deal with coupled equations
 

Hello;

Actually, I am working on simulating the battery characteristics based on the control volume discretization. But, two equations in my model are coupled non-linearly. First equation is for concentration of lithium ions and second is for charge distribution across the battery (I attached a photo of these two Eqs). The later equation consist of a term as follows:



where kappa is a constant and c is the concentration of Lithium ion.

I decided to lag this term and use the concentrations from the previous iteration, so I sent this term to RHS and dealt with it as a source term. But, it caused a large amount of error.

I do not know how can I treat this term differently. So, any new idea is very welcome.

I really appreciate your helps in advance.