Extrapolationsmethoden zur Bestimmung der Beweglichen Singularitäten von Lösungen Gewöhnlicher Differentialgleichungen

  • Helmut Werner
Part of the ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique book series (ISNM, volume 49)


In this paper we describe a technique for the localization of the movable singularities that arise with the solutions y(x) of initial value problems of ordinary differential equations. The main tool are non linear splines u(x) that approximate y(x) with respect to its singular behaviour, containing the location x* and the order of the singularity as parameters used to achieve a good matching of u(x) to y(x). Furthermore an extrapolation technique is employed to get upper and lower bounds for x*.


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    H. Arndt, Lösung von gewöhnlichen Differentialgleichungen mit nichtlinearen Splines Schriftenreihe des Rechenzentrums der Universität Münster, Heft Nr. 35 (1979).Google Scholar
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    W. W. Golubew, Vorlesungen über Differentialgleichungen im Komplexen. Deutscher Verlag der Wissenschaften, Berlin 1958.Google Scholar
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    H. Werner, An Introduction to Non Linear Splines in: Polynomial and Spline Approximation, edited by B. N. Sahney, Reidel Publishing Co. Dordrecht 1979. (Dieser Übersichtsartikel enthält weitere Literaturangaben. )Google Scholar

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© Springer Basel AG 1979

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  • Helmut Werner

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