Any help with the following question would be appreciated.
Consider:
$u_{xx}+u_{yy}=0$
in $0
with $u=0$ when $x=0,\ x=1,\ y=1$ and
$u=256x^2(1-x)\ \mathrm{when}\ y=0$
calculate an approximation to the solution of this problem using finite differences with the coarse grid $\Delta x=\Delta y = 1/4$
Thank you for your help.