# Potential function - numerical simulation

Using MATLAB, I fixed the potential in a region inside a rectangular plate (100 V) and in the border (50 V). I got the following result of the potential along the plate:

I can't find an intuitive explanation why the potential would decrease to values below the least potential (50 V).

The figure above is wrong because the number of iterations was not enough (200). Here is the same plate with 1000 iterations:

• What math/physical laws did you feed into MATLAB?
– Gert
Commented Jul 22, 2016 at 0:34
• I used the Finite Difference Method, iterating over the matrix of potentials 200 times and updating v(i,j) = 0.25 * ( v(i+1,j) + v(i-1,j) + v(i,j+1) + v(i,j-1) ). Commented Jul 22, 2016 at 0:39
• This method is fun to try when you learn the elegant average-over-boundary property of Laplace's equation -I'm betting you'll find a large number of people on this site who tried it before they began formal training, But it is abominably slow - as you've found, convergence is snail paced. This is therefore a great question for this site. Commented Jul 22, 2016 at 2:41