Question: % Define problem parameters a = 2; b = 1; alpha = 1; epsilon = 0.01; T1 = 100; T2 = 100; T3 = 100;
% Define problem parameters
a = 2;
b = 1;
alpha = 1;
epsilon = 0.01;
T1 = 100;
T2 = 100;
T3 = 100;
T4 = 0;
% Discretize the plate into a grid of points
dx = 0.05;
dy = 0.05;
x = 0:dx:a;
y = 0:dy:b;
[X,Y] = meshgrid(x,y);
% Initialize the temperature at each point on the grid
T = (T1 + T2 + T3 + T4) / 4;
% Set the over-relaxation factor
w = 1.5;
% Iterate until convergence is achieved
while 1
% Update the temperature at each point on the grid
for i = 2:length(x)-1
for j = 2:length(y)-1
T(i,j) = (1 - w) * T(i,j) + w * (T(i-1,j) + T(i+1,j) + T(i,j-1) + T(i,j+1)) / 4;
end
end
% Calculate the L2 norm of the temperature distribution
L2norm = sqrt(sum(T.^2)) / numel(T);
% Check if the L2 norm is below the convergence criteria
if L2norm <= epsilon
break;
end
end
% Plot the final temperature distribution
contourf(X,Y,T);
colorbar;
xlabel('x');
ylabel('y');
title('Temperature Distribution');
the code is not working i need to run this code
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