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Institutes
Institute for Analysis
Workgroup Nonlinear Partial Differential Equations

Numerische Fortsetzungsmethoden (Winter Semester 2014/15)

In this lecture we will consider the zero set of nonlinear systems of
equations that also depend on one or more parameters. In this case
the zero set is typically not just a single point but a whole curve
(or manifold). Moreover, on these curves typically appear bifurcation
points. These are points, where for example the number of roots
locally changes.

In the important case, that the zero set is in fact the set of steady
states of an ODE, it may well happen that along such a curve the
qualitative behavior of the solution changes: For example a stable
equilibrium may become unstable or a stationary solution becomes a
whole periodic orbit...

We will discuss techniques on how to approximate these zero sets and
how to detect bifurcation points.

In the exercises the algorithms will also be implemented and tested.
Note that these techniques are also implemented in the software
packages auto or Matcont.

Schedule
Lecture: Tuesday 15:45-17:15 SR 3.68
Tuesday 15:45-17:15 Z 1
Problem class: Thursday 15:45-17:15 Z 1
Thursday 15:45-17:15 SR 3.68
Lecturers
Lecturer JProf Dr. Jens Rottmann-Matthes
Office hours: -
Room - Kollegiengebäude Mathematik (20.30)
Email: marion.ewald@kit.edu
Problem classes M.Sc. Robin Braun (Scholarship holder)
Office hours: Tuesday, 10:00 - 11:00 and by appointment
Room 3.031 Kollegiengebäude Mathematik (20.30)
Email: Robin.Flohr@kit.edu

References

  • E. L. Allgower, K. Georg, Numerical Continuation Methods - An Introduction, Springer Series in Computational Mathematics, Vol. 13, 1990
  • W.-J. Beyn, A. Champneys, E. Doedel, W. J. F. Govaerts, Yu. A. Kuznetsov, B. Sandstede, Numerical continuation, and computation of normal forms, Handbook of Dynamical Systems Vol. 2, 2002
  • W. J. F. Govaerts, Numerical Methods for Bifurcations of Dynamical Equilibria, SIAM, 2000
  • H. B. Keller, Numerical methods in bifurcation problems, Lectures on Mathematics and Physics. Mathematics 79, Tata Institute of Fundamental Research, Bombay, 1987

Software