TY  - JOUR
ID  - Auzinger2006
LB  - Auzinger2006
AU  - Auzinger, Winfried
AU  - Herfort, Wolfgang
TI  - A uniform quantitative stiff stability estimate for BDF schemes
ST  - A uniform quantitative stiff stability estimate for BDF schemes
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 2
SP  - 203
EP  - 227
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.2.203
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.2.203
AB  - The concepts of stability regions, \(A\)- and \(A(\alpha)\)-stability - albeit based on scalar models - turned out to be essential for the identification of implicit methods suitable for the integration of stiff ODEs. However, for multistep methods, knowledge of the stability region provides no information on the quantitative stability behavior of the scheme. In this paper we fill this gap for the important class of Backward Differentiation Formulas (BDF). Quantitative stability bounds are derived which are uniformly valid in the stability region of the method. Our analysis is based on a study of the separation of the characteristic roots and a special similarity decomposition of the associated companion matrix.
KW  - BDF schemes
KW  - stiff ODEs
KW  - stability
KW  - companion matrix
KW  - univalence
SN  - 1232-9274
ER  -