Journal
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Volume 18, Issue 3, Pages 1265-1292Publisher
SIAM PUBLICATIONS
DOI: 10.1137/18M1204395
Keywords
set-oriented numerical methods; unstable manifolds; embedding techniques; infinite dimensional dynamical systems
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Funding
- Deutsche Forschungsgemeinschaft [SPP 1881]
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In this work we extend the novel framework developed by Dellnitz, Hessel-von Molo, and Ziessler to the computation of finite dimensional unstable manifolds of infinite dimensional dynamical systems. To this end, we adapt a set-oriented continuation technique developed by Dellnitz and Hohmann for the computation of such objects of finite dimensional systems with the results obtained in the work of Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this approach for the analysis of partial differential equations and illustrate its feasibility by computing unstable manifolds of the one-dimensional Kuramoto-Sivashinsky equation as well as for the Mackey-Glass delay differential equation.
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