I am trying to establish why, I'm assuming one uses taylor series,(adsbygoogle = window.adsbygoogle || []).push({});

[itex] \frac{\partial u}{\partial t}[/itex](t+k/2, x)= (u(t+k,x)-u(t,x))/k + O(k^2)

I have tried every possible combination of adding/subtracting taylor series, but either I can not get it exactly or my O(k^2) term doesn't work out (it's O(k^1) or O(k^3) )

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# Taylor series for getting different formulas

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