what is name of this numerical scheme for ode?

what is name of this numerical scheme for ode?

Let's have system of ODEs $$ \dot x(t) = A(t)x(t) $$
I came up with this numerical scheme: $$ x_{n+1} =
e^{\frac{h}{2}A(t_{n+1})}e^{\frac{h}{2}A(t_n)}x_n $$ where $h$ is time
step, $t_n = nh$ and $x_n$ is approximate value of $x(t_n)$.
It comes from idea that at each time $t_n$ I freeze time in matrix $A$ and
move along solution of $\dot x(t) = A(t_n)x(t)$. From this I get scheme:
$$ x_{n+1} = e^{hA(t_n)}x_n. $$ To make it time reversible I modified it
to the form already mentioned.
There has to be a theory of this kind of schemes so I would like to know
its name so I can search for literature a find out more about these
schemes.