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How to fight the wrapping effect

  • Karl Nickel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 212)

Abstract

The main purpose of this paper is not to give Theorems, Algorithms, ..., but to give insight in the cause and the consequences of the wrapping effect and to derive herefrom indications of how to eliminate it.

Keywords

Matrix Function Differential Inclusion Interval Method Decimal Digit Interval Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Conradt, Jürgen: Ein Intervallverfahren zur Einschließung des Fehlers einer Näherungslösung bei Anfangswertaufgaben für Systeme von gewöhnlichen Differentialgleichungen. Diplomarbeit. Freiburger Intervall-Berichte 80/1. Institut für Angewandte Mathematik, Universität Freiburg i.Br. (1980).Google Scholar
  2. [2]
    Gambill, Thomas N. and Robert D. Skeel: Logarithmic Reduction of the Wrapping Effect with Applications to Ordinary Differential Equations. University of Illinois, Manuscript (1984).Google Scholar
  3. [3]
    Lohner, Rudolf: Anfangswertaufgaben im IRn mit kompakten Mengen für Anfangswerte und Parameter. Diplomarbeit am Institut für Angewandte Mathematik, Universität Karlsruhe (1978).Google Scholar
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    Nickel, Karl: Bounds for the Set of Solutions of Functional-Differential Equations. MRC Technical Summary Report # 1782, University of Wisconsin, Madison (1977). Annales Polonici Mathematici 42 (1983), 241–257.Google Scholar
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    Nickel, Karl: Ein Zusammenhang zwischen Aufgaben monotoner Art und Intervall-Mathematik. Numerical Treatment of Differential Equations, Proc. of a conf. held at Oberwolfach, July 4–10, 1976. Ed. by R. Bulirsch, R.D. Grigorieff, and J. Schröder, Springer Verlag, Berlin, Heidelberg, New York, 121–132 (1978).Google Scholar
  6. [6]
    Nickel, Karl: Using Interval Methods for the Numerical Solution of ODE's. MRC Technical Summary Report # 2590. University of Wisconsin, Madison (1983). Freiburger Intervall-Berichte 83/10. Institut für Angewandte Mathematik, Universität Freiburg i.Br., 13–44 (1983). To appear in ZAMM.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Karl Nickel
    • 1
  1. 1.Institut für Angewandte MathematikUniversität FreiburgFreiburg i. Br.West Germany

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