A quest for disconnected branches: a hybrid approach.

Andras A. Sipos (Budapest University of Technology and Economics)

To detect connected sets of the equilibrium paths of nonlinear boundary value problems classical methods of continuation can be applied as long as a solution is known a priori. On the other hand shooting methods can be used for scan disconnected equilibira. To gain all equilibria in a given domain requires a systematic quest.

In my talk I introduce a hybrid method which combines organized shooting with continuation. We define a finite dimensional space into which the global solution of the nonlinear BVP can be embedded. This space is the key to organize a strategy to investigate all the possible solutions systematically.

The method is highly suitable for parallelization, thus the high computational cost is partially neutralized. A recent development (by including a gradient continuation for seeking the equilibrium branches) resulted in a significant speed up and made our algorithm applicable even without the parallel environment.

(Joint work with Gabor Domokos, Imre Szeberenyi and Peter Varkonyi.)