finding the type equations for a descritized 2-D pde

[asidesi]

So for my assignment i've been tasked with solving a pde that works with heat dissipation in a solid the said solid is a 2-d plate of known width and height.
my problem is that when i've discretised said equation I find it difficult to make sense of the boundary condition in x. here's the following problem and what ive done so far. my main issue resides with not understanding the boundary conditions properly and how to form the seperate equations necessary for the approximation for this particular problem. thanks for reading.

 

[asidesi]

What I forgot to mention is that I'm required to form I believe 9 equations in the domain of the problem which I will then have to put into matrix form and put into the matlab solver to then solve the problem

 

[asidesi]

ok so i understand the boundary conditions for this problem and have managed to understand how to find the points necessary for this to work... However, I am stuck when it comes to figuring out how to find the points of a grid where I dont know the exact co-ordinates of each point. Is it possible to assume that for this I can give a range of data from one end to the other of the unknown and hope that the boundary conditions would make the problem work? Here is a detailed example of the grid that I am looking at with more detailed descriptions of what exactly the boundary conditions are. *****apparently in x- it's a nuemann boundary condition*****