Summary
The numerical computation of branch points in systems of nonlinear equations is considered. A direct method is presented which requires the solution of one equation only. The branch points are indicated by suitable testfunctions. Numerical results of three examples are given.
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Abbott, J.P.: An efficient algorithm for the determination of certain bifurcation points. J. Computational and Applied Math.4, 19–27 (1978)
Crandall, M.G., Rabinowitz, P.H.: Bifurcation from simple eigenvalues. J. Functional Anal.8, 321–340 (1971)
Haselgrove, C.B.: The solution of non-linear equations and of differential equations with two-point boundary conditions. Comput. J.4, 255–259 (1961)
Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems. In: Applications of bifurcation theory (P. Rabinowitz, ed.) New York: Academic 1977
Meyer-Spasche, R.: Numerische Behandlung von elliptischen Randwertproblemen mit mehreren Lösungen und von MHD Gleichgewichtsproblemen. Report 6/141 of the Institut für Plasmaphysik, Garching/München (1975)
Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. New York: Academic 1970
Poenisch, G., Schwetlick, H.: Ein lokal überlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven. Bericht 07-30-77 der Technischen Universität Dresden, 1977
Rheinboldt, W.C.: Numerical methods for a class of finite dimensional bifurcation problems. SIAM J. Numer. Anal.15, 1–11 (1978)
Seydel, R.: Numerical computation of branch points in ordinary differential equations. Numer. Math.32, 51–68 (1979)
Stoer, J., Bulirsch, R.: Einführung in die Numerische Mathematik II. Heidelberger Taschenbuch, Band 114. Berlin-Heidelberg-New York: Springer 1978
Simpson, R.B.: A method for the numerical determination of bifurcation states of nonlinear systems of equations. SIAM J. Numer. Anal.12, 439–451 (1975)
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Seydel, R. Numerical computation of branch points in nonlinear equations. Numer. Math. 33, 339–352 (1979). https://doi.org/10.1007/BF01398649
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DOI: https://doi.org/10.1007/BF01398649