Use the nonlinear finite difference method $($Newton$\text{'}$s method$)$ solve the boundary value problem:

$u^{\text{'}\text{'}}=-(u^{\text{'}}{)}^2-u+lnx,1x2,u(1)=0,u(2)=ln2$

$($a$)$ Set $h=0\mathrm{.}5$ to approximate the solution of $u(x).$ Compare your results to the actual solution

$u(x)=lnx.$

$($b$)$ Now, solve the boundary value problem with $h=[0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1,0\mathrm{.}25].$ Plot your results and the

actual solution.

Note: Please utilize only loops and conditionals in your script. You can use scipy.linalg.solve$()$

function in Python, or the $\frac{\frac{?}{?}}{?}$ operator in MATLAB.