This is ASCEND wrapper for the RADAU5 solver, by Ernst Hairer, also referenced in the book by Ascher & Petzold, and with source code available here. From Hairer's webpage, RADAU5 implements "implicit Runge-Kutta method of order 5 (Radau IIA) for problems of the form with possibly singular matrix ; with dense output (collocation solution)."
This means that, in principle, RADAU5 can solve a sub-set of possible DAE systems. However since this imposes restrictions on the possible equation forms that can be passed to this solver, whereas the ASCEND language itself imposes no such limitation, we therefore need to find a way to check the equation structure is acceptable before attempting to pass the system to RADAU5 for solution. This work is ongoing.
Shrikanth Ranganadham is working on integrating RADAU5 into ASCEND as part of his current Masters project.