How to Implement the ADI Method for a 2D Heat Equation in Matlab?

[seyfi]

Hi all
Do you know how to write code Alternating Direct Implicit(ADI) method in Matlab?
I have given 2d heat equation for this.

Thank you

 

[gtoguy97]

The following code can be used to implement the Alternating Direction Implicit (ADI) method in Matlab for a 2-dimensional heat equation:% define parameters Nx = 10; Ny = 10; hx = 1/(Nx+1); hy = 1/(Ny+1); dt = 0.001;% define the matrix A, B, C A = (1/hx^2)*(diag(ones(Nx-1,1),-1) - 2*diag(ones(Nx,1)) + diag(ones(Nx-1,1),1));B = (1/hy^2)*(diag(ones(Ny-1,1),-1) - 2*diag(ones(Ny,1)) + diag(ones(Ny-1,1),1));C = eye(Nx*Ny);% initial conditions U_init = zeros(Nx*Ny,1);% solve the problem using the ADI method U = U_init;for t=1:1000 % X-direction U_temp = reshape(U,Nx,Ny); for j=1:Ny b(:,j) = U_temp(:,j); end U_temp = A\b; % Y-direction U_temp = reshape(U_temp',Ny,Nx); for i=1:Nx b(:,i) = U_temp(:,i); end U_temp = B\b; U_temp = reshape(U_temp',Nx*Ny,1); % update solution vector U = C*(U + dt*U_temp);end