Hi, thanks a lot for helping me clear this problem.
As i mentioned before,: I am trying to solve a nanometric species transport problem. Where the species have to travel from the bottom face of a cuboid box (25nm x 25nm x100nm) to the top face (where they exit). I inspected the jacobian matrix carefully and i came to understand that at some elements, the influx rate was orders higher than the outflux rate. This did not let the possibility of species decay/transport out of that element (if they flow out they will be pushed back into that element). This probably resulted in undamped oscillations in the system’s dynamics. This was the main reason for ODE solver failure.
I Identified the specific locations where this occured and added an additional decay mode to the existing dynamics to force the species to decay in such elements. Now after doing the same, CVODE_BDF works just fine. QNDF also works fine. Exponential solvers Exprb32 and 43 are extremely slow for the working problem. It was more of a Physics related issue than an ODE-related issue (Sorry for being the Patrick)
Also, I work on a lot of physics-based modelling for high voltage applications, FEM and wireless power transfer. So if you had any problems in such domains, I would be happy to reciprocate.