A uniform quantitative stiff stability estimate for BDF schemes

• Autorzy: Auzinger W. , Herfort W.
• Języki publikacji: EN

Abstrakty

EN

The concepts of stability regions, A- and A(α)-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.

Słowa kluczowe

EN

BDF schemes; stiff ODEs; stability; companion matrix; univalence

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2006
• Tom: Vol. 26, no. 2
• Strony: 203--227
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Auzinger W.

autor

Herfort W.

• Vienna University of Technology. Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/101, A-1040 Wien, Austria, EU,

Bibliografia

• [1] Auzinger W., Kirlinger G., Canonical forms for companion matrices and applications, in preparation.
• [2] Burckel R. B., An Introduction to Classical Complex Analysis, Vol. 1, Pure and Applied Mathematics, 82. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979.
• [3] Eder A., Kirlinger G., A normal form for multistep companion matrices, Math. Models and Methods in Applied Sciences, 11 (2001) 1, 57-70.
• [4] Hairer E., Norsett S.P., Wanner G., Solving Ordinary Differential Equations I Nonstiff Problems, 2nd ed., Springer-Verlag, 1987.
• [5] Hairer E., Wanner G., Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Springer-Verlag, 1996.
• [6] Kirlinger G., On the convergence of backward differentiation formulas for non-autonomous stiff initial value problems, BIT 41, 5 (2001), 1039-1048.
• [7] Markushevich A. I., Theory of Functions of a Complex Variable, Vol. I, II, III, translated and edited by R. A. Silverman, Second English edition, Chelsea Publishing Co., New York, 1977.