Abstract
This paper deals with a numerical approximation of a bifurcation problem with corank 2. In the neighborhood of the bifurcation point the nonlinear equation is embedded into an extended system. The regular solution of this system including bifurcation point and null space of the corresponding operator derivative allows approximate computation of the bifurcation point and the null space via general discretization and Newton-like methods. In addition, numerical examples are discussed.
Zusammenfassung
Die numerische Approximation eines Verzweigungsproblems mit Korang 2 wird hier behandelt. In der Umgebung des Verzweigungspunktes wird die nichtlineare Gleichung in ein erweitertes System eingebettet. Die reguläre Lösung dieses Systems, die den Verzweigungspunkt und den Nullraum des entsprechenden Ableitungsoperators enthält, erlaubt die näherungsweise Berechnung von Verzweigungspunkt und Nullraum von allgemeinen Diskretisierungsmethoden und Newton-ähnlichen Verfahren. Anschließend werden numerische Beispiele diskutiert.
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The work of this author is supported by the Friedrich-Naumann Foundation.
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Böhmer, K., Zhen, M. Regularization and computation of a bifurcation problem with corank 2. Computing 41, 307–316 (1989). https://doi.org/10.1007/BF02241220
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DOI: https://doi.org/10.1007/BF02241220