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.

MINISIMPOSIUM SESSION: 6. Novel methods for ODEs