Boundary-layer averaging for standard systems with lag

Abstract

The $k$-th-order asymptotic solution of a standard system with lag is constructed along trajectories calculated according to the averaging scheme of A. N. Filatov. If the perturbation parameter $ε ≪ 1$, then the use of the step method for finding the solution is connected with cumbersome calculations because the number of required steps is inversely proportional to $ε$. We suggest another approach in which the step method is used only $k$ times for $t \in [0,k]$ and justify the asymptotic method.