Esempio: funzione aumentata di Jacobi per Stiffb e Stiffr

Funzioni > Soluzione e ottimizzazione > Solutori di equazioni differenziali > Esempio: funzione aumentata di Jacobi per Stiffb e Stiffr

Utilizzare la funzione Jacob per calcolare la matrice aumentata di Jacobi per un'equazione differenziale ordinaria (ODE) e quindi specificarla come input per i solutori Stiffb e Stiffr.

1. Definire un sistema di quattro incognite:

Le variabili yi sono funzioni di x.

2. Definire le costanti nel sistema.

3. Definire i valori iniziali.

4. Definire una funzione vettore D(x,y) corrispondente al lato destro del sistema.

5. Utilizzare la funzione augment per creare la matrice aumentata di Jacobi:

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6. Chiamare le funzioni Stiffb e Stiffr:

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Le matrici restituite contengono 5 colonne corrispondenti al numero di punti e le soluzioni per le quattro incognite.

7. Estrarre le soluzioni per le quattro incognite dalle matrici Stiffb e Stiffr restituite:

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8. Confrontare le soluzioni restituite per ogni incognita delle due funzioni e tracciarne i grafici:

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