I am trying to solve a set of linear equations of heat transfer conduction using gauss seidel iteration, but my solutions seem not to correct compared to the exact or analytic solution.

this are the codes below.

clear all;

N=4; % Number of columns
M=4; % Number of rows
error_T=ones(4,4);
T_amb = 300;% initial emperatures in matrix
T=ones(4,4)*T_amb;% create 4x4 matrix with Tamb
T_old=zeros(4,4);
T(:,1)=100;% boundary condition at the left
T(:,4)=100;% boundary condition at the right
T(1,:)=500;% boundary condition at the top
T(4,:)=100;% boundary condition at the bottom  
for m=2:M-1;
    for n=2:N-1
        % Calculcate temperature at
        while error_T(m,n)>= 0.01
            T_old=T(m,n);

                  T(m,n) = 1/4*(T(m+1,n)+T(m-1,n)+T(m,n+1)+T(m,n-1)); 

                  error_T(m,n)=abs((T(m,n)-T_old)/T(m,n))*100;

          end
      end
  end