Need help with jacobi iterative method computation - matlab code

I'm having trouble getting my code to work for a jacobi iteration problem. The problem is for a class project titled Numerical solution of heat equation on a 2D rectangular plate, here's a pic of the guidelines:

http://imgur.com/a/a2h9q

heres my code:

%%Part 1- Define N+1 by 2N+1 matrix 

n=10 ;
old_Temp=zeros(n+1,2.*n+1) ;
old_Temp(:,(2.*n+1))=1 ;
old_Temp(n+1,:)=1   ;
old_Temp;

new_Temp=old_Temp;

% Part 2- Define 3 loops

% outermost loop

No=10;
tol=(1*10^-6);
iterations=0;
old_Temp=new_Temp;

while abs(new_Temp-old_Temp) <= tol  % convergence check

for i=2:2*N    % inbetween loop
for j=2:N   % innermost loop

new_Temp(i,j) = (old_Temp(i+1,j) + old_Temp(i-1,j) + old_Temp(i,j+1) + old_Temp(i,j-1))/4; %jacobi computation

end
end

old_Temp(i,j)=new_Temp(i,j);

iterations=iterations+1; % iteration counter

end

| I can't seem to figure out what's wrong with it...it keeps giving me the error

Attempted to access old_Temp(12,2); index out of bounds because size(old_Temp)=[11,21].|

[Walter Roberson]

The code does not define N

Answer 1

[Walter Roberson]

You create a (10+1) * (2*10+1) matrix, but your first index into it, "i", is set to go up to 2*N and your second index "j" is set to go up to N. It appears that you have the limits of the two "for" loops reversed.

[Steven Benmoha]

Hey walt, I actually made a little bit of headway since I posted this, however I have a new problem now. Here's my new code:

% Numerical Solution of Heat Equation
% on a 2-D Rectangular Plate

%%Part 1- Define N+1 by 2N+1 matrix 

n=10 ;
old_Temp=zeros(n+1,2.*n+1) ;
old_Temp(:,(2.*n+1))=1 ;
old_Temp(n+1,:)=1   ;
old_Temp;

new_Temp=old_Temp;

% Part 2- Define 3 loops

% outermost loop

N=10;
tol=(1*10^-6);
iterations=0;
old_Temp=new_Temp;
delta=0;

while delta <= tol  % convergence check

for j=2:2*N   % inbetween loop
for i=2:N  % innermost loop

new_Temp(i,j) = (old_Temp(i+1,j) + old_Temp(i-1,j) + old_Temp(i,j+1) + old_Temp(i,j-1))/4; %jacobi computation

end
end

x=mean(new_Temp(:,N)); 
y=mean(old_Temp(:,N));
delta=abs(x-y);

old_Temp(i,j)=new_Temp(i,j);

iterations=iterations+1; % iteration counter

iterations

% [C,h]=contour(new_Temp,10)
% clabel(C,h)
% title('number of iterations, convergence criterion')
% xlabel('abcd')
% ylabel('efgh')
% pause(1/24)

end

new_Temp

My problem is that it goes through one iteration but then stops and I believe it's because my convergence check is wrong. If you could look at it and maybe tell me what's wrong I'd appreciate it. The convergence criteria

 " must be the absolute difference of the following value between two successive iterations:
the average value of computed temperature on horizontal line j=N "

[Walter Roberson]

Have you considered using

conv2(old_Temp, [0 1 0; 1 0 1; 0 1 0]/4, 'same')

instead of your double-for loop?

[Walter Roberson]

You know that the

old_Temp(i,j)=new_Temp(i,j);

is taking place after the double "for" loop has ended, so the values of "i" and "j" are whatever they happened to last be as a result of the loop? In particular i will be 2*N and j will be N ? So you are modifying only the bottom right hand corner ? But your delta is based upon the middle column, which isn't going to change?

[Steven Benmoha]

The only reason I am using the double for loop is because the project guidelines want the algorithm written out a certain way.

[Walter Roberson]

You could be doing the entire matrix in one step, without even using conv2(). Ah well. In any case look at the other issues I raised.