Abstract
The accurate location of turning and bifurcation points for ordi-nary differential equations is a problem that has received much attention recently. See, for example, the conference proceedings edited by Mittelmann and Weber [l2], the papers [2], [10], [l6], and several of the articles in the proceedings of the conference at which this paper was presented. The procedures we will describe here are not curve tracing methods, but rather they take the basic equation and imbed it in a larger system so that the füll system is nonsingular and can be solved directly by Newton’s method or a, quasi-Newton method. The efficient characterization of these points is important, in addition to its own sake, for multiparameter problems where branches of such points are computed. See in addition to articles in these proceedings the paper of Doedel [5].
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Griewank, A., Reddien, G.W. (1984). Computation of Generalized Turning Points and Two-Point Boundary Value Problems. 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_27
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