Abstract
This set of lecture notes provides an introduction to the numerical solution of bifurcation problems. The lectures are pitched at UK MSc level and the theory is given for finite dimensional operators — so we shall require only matrix theory, finite dimensional calculus, etc. Only the basic principles for three of the most common bifurcations will be discussed, but the hope is that after reading these notes a student should be able to tackle the original journal papers. Almost all the results extend to infinite dimensional operators defined in an appropriate setting, e.g. Banach or Hilbert Spaces.
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Spence, A., Graham, I.G. (1999). Numerical Methods for Bifurcation Problems. In: Ainsworth, M., Levesley, J., Marletta, M. (eds) The Graduate Student’s Guide to Numerical Analysis ’98. Springer Series in Computational Mathematics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03972-4_5
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