\)$ errors with a computational effort that grows like $\(H^{-1}\)$ (the inverse of the stepsize), uniformly in the forcing frequency Omega.