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On the numerical approximation of secondary bifurcation problems

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Numerical Solution of Nonlinear Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 878))

Abstract

We discuss stable numerical methods for the approximation of the solutions of a nonlinear parameter - dependent equation near a non-trivial bifurcation point. The problem of finding the bifurcation point is reformulated as a well-posed equation of higher dimension. The nearby branches can be calculated in a stable manner after applying a certain transformation having its origin in the Lyapunov — Schmidt theory. We also treat the perturbed bifurcation problem and present numerical results.

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Authors and Affiliations

  1. Abteilung Mathematik, Universität Dortmund, Postfach 50 05 00, D-4600, Dortmund 50, Deutschland

    H. Weber

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  1. H. Weber
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Eugene L. Allgower Klaus Glashoff Heinz-Otto Peitgen

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© 1981 Springer-Verlag

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Weber, H. (1981). On the numerical approximation of secondary bifurcation problems. In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090690

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  • DOI: https://doi.org/10.1007/BFb0090690

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10871-9

  • Online ISBN: 978-3-540-38781-7

  • eBook Packages: Springer Book Archive

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