The numerical approximation of center manifolds in Hamiltonian systems

Du WH, Beyn W-J (2003)
Journal of Mathematical Analysis and Applications 288(1): 28-46.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
In this paper we develop a numerical method for computing higher order local approximations of center manifolds near steady states in Hamiltonian systems. 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 solver and a low-dimensional invariant subspace is available. Our method combines this restriction from linear algebra with the requirement that the center manifold is parametrized by a symplectic mapping and that the reduced equation preserves the Hamiltonian form. Our approach can be considered as a special adaptation of a general method from Numer. Math. 80 (1998) 1-38 to the Hamiltonian case such that approximations of the reduced Hamiltonian are obtained simultaneously. As an application we treat a finite difference system for an elliptic problem on an infinite strip. (C) 2003 Elsevier Inc. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
Journal of Mathematical Analysis and Applications
Band
288
Ausgabe
1
Seite(n)
28-46
ISSN
PUB-ID

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Du WH, Beyn W-J. The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications. 2003;288(1):28-46.
Du, W. H., & Beyn, W. - J. (2003). The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications, 288(1), 28-46. doi:10.1016/j.jmaa.2003.05.001
Du, W. H., and Beyn, W. - J. (2003). The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications 288, 28-46.
Du, W.H., & Beyn, W.-J., 2003. The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications, 288(1), p 28-46.
W.H. Du and W.-J. Beyn, “The numerical approximation of center manifolds in Hamiltonian systems”, Journal of Mathematical Analysis and Applications, vol. 288, 2003, pp. 28-46.
Du, W.H., Beyn, W.-J.: The numerical approximation of center manifolds in Hamiltonian systems. Journal of Mathematical Analysis and Applications. 288, 28-46 (2003).
Du, WH, and Beyn, Wolf-Jürgen. “The numerical approximation of center manifolds in Hamiltonian systems”. Journal of Mathematical Analysis and Applications 288.1 (2003): 28-46.