Backward differentiation formulas applied to stiff problems

Gabriela Kirlinger

Institut für Angewandte und Numerische Mathematik, Technische Universität Wien,
Wiedner Hauptstraße 8-10, A-1040 Wien, Austria

g.schranz-kirlinger@tuwien.ac.at

http://www.math.tuwien.ac.at/~gaby

Poster

We present convergence results of backward differentiation formulas applied to several classes of stiff initial value problems and discuss application of these methods to nonlinear stiff problems. An essential tool is the application of an appropriate (nonlinear) transformation to the problem. The influence of the corresponding time-dependent transformation to the numerical method is studied. The approach here is based on the idea to write multistep methods as one-step methods in higher dimensional space. It uses further a non-diagonalizing decompostion of the companion matrix [1], and a suitable variable norm. For details, see [2].