# Thread:

1. ## Finite difference method on boundary value problem

I want to solve boundary value problem in n points, $x_{n}\in(0,1)$:

$-u'(x)(ku'(x))=12x^{2}$

where:
$u(x)\in[0,1]$
$u(0)=0$
$ku'(1)+hu'(1)=hu_{z}$
$x\in R$
with finite difference method instead of finite element method.

I substituted finite difference:
$u'(x)=\frac{u(x_{i-1})-u(x_{i+1})}{2h}$
$h=\frac{1}{n}$

and obtained:
$-kn^{2}[u(x_{i-1})-u(x_{i+1})]^{2}=3x_{i}^{2}$
$i=1,...,n$

And I don't know how to turn that into the matrix equation. Is there a way to do it?
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