A stroboscopic averaging algorithm for highly oscillatory delay problems

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.