Beispiel: Lösungsblöcke mit Randbedingungen

Lösungsblöcke > Beispiel: Lösungsblöcke mit Randbedingungen

Nutzen Sie das Lösen von Blöcken beim Lösen eines Systems von Gleichungen mit Randbedingungen.

Betrachten Sie den Schnittpunkt eines Kreises und einer Linie. Ohne Randbedingungen bestimmen die Schätzwerte, welche Lösung bei mehreren vorhandenen Lösungen gefunden wird.

1. Fügen Sie einen Lösungsblock ein, legen Sie die Schätzwerte und die Randbedingungen fest, und verwenden Sie anschließend die Gleichungslöserfunktion find, um den Schnittpunkt zwischen der Linie und dem Kreis zu ermitteln.

2. Plotten Sie den Kreis, die Linie und den Schnittpunkt.

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Das Diagramm zeigt, dass diese Lösung einem der beiden Schnittpunkte entspricht; der Problemlöser hat jedoch den Punkt ausgewählt, der den Schätzwerten am nächsten liegt.

3. Ändern Sie die Schätzwerte und berechnen Sie die Lösung neu.

4. Plotten Sie den Kreis, die Linie und den Schnittpunkt.

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Das Diagramm zeigt, dass diese Lösung dem zweiten Schnittpunkt entspricht, da der Problemlöser den Punkt ausgewählt hat, der den neuen Schätzwerten am nächsten liegt.

5. Führen Sie eine zusätzliche Randbedingung der Form x > a ein, wobei a eine Konstante ist. Der Bereich links von der Linie wird jetzt nicht mehr berücksichtigt.

6. Plotten Sie den Kreis, die Linie und den Schnittpunkt. Verwenden Sie eine vertikale Markierung, um die Linie a anzuzeigen.

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Das Diagramm zeigt, dass diese Lösung dem ersten und allein möglichen Schnittpunkt entspricht, da der Problemlöser die neue Randbedingung erfüllen muss.

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