Need help with jacobi iterative method computation - matlab code

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Steven Benmoha 2015-5-13

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评论： Walter Roberson 2015-5-13

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].|

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Walter Roberson 2015-5-13

The code does not define N

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Answer 1

Walter Roberson 2015-5-13

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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.

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Steven Benmoha 2015-5-13

编辑：Steven Benmoha 2015-5-13

在 MATLAB Online 中打开

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 "

Steven Benmoha 2015-5-13

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 2015-5-13

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.

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