PLease solve "your code here part" in matlab

In class we numerically solved the Laplace equation in $20$ :

$m_{mx}+s_y=0$

$w_{l-1,j}+w_{i+1,j}+w_{l,j-1}+w_{l,j+1}-4w_{l,j}=0$

The $9$ unknowns, $9$ linear equations were put into matrix form:

We could then solve for the unknown interior points wint using backslash, and thus, put together the whole matrix of $w(x,y)$ points $($including exterior points$)$

Much of the code is already provided. You need to create the A matrix and $b$ vector. Then solve for wint using backslash.

Indexing is critical. Your $f$ vector containing the boundary conditions should start at the bottom left of the square and rotate counter$-$clockwise around the edge, not including corners. That is:

Your uint vector should contain the interior nodes in the ordering:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}={\left[\begin{array}{ccccccccccccc}{u}_{1,1}& u_{2,1}& \text{c}\text{d}\text{o}\text{t}\text{s}& u_{-1,1}& u_{1,2}& u_{2,2}& \text{c}\text{d}\text{o}\text{t}\text{s}& u_{n-1,2}& \text{c}\text{d}\text{o}\text{t}\text{s}& u_{1,n-1}& u_{2,n-1}& \text{c}\text{d}\text{o}\text{t}\text{s}& u_{-1,n-1}\end{array}\right]}^T$

My code will reshape your uint vector and put it in the right place in the $u$ matrix. My code will also display some plots. Matlab Grader will check your values of the $f,b,$ wint vectors and A matrix.

Script