On formal solutions of linear matrix differential–difference equations Original Research Article

In this paper, we construct a formal solution to the matrix differential–difference equation (dde) Y′(t)=A(t)Y(t−1), where A(t) is a matrix power series in t−1. In many cases solutions to the latter equation and to the matrix differential equation Y′(t)=A(t)Y(t) have the same form. However, these solutions may have different forms when the spectrum of A0, the leading term of A(t), contains −e−1.