Solving Fick's Law by Finite Difference Method

[Stefanie]

Hi, i need help in solving a Fick's Law [ (∂c_k)/∂t = D_k (∂^2 c_k)/(∂x^2 ) ] by Finite Difference Method.
Previously, I tried solving the Fick's Law by using the Separation of Variable method but that was not the correct way as told by my Prof as the correct way is to use Finite Difference Method.

Can anyone teach or guide me on how to solve as I had never learn finite difference method before?

Thanks a lot.

 

[HallsofIvy]

What, exactly, is the problem you are trying to solve? The "finite difference method" is a method of numerically solving differential equations where we are given values at the boundary of a region. Whether "separation of variables" will work on any partial differential equation depends strongly on the geometry of the region. "Fick's law" (also called the "diffusion" or "heat" equation) certainly can be solved by separation of variables on a rectangular region (Fourier series solutions), on a circular or cylindrical region (series of Bessel functions) or on a spherical region (series of spherical harmonics).

 

[Stefanie]

My project is actually on a MatLab simulation but since I'm not required to write out the source code, my Prof wants me to show how can this differential equation can be used to solve using finite difference method instead of a separation variable method. For instance, to transfer the differential equation into the same form as finite difference method.

I look up a few reference book but i still can't seems to understand. Hence, will like to seek help from here.

Thanks.