Numerical Analysis Questions & Answers | |
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You're on the right track but it's not as well explained as it could be. 2 points bonus.
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Yes, very good explanation. 3 points bonus.
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Fixed. Good observation, 2 points bonus.
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I don't understand. The relative of $x$? What does this mean? The $x$ interval has been changed to $1\le x\le 2$ everywhere.
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It's not so simple because you need to show that $\Delta t f(t_{n+1/2}, \phi_{n}+\frac{\Delta t}{2}f(t_{n},\phi_{n}+O(\Delta t^2))$ scales with $O(\Delta t^3)$. Note that you can not simply take $O(\Delta t^2)$ out of $f$ as you did. This needs to be done more carefully.
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$\pi$ |