central difference coefficient matrix

Faraz Vossoughian

2020 5 4

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Hi im trying to code the following coefiicient matrix A in a for loop in Matlab. N is the total number of elements. And i and j are obtained from k. could someone help me please code the A matrix correctly for any N value.

for k=1:N
    A(k,k) = 4; % the diagonal element, corresponding to Tij, is always 4
%     In the following, we look at the four neighbours of (i,j) that are
%     involved in the 5-point formula
    i = mod(k-1,nx)+1; j = (k-i)/nx+1; %get (i,j) from k
%boundary condtion
    if i==1
        b(k,1)=Tl;
   
    elseif i==nx
        b(k,1)=Tr;
        
    elseif j==1
        b(k,1)=Tb;
    elseif j==ny
        b(k,1)=Tt;
    end
%A matrix construction
if i>1 && j>1
if i==j
            A(j-1,i)=-1;
            A(j,i+1)=-1;
            A(j,i-1)=-1;
            A(j+1,i)=-1;
  
end
end
    
end