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G. Schranz-Kirlinger:
"Numerical solution of stiff systems I";
Talk: Stability of ODEs, DAEs, PDAEs and Their Discretizations, 2nd Workshop, Berlin, Humbold-Universitaet (invited); 2004-10-08 - 2004-10-12.

The numerical approximation of solutions of differential equations has been and continues to be one of the principal concerns of numerical analysis. Linear multistep methods, in particular Backward Differentiation Formulas (BDF) are widely used for the numerical integration of differential equations and in particular for stiff systems. Such stiff problems appear in a variety of applications. We present several aspects of the concept of stiffness.



The classical convergence theory for linear multistep methods is quite well developed, but there is no comprehensive stiff convergence theory. Convergence results for special classes of stiff problems are given. The influence of a time-dependent transformation to a numerical method is studied.


The approach here is based on the idea to write multistep methods as one-step methods in a higher dimensional space. A special non-diagonalizing decomposition of the occuring companion matrix is introduced. Furthermore some interesting properties of these matrices are presented.