where f and g are smooth functions and g is
chosen such that the BVP is well-posed. In order to solve the BVP
we apply single and parallel shooting to reduce the problem
to a set of initial value problems (IVPs) which are integrated from left
to right.
Convergence properties
of the solution of the boundary value problem
are investigated
under the assumption that a
numerical method for IVPs with a level of accuracy of
O(h^{p}) is used.
For these considerations we have to use some nonstandard techniques to
show that the shooting method is well-defined for well-posed singular
BVPs, prove perturbation results for singular IVPs
and the smooth dependence on parameters for the IVPs, which
does not follow from classical theory. Finally, a convergence
result for the perturbed Newton iteration, which
occurs in the solution process of
the sets of nonlinear algebraic equations involved,
is given.