UnstableManifoldCompactMap swMATH ID: 22780 Software Authors: Mireles-James, J.D. Description: Fourier-Taylor Approximation of Unstable Manifolds for Compact Maps: Numerical Implementation and Computer Assisted Error Bounds. We develop and implement a semi-numerical method for computing high order Tay- lor approximations of the unstable manifold at a hyperbolic fixed point of a compact infinite dimensional analytic map. Even though the method involves several layers of truncation our goal is to obtain a representation of the invariant manifold which is accurate in a large region about the fixed point. In order to insure the accuracy of our computations we develop a-posteriori error bounds for the approximations. Numerical implementation of the a-posteriori theory, combined with deliberate control of float- ing point round-off errors (or interval arithmetic), leads to mathematically rigorous computer assisted theorems describing precisely the truncation errors for the approxi- mation of the invariant manifold. The method is illstrated for the Kot-Schaffer model of population dynamics. Homepage: http://cosweb1.fau.edu/~jmirelesjames/unstableManifoldCompactMapPage.html Dependencies: Matlab Related Software: INTLAB; Matlab Cited in: 1 Publication Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds. Zbl 1383.37066Mireles-James, J. D. 2017 Cited by 1 Author 1 Mireles-James, Jason D. Cited in 1 Serial 1 Foundations of Computational Mathematics Cited in 3 Fields 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Numerical analysis (65-XX) Citations by Year