TITLE: What is state of the art for the Shooting Method?
QUESTION [5 upvotes]: I am interested in examples where the Shooting Method has been used to find solutions to systems of ordinary differential equations that are either 

reasonably large systems, or 
the search algorithm in the shooting parameters is somewhat prohibitive because of the nature of the solutions, or
both of the above.

Any references, descriptions, recent progress, folklore, in the ballpark would be of interest. Feel free to interpret "reasonably large" subjectively if necessary.

REPLY [5 votes]: Another shameless plug ... Coworkers and I used the Evans function formalism, which is a variant of the shooting method to deal with unstable directions (probably the same problem as mentioned by yfarjoun), on a boundary value problem of the form $y'(t) = (\lambda A_1 + A_2(t)) y(t)$ with $y$ specified as $t \to \pm \infty$. This is very similar to a Sturm-Liouville problem except that the differential operator is not self-adjoint. The application we're interested in is to do stability analysis of a travelling wave of a 2d reaction-diffusion equation. The main problem is that $y(t)$ is a fairly big vector with up to about 200 entries. 
For details, please ask or see the paper at http://arxiv.org/abs/0805.1706 and references therein.