# The final Boundary Condition is Unknown, Is Backward Euler is still valid to be implemented?

I am working on conductive polymer modeling and supposed to do one-dimensional diffusion model in the thickness of the polymer, however, due to the small value of thickness in micro, when I use the forward approach it leads to instability, no matter how I decrease the number of nodes.

I have to use Backward Euler to counter this issue, however, due to the nature of our system, we can only know the initial boundary condition and not the final value, how I can solve this issue.

The question: Is there any alternative techniques I can use in numerical analysis while the final boundary condition is unknown?

The mathematical modeling: For modelling the system, I am using RC transmission line, the mathematical description here: http://www.swarthmore.edu/NatSci/echeeve1/Ref/trans/Infinite.html • Backward Euler (or implicit euler) does not require knowledge of the final bound conditions or values. You should read about the actual derivation and implementation of the backward euler method. – EMP Apr 25 '19 at 15:48
• Yes, I read it carefully in this helpful link: hplgit.github.io/num-methods-for-PDEs/doc/pub/diffu/html/… – Monika Apr 25 '19 at 15:55
• If you read it carefully and understood it, you wouldn't have this posted this question as the link makes it clear it does not step back in time – EMP Apr 25 '19 at 15:56
• what do you mean by you have no boundary conditions? are you saying you need to solve a problem without boundary or initial conditions? how about you post the actual mathematical description of the problem. – EMP Apr 25 '19 at 16:02
• Hi, there. I assume that you are supposed to model and simulate the conductive properties of your polymer. If you are in a lab, the only way to do that is to connect the ends of it to some sort of connector. In order to do a numerical Simulation, you have to have certain boundary conditions. Lets say you connect one end of your conductor to 1V and the other to a good conductor connected to ground. Then you would have boundary conditions! What are these in your case? Do you really need a time dependent simulation? (i.e. are you testing your polymer with sinosoidal signals?) – MPIchael Apr 26 '19 at 13:29