The solvability of a certain class of singular nonlinear initial value
problems is discussed. Particular attention is paid to the structure of
initial conditions necessary for a bounded solution to exist. The implicit
Euler rule applied to approximate the solution of the singular system is
shown to be stable and to retain its classical convergence
order. Moreover, the asymptotic error expansion for the global error of the
above approximation is proven to have the classical structure. Finally,
experimental results showing the feasibility of the approximation obtained
by the Euler method to serve as a basic method for the acceleration
technique known as the Iterated Defect Correction are presented.