Beispiel: Vermehrte Jacobi-Matrix für Stiffb und Stiffr

Funktionen > Lösen und Optimieren > Lösungsalgorithmen für Differentialgleichungen > Beispiel: Vermehrte Jacobi-Matrix für Stiffb und Stiffr

Verwenden Sie die Funktion Jacob, um die vermehrte Jacobi-Matrix für eine gewöhnliche Differentialgleichung zu berechnen, und stellen Sie sie anschließend als Eingabe für die Gleichungslöser Stiffb und Stiffr bereit.

1. Definieren Sie ein System mit vier Unbekannten:

Die yi-Variablen sind Funktionen von x.

2. Legen Sie die Konstanten im System fest.

3. Legen Sie die Anfangswerte fest.

4. Definieren Sie eine Vektorfunktion D(x,y), die der rechten Seite des Systems entspricht.

5. Verwenden Sie die Funktion augment, um die vermehrte Jacobi-Matrix zu erstellen:

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6. Rufen Sie die Funktionen Stiffb und Stiffr auf:

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Die zurückgegebenen Matrizen enthalten fünf Spalten, die der Anzahl von Punkten und den Lösungen für die vier Unbekannten entsprechen.

7. Extrahieren Sie die Lösungen für die vier Unbekannten aus den zurückgegebenen Matrizen Stiffb und Stiffr:

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8. Plotten und vergleichen Sie die zurückgegebenen Lösungen für jede Unbekannte in den beiden Funktionen:

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Die Diagramme zeigen, dass die beiden GDGL-Gleichungslöser identische Lösungen zurückgeben.

Zugehörige Themen

GDG-Löser

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