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The numerical calculation of cusps, bifurcation points and isola formation points in two parameter problems. (English) Zbl 0547.65047

Numerical methods for bifurcation problems, Proc. Conf., Dortmund/Ger. 1983, ISNM 70, 502-514 (1984).
[For the entire collection see Zbl 0535.00021.]
The numerical computation of solutions of nonlinear two parameter problems of the form \(f(x,\lambda,\alpha)=0\) are discussed. Here \(x\in {\mathbb{R}}^ n\) is a state variable, \(\lambda\) and \(\alpha\) are real parameters, and f is a smooth function. In physical applications often the main interest is in the calculation of the singular points of f, i.e. the points where \(f_ x(x,\lambda,\alpha)\) is singular. The main aims of the paper are to describe what types of singular points occur generically in \(f(x,\lambda,\alpha)=0\) when \(Rank(f_ x)=n-1,\) and to outline a general approach for the numerical computation of these points. The case \(Rank(f_ x)=n-2\) is also discussed briefly.

MSC:

65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems

Citations:

Zbl 0535.00021