I am trying to solve a coupled reaction-diffusion equations, using Crank Nicolson (implicit Finite Differences Method). I know how to solve them separately, but not simultaneously.

Coupled PDE's equations

I transform it to Crank Nicholson form and I obtain:

Crank Nicolson form for equations

Is the equation for Cb(x,t) correct? How can I couple them? I know how to solve them separately applying boundary conditions (Dirichlet both sides for Cf), and Neumann both sides for Cb.

Thank you very much!


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