MATLAB: 1D diffusion-reaction model across two-layered slab using pdepe

coupling ode with pdediffusion-reaction modeldiscountinous solutionpdepesystem of pde's

I have a diffusion-reaction model across a two-layered slab (see attachment). Two kind of problems arise when I solve with MATLAB:
1) In each layer, we have a coupling between an ODE and a PDE: How do you cope this with MATLAB? I use PDEPE to solve the system but the BC's for one variable are lacking. Any idea?
2) Because of the interface conditions, the solution may be not continuous in the whole domain, so I believe I cannot solve in one domain with PDEPE. An idea is to solve in two separate domains with PDEPE in an iterative way, imposing conditions coming from the other domain. What do you think?

Best Answer

I am doubtful that pdepe can be used to solve this system.
I suggest using finite differences to discretize in the spatial direction and then use ode15s to solve the resulting system of ODE.
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