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Grid-Computing pp 149–205Cite as

Numerische Verfahren für gewöhnliche Differentialgleichungen

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Zusammenfassung

Die mathematische Modellierung naturwissenschaftlicher, technischer und ökonomischer Prozesse basiert sehr häufig auf Systemen gewöhnlicher Differentialgleichungen. Durch die Hinzufügung algebraischer Gleichungen an einem oder beiden Rändern des zugrunde liegenden Intervalls entstehen daraus Anfangs- bzw. Zweipunkt-Randwertprobleme. Da geschlossene analytische Lösungen derartiger Probleme nur in wenigen Ausnahmefällen zur Verfügung stehen, müssen numerische Verfahren zum Einsatz kommen. In diesem Kapitel sollen die für das Grid Computing geeigneten Mehrfach-Schießverfahren zur Lösung von Zweipunkt-Randwertproblemen sowie die Klasse der Runge-Kutta-Verfahren zur Lösung von Anfangswertproblemen dargestellt werden. Dabei stellen die Runge-Kutta-Verfahren auch einen wichtigen Baustein der Schießverfahren dar.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, 07743, Jena, Geramny

    Martin Hermann

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  1. Martin Hermann
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Correspondence to Martin Hermann .

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  1. Fak. Mathematik und Informatik, Inst. Informatik, Universität Jena, Ernst-Abbe-Str. 2, Jena, 07743, Germany

    Dietmar Fey

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Hermann, M. (2008). Numerische Verfahren für gewöhnliche Differentialgleichungen. In: Fey, D. (eds) Grid-Computing. eXamen.press. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79747-0_8

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