Include your x and y vectors when plotting. You'll have to do some manipulation of y since you create it starting at 2 and decrement to 0. You can also specify the number of contour levels if you want that to match.
You'll also want to format the axes so they use the same spacing (axis equal)
%Defining the constants
L=1; % length
H=2; % Height
deltax=0.05;
deltay=0.05;
Beta=deltax/deltay;
Beta2=Beta^2;
jn=H/deltay; % Maximum number of grid points along y
im=L/deltax; % Maximum number of grid points along x
T1=100; T2=0; T3=0; T4=0; % boundary conditions
y=2:-deltay:0;
x=0:deltax:L;
% initialize T_old to the initial guess values
T_old=zeros(jn+1,im+1);
% set boundary conditions
T_old(1,1:im+1)=T1;
T_old(jn+1,1:im+1)=T3;
T_old(2:jn+1,1)=T2;
T_old(2:jn+1,im+1)=T4;
T_new = T_old;
Error = 0.011; % could be any number that is greater than Errormax
Errormax=0.01;
t=0;
while Error > Errormax
t=t+1;
for i=2:jn
for j=2:im
T_new(i,j)=(1/(2*(1+Beta2)))* (T_new(i-1,j)+T_new(i+1,j)+Beta2*(T_new(i,j+1)+T_new(i,j-1)) ) ;
end
end
Error = sum(sum(abs(T_old-T_new),2)) ;
T_old = T_new;
end
%% create contour plot
contour(x,fliplr(y),T_new,17,'k')
xlabel('X')
ylabel('Y')
axis equal
