How do I generate a matrix based on a formula?

I am currently trying to solve a system of equations and having a problem doing it with matlab. The most noteworthy problem is I don't want to enter the entire matrix manually as it would be massive. Could anyone tell me how to generate a matrix based on the formula?

The formula itself is as follows: -4T(i,j)+T(i+1,j)+T(i,j+1)+T(i-1,j)+T(i,j-1)= Known value

Effectively i and j are the points on a plain and the entire plain is 9x9.

A second question I have is how would I tell matlab that if i or j is 0 the value at that point is 0 as well as if i or j is 9 the value at that point is 0?

[Sam Harris]

I have a similar problem! Did you figure it out in the end?

Answer 1

[Sarah Wait Zaranek]

You can use backslash to solve this:

n = 9;

% Fill in the correct terms for your non-zeros values.

A =diag(-4*ones(n,1),0)  + diag(ones(n-1,1),-1) + ...
    diag(ones(n-1,1),1) + diag(ones(n-(sqrt(n)+1),1),sqrt(n)+1) +...
    diag(ones(n-(sqrt(n)+1),1),-sqrt(n)-1) ;

b would be your known values in a 9x1 matrix. (List them by column all rows in a column and then move to the next column)

Solve by:

x=A\b

You need to worry about boundaries values when + or - j (or i) aren't defined. I ignored them here.