A stroboscopic averaging algorithm for highly oscillatory delay problems

Abstract

Abstract We propose and analyse a heterogeneous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic forcing. The stroboscopic averaging method suggested here may provide approximations with $\mathscr{O}\big (H^{2}+1/\varOmega ^{2}\big )$ errors with a computational effort that grows like $H^{-1}$ (the inverse of the step size), uniformly in the forcing frequency $\varOmega $.