Abstract
Instead of the elliptic equation ℒ (u) = 0 we consider the family of nonlinear equations
depending on the scalar parameter λ For ease of notation we assume that Eq. (1) is defined for λ≧O. For each λ≧O there may exist several solutions u (λ) of Eq. (1). A smooth curve (u(λ),λ)∈u×ℝ is called a solution branch. Intersection points of branches are called bifurcation points. At such points ∂ℒ(u*,λ*)/∂u is singular (see λ A in Fig. 13.1.1). For the computation of bifurcation points we refer to § 12.5 and the approaches of Weber [1] and Mittelmann-Weber [1].
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© 1985 Springer-Verlag Berlin Heidelberg
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Hackbusch, W. (1985). Continuation Techniques. In: Multi-Grid Methods and Applications. Springer Series in Computational Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02427-0_13
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DOI: https://doi.org/10.1007/978-3-662-02427-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05722-9
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