Linear-Implizite Runge-Kutta-Methoden Und Ihre Anwendung

Name: Linear-Implizite Runge-Kutta-Methoden Und Ihre Anwendung
Brand: Vieweg+teubner Verlag
SKU: 9783815420270
Price: 5105.0 INR
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by Karl Strehmel , Rüdiger Weiner

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ISBN13: 9783815420270
Binding: Paperback
Subject: N/A
Publisher: Vieweg+teubner Verlag
Publisher Imprint: Vieweg+teubner Verlag
Publication Date: February 1, 1992
Pages: 356
Original Price: GBP 39.99
Language: German
Edition: 1992
Item Weight: 372 grams
BISAC Subject(s): Engineering (General)

About The Book

Die mathematische Modeliierung von physikalisch-technischen sowie auch von biologischen Prozessen führt häufig auf Anfangswertprobleme für Systeme gewöhnlicher Differentialgleichungen, retardierter Diffe- rentialgleichungen, Algebra-Differentialgleichungen vom Index 1 sowie auf Anfangs-Randwertprobleme parabolischer Differentialgleichungen. Ihre analytische Lösung ist i.allg. nicht möglich. um quantitative Aussagen über das Verhalten dieser Systeme zu bekommen, sind daher numerische Methoden für die Lösung der vorliegenden Aufgabenklassen von zentraler Bedeutung. Viele der gewöhnlichen und retardierten Differentialgleichungssy- steme besitzen Lösungskomponenten mit stark unterschiedlichem Wachs- tumsverhalten. Man spricht in diesem Fall von steifen Systemen. Stei- fe Differentialgleichungssysteme entstehen auch bei der Behandlung parabolischer Anfangs-Randwertprobleme mittels der longitudinalen Li- nienmethode. Algebra-Differentialgleichungssysteme können als Grenz- fall singulär gestörter Systeme (spezielle steife Systeme) betrachtet werden. Der numerischen Behandlung steifer Systeme wurde in den letzten 30 Jahren gro e Aufmerksamkeit gewidmet. Obwohl seit ungefähr 15 Jahren für derartige Probleme effiziente Software zur Verfügung steht, kön- nen die Untersuchungen zu dieser Thematik bis heute nicht als abge- schlossen angesehen werden. Die Hauptursache hierfür besteht darin, da das Problem der Steifheit sehr vielschichtig sein kann und die verwendeten Diskretisierungsmethoden nicht in allen Fällen zufrieden- stellend arbeiten. Numerische Methoden zur Lösung von Algebra- Differentialgleichungen werden seit Beginn der 70er Jahre und ver- stärkt seit den BOer Jahren untersucht. Steife Systeme stellen hohe Anforderungen an die Stabilität einer Diskretisierungsmethode. Explizite Runge-Kutta-Methoden sind aufgrund ihres begrenzten Stabilitätsgebietes für die Lösung derartiger Syste- me nicht geeignet. Implizite Runge-Kutta-Methoden besitzen ausge- zeichnete Stabilitätseigenschaften, erfordern aber in jedem Integra- tionsschritt die Lösung nichtlinearer Gleichungssysteme.

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