I have trouwble discretisizing the following Non-linear differential equation with stepsize $\displaystyle h=\frac{1}{2}$:

$\displaystyle -y''+y^3=0$ with $\displaystyle y(0)=1, y'(1)=0$

where $\displaystyle y'(1)=0$ is approximated with a second order differential formula.

I'm clueless, I don't quite understand what must be done here. Can someone offer me some guidelines?