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Shooting Methods for Bifurcation Problems in Ordinary Differential Equations

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Bifurcation Problems and their Numerical Solution

Abstract

We consider multiple shooting methods for bifurcation problems involving boundary value problems for ordinary differential equations. The case of bifurcation from a simple eigenvalue is treated as well as the solution of perturbed bifurcation problems. The original problem is discretizised via shooting techniques. This yields a finite-dimensional bifurcation problem which is solved by a special iteration scheme, having its origin in the theory of Lyapunov and Schmidt. A numerical example demonstrates that our algorithm workes well.

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Authors and Affiliations

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

    Helmut Weber

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  1. Helmut Weber
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  1. Dortmund, Germany

    H. D. Mittelmann  & H. Weber  & 

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© 1980 Springer Basel AG

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Weber, H. (1980). Shooting Methods for Bifurcation Problems in Ordinary Differential Equations. In: Mittelmann, H.D., Weber, H. (eds) Bifurcation Problems and their Numerical Solution. ISNM: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 54. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6294-3_10

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  • DOI: https://doi.org/10.1007/978-3-0348-6294-3_10

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1204-6

  • Online ISBN: 978-3-0348-6294-3

  • eBook Packages: Springer Book Archive

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