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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

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

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:

I am working on designing a model of artificial muscle to predict the force along with the spatial domain while voltage is applied to the actuator. We consider the artificial muscle as a beam where the charges diffuse along the length. I just know the voltage applied in the clamping, but we don't know the final value of the voltage at the tip so that we can estimate the force at the tip.

The reference: https://iopscience.iop.org/article/10.1088/1361-665X/aae456

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

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?

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:

I am working on designing a model of artificial muscle to predict the force along with the spatial domain while voltage is applied to the actuator. We consider the artificial muscle as a beam where the charges diffuse along the length. I just know the voltage applied in the clamping, but we don't know the final value of the voltage at the tip so that we can estimate the force at the tip.

The reference: https://iopscience.iop.org/article/10.1088/1361-665X/aae456