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(Un)Stable Manifold Computation via Iterative Forward-Backward Runge-Kutta Type Methods

Zhigunov, Dmitriy
Abstract
I present numerical methods for the computation of stable and unstable manifolds in autonomous dynamical systems. Through differentiation of the Lyapunov-Perron operator in [Casteneda, Rosa 1996], we find that the stable and unstable manifolds are boundary value problems on the original set of differential equation. This allows us to create a forward-backward approach for manifold computation, where we iteratively integrate one set of variables forward in time, and one set of variables backward in time. Error and stability of these methods is discussed.
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2016-12-01
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Undergraduate Honors Theses
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Advisor
Chung, Yu-Min
Day, Sarah
Tracy, Eugene R.
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Mathematics
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https://scholarworks.wm.edu/handle/internal/12767
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