Date Thesis Awarded

12-2016

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Yu-Min Chung

Committee Members

Sarah Day

Eugene R. Tracy

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.

Recommended Citation

Zhigunov, Dmitriy, "(Un)Stable Manifold Computation via Iterative Forward-Backward Runge-Kutta Type Methods" (2016). Undergraduate Honors Theses. William & Mary. Paper 999.
https://scholarworks.wm.edu/honorstheses/999