Mathematics behind the Stan in solving multiple ODEs (for e.g., PKPD modelling)

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

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

Thank you very much.

I don’t think there is a silver bulet that solves all cases, but I suggest you look at this detailed case study.

https://mc-stan.org/users/documentation/case-studies/lotka-volterra-predator-prey.html