# (x,y)' ist (x^2-ty,txy)/Polygonzugverfahren/Beispiel/Hohe Berechnung/Computer/Aufgabe

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a) Schreibe ein Computerprogramm, das zu dem Vektorfeld aus Beispiel zu einem Startzeitpunkt ${\displaystyle {}t_{0}}$, einem Startpunkt ${\displaystyle {}P_{0}={\begin{pmatrix}a\\b\end{pmatrix}}}$ und einer vorgegebenen Schrittweite ${\displaystyle {}s>0}$ die approximierenden Punkte ${\displaystyle {}P_{n}}$ berechnet.

b) Berechne mit diesem Programm die Punkte ${\displaystyle {}P_{n}}$ für

1. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1\\1\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{10}}}$, ${\displaystyle {}n=0,1,2,3,4,5,10}$.
2. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1\\1\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{100}}}$, ${\displaystyle {}n=100}$.
3. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1\\1\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{1000}}}$, ${\displaystyle {}n=1000}$.
4. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1,001\\0,999\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{1000}}}$, ${\displaystyle {}n=1000}$.
5. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1,01\\0,99\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{1000}}}$, ${\displaystyle {}n=1000}$.
6. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1,1\\0,9\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{1000}}}$, ${\displaystyle {}n=1000}$.
7. ${\displaystyle {}t_{0}=-3}$, ${\displaystyle {}P_{0}={\begin{pmatrix}-2\\5\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{10}}}$, ${\displaystyle {}n=100}$.
8. ${\displaystyle {}t_{0}=0}$, ${\displaystyle {}P_{0}={\begin{pmatrix}1\\0\end{pmatrix}}}$, ${\displaystyle {}s={\frac {1}{1000}}}$, ${\displaystyle {}n=1000}$.