6.4.3 Shooting Method

In this section we derive the stabilized march algorithm used. We start with the description of single or simple shooting, i.e., the integrations are performed over the whole interval, then present shooting with reduced superposition, before we come to multiple shooting. The first improvement reduces the numerical costs, whereas the latter one enhances the stability of the algorithm. By introducing marching techniques like decoupling and reorthogonalization the powerful stabilized march algorithm is obtained. The discussion closely follows the one presented in [200, ch. 4]. The notation in this section has been changed by denoting the dimension of the ODE system simply by N instead of N_ODE to obtain more compact formulae.