The steady state concentration of a chemical in a two-dimensional rectangular box can be described by the Laplace equation:
∂²C/∂x² + ∂²C/∂y² = 0
Given the spatial domain x € [0,4], y € [0,2] and the boundary conditions:
C(0,y) = 75, C(4, y) = 25, C(x,0) = 100, C(x, 2) = 50
Using a finite difference approach with step sizes ∆x = ∆y = 1, solve for the concentration C(x, y) at all internal nodes.
