Multiple shooting is a standard technique for the numerical solution
of boundary value problems. We discuss the application of multiple
shooting techniques to a certain class of nonlinear singular boundary
value problems. Particular attention is paid to the methodology for
the integration of the underlying initial value problems. To this end
we use the implicit Euler scheme, serving as a basic method for the
acceleration technique known as Iterated Defect Correction. This yields
a stable inital value integrator realizing a high order approximation
for the singular case (a nontrivial result). Simple shooting based on
this integration method performs successfully, and the extension to
multiple shooting is straightforward. A number of experimental results
illustrating this approach are presented.