Linear multistep matrix methods for a class of functional differential equations: Convergence and error bounds

In this paper, multistep matrix methods for a class of functional differential equations with delay are proposed. Such methods avoid vectorization techniques and do not increase the problem dimension. Two approximation mappings are described appropriate to operators concerning the past history of the solution. Error bounds for the discretization error in terms of the data are given. It is proved that a consistent and zero-stable multistep matrix method with suitable conditions on the approximation mappings is convergent.