Dymola offers a wide range of ODE and DAE solvers, which the user can choose from depending on the application.
However, I have not been able to find any reference to the details of the related numerical methods. While I understand that some of those informations may be protected, I wonder if any public detail has been made available.
In my specific case, I am interested in the details of high order - Runge Kutta implicit methods used by Dymola: I would like to check the stability properties of those methods (are there L-stable? Or at least A-stable?). Also the RK tableau related to those methods would be a useful information
The Dymola manual in 5.4.3 Selecting the integration algorithm>Dymosim integrators has a table for the integrators and the stiff Runge-Kutta methods
Radau IIa, Esdirk23a, Esdirk34a, Esdirk45a, Sdirk34hw are all listed as A-stable.
The Radau IIa is the normal 3-stage Radau IIa method, sdirk34hw is the 5-stage sdirk-method from Hairer&Wanner Solving Ordinary Differential Equations II (as far as I recall).
The esdirk-methods should correspond to the ones in https://link.springer.com/article/10.1023/B:BITN.0000046811.70614.38
For inline integration the implicit Runge-Kutta methods and Implicit Euler are L-stable sdirk methods (the 4th order is Sdirk34hw - and the lower order ones are uniquely given - see Hairer&Wanner Solving Ordinary Differential Equations II pg 106); and the Rosenbrock methods should be L-stable as well.
The other methods are not A-stable. The Cerk-methods should correspond to https://epubs.siam.org/doi/10.1137/0913084