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How to fight the wrapping effect

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Book cover Interval Mathematics 1985 (IMath 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 212))

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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.

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References

  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).

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  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).

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  3. Lohner, Rudolf: Anfangswertaufgaben im IRn mit kompakten Mengen für Anfangswerte und Parameter. Diplomarbeit am Institut für Angewandte Mathematik, Universität Karlsruhe (1978).

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  4. 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.

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  5. 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).

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  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.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Freiburg, Freiburg i. Br., West Germany

    Karl Nickel

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  1. Karl Nickel
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Karl Nickel

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© 1986 Springer-Verlag Berlin Heidelberg

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Nickel, K. (1986). How to fight the wrapping effect. In: Nickel, K. (eds) Interval Mathematics 1985. IMath 1985. Lecture Notes in Computer Science, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16437-5_12

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  • DOI: https://doi.org/10.1007/3-540-16437-5_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16437-1

  • Online ISBN: 978-3-540-39779-3

  • eBook Packages: Springer Book Archive

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