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Numerische Integration. Ausarbeitung zum numerischen Praktikum by Kasten, Felix

Numerische Integration. Ausarbeitung zum numerischen Praktikum

by Felix Kasten
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Book cover type: Paperback
  • ISBN13: 9783656375159
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Publication Date:
  • Pages: 28
  • Original Price: USD 25.5
  • Language: German
  • Edition: N/A
  • Item Weight: 50 grams
  • BISAC Subject(s): Reference

Studienarbeit aus dem Jahr 2010 im Fachbereich Mathematik - Angewandte Mathematik, Universität Rostock (Institut für Mathematik), Veranstaltung: Numerisches Praktikum, Sprache: Deutsch, Abstract: In diesem Praktikumsbericht sollen theoretische Grundlagen der numerischen Integration aufgezeigt werden, die ma geblich an der Lösung der Aufgabe beteiligt sind. Hierfür ist es von Bedeutung, grob auf die Verfahren für die numerische Integration einzugehen und anschlie end zu erläutern, wie man mit Hilfe weniger Umformungen des Integrals in ein Anfangswertproblem dieses mittels des Runge- Kutta Verfahrens lösen kann. In diesem Zusammenhang soll auch die MATLAB- Routine ode45 beschrieben werden. An die Vorbetrachtungen schlie t sich die Erklärung der Implementierung an. Dies soll aber nicht nur die Darstellung des Programm- codes beinhalten, sondern auch auf Schwierigkeiten, die bei der Bearbeitung aufgetreten sind, eingehen. Die Gau - Quadratur wird zum einen in einfacher Form, zum anderen mittels der Legendre- Polynome durchgeführt. Die so entstehenden Werte werden zusammen mit dem Ergebnis des implementierten klassischen Runge- Kutta-Verfahrens mit dem analytischen Wert und dem Wert der MATLAB- Routine ode45 verglichen. Es soll also ein Vergleich der Verfahren erfolgen, in dem dann die verschiedenen Methoden und die aus ihnen gewonnenen Ergebnisse, insbesondere mit der analytischen Lösung, verglichen werden. Abschlie end wird eine Schlussfolgerung aus dem Praktikum gezogen. Hierbei sollen persönliche Eindrücke erläutert werden.

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