The Role of Conditioning in Shooting Techniques

This paper examines shooting and multiple shooting as a technique for the analysis of numerical schemes applied to two point boundary value problems. The aim of the analysis is to deduce convergence of a numerical scheme by establishing the convergence of the scheme when applied to a number of subproblems. Since such an approach is useful only if the subproblems are reasonably well conditioned, the question of conditioning is addressed. It is shown that there exist subproblems that are at least as well conditioned as the original problem. Two examples are presented for which the shooting approach leads to a substantial simplification in the analysis.