Families of discrete advection–reaction operators investigated via divided differences

An infinite matrix formulation of the families of discrete advection–reaction operators is given in order to investigate their relevance to interpolation theory. A basic characteristic under study is the connection of each iteration of the operators to a series of interpolation problems for the canonical polynomial base for selected initial conditions. In order to generalize our results, we extend the definition of advection–reaction operators to sequences of polynomials.