I encounter this problem $$\frac{df(u(x))}{dx} = g(x)$$ with $$u(0) = u(1) = 0$$ I first convert it to weak form $f(u(x))v(x)]^1_0 - \int^{1}_0 \frac{dv(x)}{dx}f(u(x))dx =- \int^{1}_0 \frac{dv(x)}{dx}f(u(x))dx = \int^{1}_0v(x)g(x)dx $ by multiplying a test function $v(x)$. Then how should I write it in matrix form? The right hand side does not depend on $u$ explicit.
Thanks in advance.