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Differenzengleichungen Und Diskrete Dynamische Systeme

Differenzengleichungen Und Diskrete Dynamische Systeme


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About the Book

Dieses Buch befaßt sich mit der mathematischen Analyse von dynamischen Prozes- sen, deren zeitliche Entwicklung nicht kontinuierlich fließend, sondern in diskreten Zeit- schritten modelliert wird. In den Naturwissenschaften, den Ingenieurwissenschaften und den Wirtschaftswissenschaften wird häufig bei der Untersuchung dynamischer Vorgänge zunächst ein Modell in diskreter Zeit formuliert, also eine Differenzengleichung oder ein (zeit-) diskretes dynamisches System. Anschließend wird dann gewöhnlich durch einen Grenzübergang, bei dem die Länge eines Zeitschritts gegen Null strebt, das diskrete Modell in eine oder mehrere Differentialgleichungen verwandelt. Dieses Vorgehen, das besonders in der Physik sehr erfolgreich ist mit Ausstrahlungen bis hin in die Sozialwis- senschaften, hat den großen Vorteil, daß sich dabei das hochentwickelte mathematische Instrumentarium der Differentialgleichungen und differenzierbaren dynamischen Syste- me anzapfen läßt. Ein Nachteil liegt jedoch darin, daß für eine numerische Auswertung des Modells zum Zwecke der empirischen Überprüfung, das kontinuierliche Modell wie- der in ein diskretes Modell zurückverwandelt werden muß. Das scheint nicht nur ein Umweg zu sein, insbesondere angesichts eines zunehmenden Einsatzes von Computern, sondern birgt auch zusätzliche Probleme, da es trotz gewisser Analogien keine systemati- schen Übersetzungsregeln zwischen Differentialgleichungen und Differenzengleichungen gibt, vor allem nicht, wenn nichtlineare Vorgänge im Spiel sind. Auch aus diesem Grund bildet sich mehr und mehr eine Tendenz heraus, das erstellte diskrete Modell direkt mit Methoden der Differenzengleichungen und diskreten dynamischen Systeme zu untersu- chen; dieses Vorgehen ist etwa in der Biologie und der Ökonomie seit jeher gebräuchlicher als z. B. in der Physik.
About the Author: Ulrich Krause, University of Bremen, Germany; Tim Nesemann, Sparkasse Bremen, Germany.


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Product Details
  • ISBN-13: 9783519026396
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Height: 244 mm
  • No of Pages: 246
  • Series Title: German
  • Sub Title: Eine Einführung in Theorie Und Anwendungen
  • Width: 170 mm
  • ISBN-10: 3519026392
  • Publisher Date: 01 Apr 1999
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Spine Width: 13 mm
  • Weight: 458 gr


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