The conditioning of linear boundary value problems

Investigation is made into the sensitivity of solutions of linear boundary value problems to perturbations of the boundary condition. We derive a useful quantity to decide for well or ill conditioning. From this it is deduced which kind of requirements the boundary conditions should meet in order to have a well conditioned problem. It is shown that this quantity can fruitfully be used to explain why, e.g., the multiple shooting technique is stable (in contrast to the single shooting one) for certain well posed problems having solutions with different growth behavior. The results are sustained by a number of examples