Abstract
A family of discrete delay advection–reaction operators is introduced along with an infinite matrix formulation in order to investigate the asymptotic behaviour of the orbits of their iterates. The infinite matrices obtained are triangular matrices with only one non-zero subdiagonal. We show that the elements of powers of these matrices can be written as distinctive products of two factors, one of them involving derivatives of the Lagrange polynomials of basic functions with the diagonal elements as nodes. The other factor consists of products of the subdiagonal elements. Consequently the convergence of the iterates of the operators depends on their eigenvalues and the products of their subdiagonal elements.
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