= Solution
Substituting the exact solution and expanding about $t_n$ gives the <local truncation error>
$$
y(t_{n+1})-y(t_n)-\frac h2\bigl(y'(t_n)+y'(t_{n+1})\bigr)
=-\frac{h^3}{12}y'''(t_n)+O(h^4).
$$
Thus the method is consistent of order two; as a stable one-step method it has \b[global convergence order $k=2$].
The order cannot be higher. For $y'=t^2$, $y(0)=0$, the exact solution is $y=t^3/3$, and direct substitution makes the local truncation error exactly
$$
\boxed{-\frac16h^3.}
$$
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