Numerical Taylor expansions of invariant manifolds in large dynamical systems

Beyn W-J, Kleß W (1998)
Numerische Mathematik 80(1): 1-38.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Beyn, Wolf-JürgenUniBi; Kleß, Winfried
Abstract / Bemerkung
In this paper we develop a numerical method for computing higher order local approximations of invariant manifolds, such as stable, unstable or center manifolds near steady states of a dynamical system. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear (black box) solver and a low dimensional invariant subspace is available, but for which methods like the OR-Algorithm are considered to be too expensive. Our method is based on an analysis of the multilinear Sylvester equations for the higher derivatives which can be solved under certain nonresonance conditions. These conditions are weaker than the standard gap conditions on the spectrum which guarantee the existence of the invariant manifold. The final algorithm requires the solution of several large linear systems with a bordered Jacobian. To these systems we apply a block elimination method recently developed by Govaerts and Pryce [12, 14].
Erscheinungsjahr
1998
Zeitschriftentitel
Numerische Mathematik
Band
80
Ausgabe
1
Seite(n)
1-38
ISSN
0029-599X
Page URI
https://pub.uni-bielefeld.de/record/1625075

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Beyn W-J, Kleß W. Numerical Taylor expansions of invariant manifolds in large dynamical systems. Numerische Mathematik. 1998;80(1):1-38.
Beyn, W. - J., & Kleß, W. (1998). Numerical Taylor expansions of invariant manifolds in large dynamical systems. Numerische Mathematik, 80(1), 1-38. doi:10.1007/s002110050357
Beyn, W. - J., and Kleß, W. (1998). Numerical Taylor expansions of invariant manifolds in large dynamical systems. Numerische Mathematik 80, 1-38.
Beyn, W.-J., & Kleß, W., 1998. Numerical Taylor expansions of invariant manifolds in large dynamical systems. Numerische Mathematik, 80(1), p 1-38.
W.-J. Beyn and W. Kleß, “Numerical Taylor expansions of invariant manifolds in large dynamical systems”, Numerische Mathematik, vol. 80, 1998, pp. 1-38.
Beyn, W.-J., Kleß, W.: Numerical Taylor expansions of invariant manifolds in large dynamical systems. Numerische Mathematik. 80, 1-38 (1998).
Beyn, Wolf-Jürgen, and Kleß, Winfried. “Numerical Taylor expansions of invariant manifolds in large dynamical systems”. Numerische Mathematik 80.1 (1998): 1-38.