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

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?

Answer 1

[Bill Greene]

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.

[Giuseppe Pontrelli]

You are perfectly right, and I will do as you suggest. However, I want (to avoid the space discretization and solution of a linear system) to try first an iterative procedure as follows:

AT EACH TIME STEP:

0) make a guess of the solution in domain 1 and 2

1) solve the continuous PDE with pdepe in domain 1 imposing as BC the values coming from 2) (or 0 at the first iteration) 2) solve the continuous PDE with pdepe in domain 2 imposing as BC the values coming from 1)

iterate 1-2 till (hopefully) convergence. do you think it is feasible?