Abstract
This paper is concerned in a class of bifurcation problems in ordinary differential equations. It is shown how some basic aspects of bifurcation can be handled by standard methods of numerical analysis. The procedure is illustrated by four examples.
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References
R. Bulirsch: Lecture on the Working Conference on Codes for Boundary Value Problems in ODE’s. May 14–17, 1978 in Houston. To be published in Springer Lecture Notes.
R. Bulirsch, J. Stoer, P. Deuflhard: Numerical Solution of Nonlinear Two-Point Boundary Value Problems I. To appear in Numer. Math., Handbook Series Approximation.
M.A. Krasnosel’skii: Topological Methods in the Theory of Nonlinear Integral Equations. New York: Pergamon Press 1964.
W.F. Langford: Numerical Solution of Bifurcation Problems for Ordinary Differential Equations. Numer. Math. 28, 171–190 (1977).
W.E. Olmstead: Extent of the Left Branching Solution to Certain Bifurcation Problems. SIAM J. Math.Anal. 8, 392–401 (1977).
G.H. Pimbley: Eigenfunction Branches of Nonlinear Operators, and their Bifurcations. Lecture Notes, Vol. 104. Berlin-Heidelberg-New York: Springer 1969.
J. Scheurle: Ein selektives Projektions-Iterationsverfahren und Anwendungen auf Verzweigungsprobleme. Numer. Math. 29, 11–35 (1977).
R. Seydel: Numerical Computation of Branch Points in Ordinary Differential Equations. Numer. Math. 31 or 32.
J. Stoer, R. Bulirsch: Einführung in die numerische Mathematik II. Heidelberger Taschenbuch, Band 114. Berlin-Heidelberg-New York: Springer 1973.
H. Unger: Nichtlineare Behandlung von Eigenwertaufgaben. ZAMM 30, 281–282 (1950).
M.M. Vainberg: Variational Methods for the Study of Nonlinear Operators. San Francisco-London-Amsterdam: Holden-Day 1964.
H. Wielandt: Das Iterationsverfahren bei nicht selbstadjungierten linearen Eigenwertaufgaben. Math. Zeitschrift 50, 93–143 (1944).
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Seydel, R. (1979). Numerical Computation of Primary Bifurcation Points in Ordinary Differential Equations. In: Albrecht, J., Collatz, L., Kirchgässner, K. (eds) Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Serie Internationale D’Analyse Numerique, vol 48. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6283-7_13
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DOI: https://doi.org/10.1007/978-3-0348-6283-7_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1098-1
Online ISBN: 978-3-0348-6283-7
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