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Numerische Methoden für Anfangswertprobleme

In: Eine Einführung in gewöhnliche Differentialgleichungen

Author

Listed:
  • Martin Hermann

    (Friedrich Schiller University, Institute of Applied Mathematics)

  • Masoud Saravi

    (Shomal University, Department of Technical and Engineering)

Abstract

Zusammenfassung Mit diesem Kapitel beginnt der numerische Teil des Buches. Hier werden numerische Methoden für Anfangswertprobleme von Systemen von Differentialgleichungen erster Ordnung untersucht. Beginnend mit dem Konzept der Diskretisierung von Differentialgleichungen wird die Klasse der Runge-Kutta-Verfahren eingeführt. Die Butcher-Schemata einer Vielzahl von Runge-Kutta-Verfahren werden angegeben. Weitere Themen sind Konsistenz, Konvergenz, Schätzung des lokalen Diskretisierungsfehlers, Schrittweitensteuerung, A-Stabilität und Steifheit.

Suggested Citation

  • Martin Hermann & Masoud Saravi, 2024. "Numerische Methoden für Anfangswertprobleme," Springer Books, in: Eine Einführung in gewöhnliche Differentialgleichungen, chapter 0, pages 181-233, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-3996-3_7
    DOI: 10.1007/978-81-322-3996-3_7
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