Analysis of Singular Initial and Terminal Value Problems

Abstract

this paper provides the study of the analytical properties of (1) and (2) which have to be examined before beginning the convergence analysis of underlying one-step or multi-step method. Here, existence and uniqueness of bounded solutions, as well as their smoothness, will be discussed. Because of numerous applications occurring in the form of singular boundary value problems this class of singular systems has been extensively studied, while there are only very few papers dealing with the approximation of initial value problems (see [10], [12] and [15]). Moreover, as far as we are aware, there is no framework discussing the solvability of (1) and (2) although this theory is quite important in the context mentioned abov