Abstract
An approach of B. Lindberg [3] to the estimation and control of a norm of the global error is modified and applied to systems of stiff ODE's in partitioned form.
Keywords
- Global Error
- Local Truncation Error
- Stiff Problem
- Implicit Euler Method
- Backward Differentiation Formula
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References
Dahlquist, G., Edsberg, L., Sköllermo, G. and Söderlind, G.: Are the Numerical Methods and Software Satisfactory for Chemical Kinetics? Report TRITA-NA-8005, Dept. of Numerical Analysis and Computing Science, Royal Inst. Technology, Stockholm, 1980. To appear in Springer Lecture Notes from a Symposium at Bielefeld, April 1980.
Dahlquist, G., Liniger, W. and Nevanlinna, O.: Stability of Two-Step Methods for Variable Integration Steps. IBM Research Report RC 8494, September 1980; submitted to SIAM J. Numer. Anal.
Lindberg, B.: Characterizations of Optimal Stepsize Sequences for Methods for Stiff Differential Equations. SIAM J. Numer. Anal., vol. 14, 859–887, (1977).
Skelboe, S. and Christensen, B.: Backward Differentiation Formulas with Extended Regions of Absolute Stability. BIT, vol. 21, 221–231, (1981).
Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations. J. Wiley & Sons 1962.
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© 1982 Springer-Verlag
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Dahlquist, G. (1982). On the control of the global error in stiff initial value problems. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093147
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DOI: https://doi.org/10.1007/BFb0093147
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11199-3
Online ISBN: 978-3-540-39009-1
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