Construction of an asymptotic expansion for the solution of a linear system of equations of neutral type with a small delay in the absence of a boundary layer

In this paper we simplify the algorithm for constructing the asymptotic expansion for the solution of a linear system of neutral type at a large distance from the origin. After using the Laplace transformation to determine the asymptotic expansion near the initial point, we succeed in reducing the problem of determining the initial conditions to the computation of the residues of certain functions for which we have recurrence formulas.