I know the difference between the forward (explicit) Euler method and backward (implicit) Euler method in the context of approaching solutions to ODEs.
However, I have a doubt regarding the following method:
$$y_{n+1}=y_n+\frac{h}{2}(f(t_n,y_n)+f(t_{n+1},y_{n+1}))$$
I am not sure whether it is an implicit or an explicit method.
I tend to say it is implicit one step methode because we have to solve an equation to calculate $y_{n+1}.$
Thank you for your help.
You're quite right.
An explicit method is given by $y_{n+1} = F(t_n,y_n)$, with no mention of $y_{n+1}$ on the RHS, and you can compute $y_{n+1}$ directly.
An implicit method is given by $F(t_n,y_n,y_{n+1})=0$, and you have to solve an equation to find $y_{n+1}$.
Both these definitions are for one-step methods: $y_{n+1}$ depends directly or indirectly just on $t_n$ and $y_n$, not on any $y_k$ for $k<n$.