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On the control of the global error in stiff initial value problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 912)

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

  1. 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.

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  2. 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.

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  3. Lindberg, B.: Characterizations of Optimal Stepsize Sequences for Methods for Stiff Differential Equations. SIAM J. Numer. Anal., vol. 14, 859–887, (1977).

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  4. Skelboe, S. and Christensen, B.: Backward Differentiation Formulas with Extended Regions of Absolute Stability. BIT, vol. 21, 221–231, (1981).

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  5. 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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