In this paper we present an overview of analytical
results and numerical methods for singular boundary
value problems for ordinary differential equations
with a singularity of the first kind.
Special attention is paid to the analysis of
shooting methods, where the associated initial value
problems are solved by the acceleration technique
known as Iterated Defect Correction (IDeC) based on
the backward Euler method, and on direct
discretization using collocation schemes. Convergence,
error estimation and mesh selection are discussed for
Moreover, we study the fixed point convergence of the IDeC
iteration, where the fixed point corresponds to a collocation solution.