2d pde, implicit euler in time, central differencing in space. time loop with jacobi solver, discretized unknown ae aw an as ap, to plot temperature on a plate a 0, 1, 2, 5, 10, 100 seconds in matlab

main.m
% Plate parameters
Lx = 1;  % length in x-direction
Ly = 1;  % length in y-direction
nx = 81; % number of grid points in x-direction
ny = 81; % number of grid points in y-direction
dx = Lx/(nx-1);
dy = Ly/(ny-1);

% Thermal diffusivity
alpha = 1;

% Time parameters
t_end = 100;
dt = 0.01;
nt = round(t_end/dt);

% Initialize temperature
T = zeros(nx,ny);

% Boundary conditions
T(1,:) = 0;    % left
T(nx,:) = 0;   % right
T(:,1) = 100;  % bottom
T(:,ny) = 0;   % top

% Coefficients
ae = alpha/dx^2;
aw = alpha/dx^2;
an = alpha/dy^2;
as = alpha/dy^2;
ap = -(2*ae + 2*as);

% Time loop
for n = 1:nt
    % Jacobi solver
    T_old = T;
    for j = 2:ny-1
        for i = 2:nx-1
            T(i,j) = (1/ap)*(...
                ae*T_old(i+1,j) + aw*T_old(i-1,j) + ...
                an*T_old(i,j+1) + as*T_old(i,j-1));
        end
    end
    
    % Plotting
    if any(n == [1,2,5,10,100])
        figure;
        imagesc(T');
        colorbar;
        title(['Temperature at t=',num2str(n*dt)]);
        xlabel('x');
        ylabel('y');
        axis equal tight;
    end
end
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