PDE Battery Model with multiple domains

I have the following set of PDEs for my battery model. They relate Cs(non-dimensional concentration of lithium in the solid), C(non-dimensional electrolyte lithium concentration) and u(non dimensional overpotential) to one another through J3 the exchange current density. Tau is the time divided by a constant. It is a 1-D model. I am trying to model all 3 domains of my battery using pdepe and initial cond's and BC's. When i run my code it is giving me a tolerance error where the time step is below the minimum limit. There are some boundary conditions on the internal surfaces between the anode and electrolyte and between the electrolyte and cathode that i also wish to input but have done so in the eqn section instead of the BC section as they are not really boundaries. Could i get some suggestions on how to make the code function? I have also included a Nernst Planck file that solves a single PDE of the Nernst Planck equation that does work, called nernstplanckdiffusion2.

[Bill Greene]

It isn't immediately obvious to me why ode15s is terminating prematurely. pdepe problems of this complexity often require considerable effort to debug.

I do not know whether you will be able to accurately model the interface jump conditions using pdepe. But you should update the description of your model to include these jump conditions, the boundary conditions, and the initial conditions. I can say for certain that the approach you have taken to account for the jump conditions will NOT work.

Beyond that, I suggest doing the following as initial steps to debug this:

1. Create the mesh so that you have mesh points exactly at the interfaces.
2. Remove the jump conditions from the model and see if pdepe can solve that model.