Abstract
Singularity theory seems to play an important role not only in the theoretical but also in the numerical analysis of bifurcation problems. In this paper we establish a relation between the concept of a universal unfolding and direct methods for the numerical computation of Singular points in bifurcation diagrams. In a direct method the unknown Singular Solution is computed as a regular Solution of a so called defining equation. In particular, we discuss a defining equation for a multiple bifurcation point and demonstrate its application to a reaction diffusion system.
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© 1984 Springer Basel AG
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Beyn, WJ. (1984). Defining Equations for Singular Solutions and Numerical Applications. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_3
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6257-8
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