Multiple shooting is a standard technique for the numerical solution of
boundary value problems (BVPs). We discuss
the application of multiple shooting techniques to a certain class
of non-linear singular boundary value problems.
Particular attention is paid to the integration of the underlying
initial value problems (IVPs). 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 initial value integrator realising
efficiently a high order approximation for the solution of the singular
problem (a nontrivial result).
Simple shooting based on this integration method performs
successfully, and the extension to multiple shooting is
straightforward. Convergence properties of the numerical solution
of the BVP are investigated. Finally, a convergence
result for the perturbed Newton iteration for non-linear algebraic
equations involved, is given. A number of
experimental results illustrating this approach are presented.