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Let's work through an example of solving Laplace's equations in two
dimensions. The problem that we will solve is the calculation of
voltages in a square region of space. The boundary conditions for
this problem involve 0 V all around the square except the top side,
which is held at 100V. What is the voltage as a function of space
inside the square? Our first step is to sample the square space so
that we can describe it using a computer. For simplicity, we will
use a 5 x 5 array of voltage values, as shown below: |
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