ON THE MULTIPLE SHOOTING CONTINUATION OF PERIODIC ORBITS BY NEWTON-KRYLOV METHODS

The application of the multiple shooting method to the continuation of periodic orbits in large-scale dissipative systems is analyzed. A preconditioner for the linear systems which appear in the application of Newton's method is presented. It is based on the knowledge of invariant sub-spaces of the Jacobians at nearby solutions. The possibility of speeding up the process by using parallelism is studied for the thermal convection of a binary mixture of fluids in a rectangular domain, with positive results.