We consider singular boundary value problems (BVPs) of the form
z'(t)=M(t)z(t)/t+f(t,z(t)), t∈ (0,1],
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(hp) 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.