How can I implement a bvp problem in a non uniform grid?

I want toconstruct a difference method for the the numerical approximation of the solution of the following boundary value problem: $u:[a,b]to mathbb{R}$ function,such that $$ -u”(x)=f(x)$$ and $u(a)=0, u(b)=0$ using a non-uniform grid of the form :

begin{align*}
x_{0} =& a
x_{1} =& x_{0} +h_{1}
x_{2} =& x_{1} + h_{2}
vdots
x_{N} =& x_{N-1} + h_{N}
x_{N+1} =& b
end{align*}

where :
$$h_{i} = x_{i} – x_{i-1}$$

for all
$$i = 1,dots,N + 1.$$

and write the resulting linear system.
But how can I do this?