Opuscula Math. 26, no. 2 (2006), 203-227

Opuscula Mathematica

# A uniform quantitative stiff stability estimate for BDF schemes

Winfried Auzinger
Wolfgang Herfort

Abstract. 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.

Keywords: BDF schemes, stiff ODEs, stability, companion matrix, univalence.

Mathematics Subject Classification: 65L06, 65L20, 15A21, 30C35.

Full text (pdf)

• Winfried Auzinger
• Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8–10/101, A-1040 Wien, Austria, EU
• Wolfgang Herfort
• Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8–10/101, A-1040 Wien, Austria, EU
• Received: 2005-10-04.

Cite this article as:
Winfried Auzinger, Wolfgang Herfort, A uniform quantitative stiff stability estimate for BDF schemes, Opuscula Math. 26, no. 2 (2006), 203-227

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.