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Gewöhnliche Differentialgleichungen

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Einführung in die Numerische Mathematik II

Part of the book series: Heidelberger Taschenbücher ((HTB,volume 114))

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Zusammenfassung

Sehr viele Probleme aus den Anwendungsgebieten der Mathematik führen auf gewöhnliche Differentialgleichungen. Im einfachsten Fall ist dabei eine differenzierbare Funktion y = y(x) einer reellen Veränderlichen x gesucht, deren Ableitung y′(x) einer Gleichung der Form y′(x) = f(x, y(x)) oder kürzer

$$y' = f(x,y)$$
((7.0.1))

genügen soll; man spricht dann von einer gewöhnlichen Differentialgleichung. Im allgemeinen besitzt (7.0.1) unendlich viele verschiedene Funktionen y als Lösungen. Durch zusätzliche Forderungen kann man gewisse Lösungen aus der Menge aller Lösungen aussondern. So sucht man bei einem Anfangswertproblem eine Lösung y von (7.0.1), die für gegebenes x 0, y 0 einer Anfangsbedingung der Form

$$y(x_0 ) = y_0$$
((7.0.2))

genügt.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, 8700, Würzburg, Deutschland

    Josef Stoer

  2. Institut für Mathematik, TU München, Postfach 202420, 8000, München 2, Deutschland

    Roland Bulirsch

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  1. Josef Stoer
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© 1978 Springer-Verlag Berlin Heidelberg

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Stoer, J., Bulirsch, R. (1978). Gewöhnliche Differentialgleichungen. In: Einführung in die Numerische Mathematik II. Heidelberger Taschenbücher, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06866-3_2

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  • DOI: https://doi.org/10.1007/978-3-662-06866-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08840-0

  • Online ISBN: 978-3-662-06866-3

  • eBook Packages: Springer Book Archive

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