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Gewöhnliche Differentialgleichungen

  • Josef Stoer
  • Roland Bulirsch
Chapter
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Part of the Springer-Lehrbuch book series (SLB)

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
$$y' = f(x,y)$$
genügt; man spricht dann von einer gewöhnlichen Differentialgleichung. Im allg. besitzt (7.0.1) unendlich viele verschiedene Funktionen y als Lösungen. Durch zusätzliche Forderungen kann man einzelne Lösungen auszeichnen. So sucht man bei einem Anfangswertproblem eine Lösung y von (7.0.1), die für gegebenes x 0, y 0 eine Anfangsbedingung der Form
$$y({x_0}) = {y_0}$$
erfüllt.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Josef Stoer
    • 1
  • Roland Bulirsch
    • 2
  1. 1.Institut für Angewandte Mathematik und StatistikUniversität WürzburgWürzburgDeutschland
  2. 2.Zentrum MathematikTechnische Universität MünchenMünchenDeutschland

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