Abstract
One class of examples of nonlinear boundary value problems whose discretizations in general inherit bifurcation properties from the continuous case are problems with symmetries. We analyze the behaviour of a generalized inverse iteration method for the numerical Solution of these problems near a symmetry-breaking pitchfork bifurcation point. While the computation of Symmetrie solutions does not represent any difficulties it is shown that a suitable form of the algorithm may be used to determine the bifurcating branch of non-symmetric solutions in a very stable and efficient way. The theoretical results are confirmed by numerical results for a classical example.
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Mittelmann, H.D. (1984). Continuation Near Symmetry-Breaking Bifurcation Points. 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_22
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_22
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6257-8
Online ISBN: 978-3-0348-6256-1
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