Numerical methods to partial differential equations

A center point (i,j) has 4 nearest neighbors.
For a uniform system

If it is none-uniform.

In a periodic boundary conditions (PBCs),
the top and the bottom are connected, so do the left and the right.
All elements are treated as inners.

When a zero-flux border Element(i,j) is visited, do the same thing,
with an additional border visit to do this:


Each corner is treated twice as a border element, no additional work needed.



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