The scheme of an ODE solver can be syntetized as follows:

The task on the top of the red rectangle are normally performed by the user.

Currently an ODE solver is concentrating on the part of this scheme below the red rectangle. A such ODE solver can be classified as of non-expert type.

If the ODE solver try to solve also the task representing the red rectangle (normally done by an human expert in numerical analysis) we can talk about an expert system for ODEs.