You have the following grid:
y
P13
P23
3
P12
P22
2
P11
P21
1
1
2
3
x
You have Poisson's equation of the form
$\nabla^2 u(x, y) = -\pi^2 y \sin(\frac{\pi}{3} x)$
The boundary conditions are mixed such that there is a Neumann condition on the top boundary
given by
$u_y(1, 3) = \frac{\sqrt{243}}{2}$
$u_y(2, 3) = \frac{\sqrt{243}}{2}$
while a Dirichlet condition of $u(x, y) = 0$ exists on the three other boundaries.
Find: Numerically determine the values at P11, P12, P13, P21, P22, and P23.
