Considering the following linear multistep method:

$y_{k+2} = y_{k+1} + \frac{h}{12} \left( -f(x_{k},y_{k}) + 8f(x_{k+1},y_{k+1})+ 5f(x_{k+2},y_{k+2}) \right)$

What is it's order? What is the maximum order that this method can attain?

To determine an upper bound for the order, insert $f(x,y)=y$ and $y_k=e^{kh}$ and compute the difference of both sides. $$ e^{2h}-e^h-\frac{h}{12}(-1+8e^h+5e^{2h}) $$ and then insert the Taylor series of the exponential.

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