Write a MATLAB code to solve the following boundary value problem using the Finite Difference Method:

$2(,)=0$ on the square $0<<1,0<<1$

subject to the boundary conditions

$(0,)=4(0\mathrm{.}5)2$

$(,0)=1$

$$

$=0$ at $=1$

$$

$=0$ at $=1.$

A code to solve the same problem using MATLAB$$s Finite Element Method toolbox has been provided for

you to compare your solution against. You should present your finite difference solution in the form of dotted

contour lines overlaying the finite element solution, in a figure like so:

Your submission should take the form of a MATLAB script or function that solves the problem as described,

and visualises the solution. You are encouraged to adapt the code you have been developing in your maths

workshops. You only need to submit your code and nothing else. We will run your code to mark it$.$