t(i, n+1) = t(i, n) + alpha * dt / dx^2 * (t(i+1, n) - 2 * t(i, n) + t(i-1, n)); in matlab

In MATLAB, you can implement the given equation using a nested for loop to iterate over the grid points and update the temperature values at each iteration. Here's an example of how you can implement it:

main.m
% Define parameters
alpha = 1;   % thermal diffusivity constant
dt = 0.1;    % time step
dx = 0.2;    % spatial step

% Define grid size
N = 10;      % number of grid points
T = zeros(N); % initialize temperature grid

% Set initial condition
T(:,1) = 0;   % initial temperature distribution at time t = 0

% Iterate over time steps
for n = 1:N-1
    for i = 2:N-1
        T(i,n+1) = T(i,n) + alpha * dt / dx^2 * (T(i+1,n) - 2 * T(i,n) + T(i-1,n));
    end
end
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In this example, N represents the number of grid points in the x-direction. We iterate over time steps n and spatial points i to calculate the updated temperature T(i,n+1) based on the given equation.

Note that this implementation assumes that the boundary conditions are already set for the temperature grid T. You may need to modify the code to include boundary conditions if necessary.