I am curious what is a principle behind the Stan in solving multiple ODEs (for e.g., PKPD modeling).

For e.g., suppose you have two ODEs:

df_1/dt = g_1

df_2/dt = g_2

which are connected via certain shared parameters in g_1 and g_2.

Plus, assume that we maynot get a closed form solution of the two ODEs.

Then

- how Stan() solve the problem? I would like to know some mathematics/statistical principle for this, and reference will be very appreciated.
- what priors is used for the parameters in g_1 or g_2?

Thank you very much.