A predictor-corrector method for the approximate solution of $y'=f(t,y)$ uses

\begin{equation} y_{n+1}-y_{n}=hf_{n} \tag P

\end{equation}

as predictor and

\begin{equation} y_{n+1}-y_{n}=\frac{h}{2}(f_{n+1}+f_{n}) \tag C

\end{equation}

as corrector. Determine the orders of the PECE,PECECE methods, with explanation.

=>

I know the PECE ($P=P* +1$)

Order of Predictor $P=1$

Order of Corrector $C=2$

So, Order of PECE is $2$

Similarly,

PECECE ($P=P* +2$)

Order of Predictor $P=1$

Order of Corrector $C=2$

So, Order of PECECE is also $2$ (limited by order of truncation error)

CAN SOMEONE PLEASE GIVE ME BETTER EXPLANATION THAN MINE.