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A fast method for approximating invariant manifolds

By J. Guckenheimer and A. Vladimirsky


The task of constructing higher-dimensional invariant manifolds for dynamical systems can be computationally expensive. We demonstrate that this problem can be locally reduced to solving a system of quasi-linear PDEs, which can be efficiently solved in an Eulerian framework. We construct a fast numerical method for solving the resulting system of discretized non-linear equations. The efficiency stems from decoupling the system and ordering the computations to take advantage of the direction of information flow. We illustrate our approach by constructing two-dimensional invariant manifolds of hyperbolic equilibria in R 3 and R 4.

Year: 2004
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