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On Discretizations of Bifurcation Problems

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Bifurcation Problems and their Numerical Solution

Abstract

It is well known that bifurcation points are usually quite sensitive to perturbations. For example, introducing an imperfection in a bifurcation problem may turn two intersecting branches into two non-intersecting ones. In this paper it is shown that discretizing a nontrivial bifurcation problem may have the same effect. In particular, a sufficient criterion is given which relates the effect to the discretization error of the bifurcation point. The theory is developed in an abstract framework in order to show the general applicability of the results. In the applications the emphasis is on finite difference methods from which also the illustrative and numerical examples are drawn

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Konstanz, Postfach 7733, D-7750, Konstanz, Germany

    Wolf-Jürgen Beyn

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  1. Wolf-Jürgen Beyn
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Editors and Affiliations

  1. Dortmund, Germany

    H. D. Mittelmann  & H. Weber  & 

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© 1980 Springer Basel AG

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Beyn, WJ. (1980). On Discretizations of Bifurcation Problems. 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_2

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  • DOI: https://doi.org/10.1007/978-3-0348-6294-3_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1204-6

  • Online ISBN: 978-3-0348-6294-3

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