## Wednesday, May 3, Lori Student Center, Room 228, 9:00am

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Matrix-Free Numerical Continuation and Bifurcation

#### Kurt Georg

Department of Mathematics

Colorado State University

A numerical continuation method traces solution branches of
a nonlinear system
H(lambda,x) = 0 where H: R times R^N -> R
which is typically obtained by discretizing a parameter
dependent operator equation. The method is called
matrix-free if the Jacobian of H is not calculated
explicitly, but its action on a vector is given via a
difference approximation of a directional derivative. In
connection with modern (transpose-free) iterative linear
solvers, this is a suitable approach for large systems. We
give an introduction into the technique of matrix-free
numerical continuation and analyze those recent approaches
to numerical bifurcation which permit a matrix-free
approach. A sequence of MATLAB codes, which can be viewed as
a blueprint for the numerical implementation of this
approach, is currently under construction and will be made
available on the internet. Parts of this talk are based on a
200 page survey by Allgower/Georg in the Handbook of
Numerical Analysis.

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Please direct any comments to

Gerhard Dangelmayr at gerhard@math.colostate.edu.