Question

Consider solving the autonomous differential equation \frac{a y}{d t}=f(y) \quad t \in\left[t_{0}, T\right], \quad y\left(t_{0}\right)=y_{0} with the following method with step size h: y_{i+1}=y_{i}+h f\left(\frac{y_{i}+y_{i+1}}{2}\right) . Assume that fis smooth. (1)Derive the leading term of the local truncation error of this numerical-method.

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