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In this work we extend the novel framework developed by Dellnitz, Hessel-vonMolo and Ziessler to the computation of finite dimensional unstable manifoldsof infinite dimensional dynamical systems. To this end, we adapt a set-orientedcontinuation technique developed by Dellnitz and Hohmann for the computation ofsuch objects of finite dimensional systems with the results obtained in thework of Dellnitz, Hessel-von Molo and Ziessler. We show how to implement thisapproach for the analysis of partial differential equations and illustrate itsfeasibility by computing unstable manifolds of the one-dimensionalKuramoto-Sivashinsky equation as well as for the Mackey-Glass delaydifferential equation.

The numerical computation of unstable manifolds for infinite dimensional dynamical systems by embedding techniques