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Lecture notes on numerical analysis of nonlinear equations. (English) Zbl 1130.65119

Krauskopf, Bernd (ed.) et al., Numerical continuation methods for dynamical systems. Path following and boundary value problems. Dordrecht: Springer (ISBN 978-1-4020-6355-8/hbk). Understanding Complex Systems, 1-49 (2007).
It is the primary aim of this exposition to give a short and concise presentation of the ideas behind some basic numerical continuation and bifurcation techniques to be used in stationary and periodic solutions, stability and transition to more complex behavior. The following are its main themes: the implicit function theorem, continuation of solutions, boundary value problems (BVPs), computing periodic solutions, computing connecting orbits, applications of BVP continuation. The material is especially designated for the effective use of the software AUTO and other packages.
For the entire collection see [Zbl 1117.65005].

MSC:

65P30 Numerical bifurcation problems
65J15 Numerical solutions to equations with nonlinear operators
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
37M20 Computational methods for bifurcation problems in dynamical systems
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