Analytical and numerical investigation of mixed-type functional differential equations

This paper is concerned with the approximate solution of a linear non-autonomous functional differential equation, with both advanced and delayed arguments. We search for a solution x(t)x(t), defined for t∈[−1,k]t∈[−1,k], (k∈Nk∈N), that satisfies this equation almost everywhere on [0,k−1][0,k−1] and assumes specified values on the intervals [−1,0][−1,0] and (k−1,k](k−1,k]. We provide a discussion of existence and uniqueness theory for the problems under consideration and describe numerical algorithms for their solution, giving an analysis of their convergence.