how to calculate the heat of an object in matlab

main.m
% Define parameters
L = 1; % length of object
N = 100; % number of grid points
dx = L/N; % grid spacing
dt = 0.01; % time step
t_final = 1; % final time
alpha = 1; % thermal diffusivity
T_initial = 0; % initial temperature
T_left = 1; % boundary temperature on left side
T_right = 0; % boundary temperature on right side

% Define initial temperature distribution
T = T_initial*ones(N+2, 1);
T(1) = T_left;
T(end) = T_right;

% Define coefficient matrix for implicit method
r = alpha*dt/dx^2;
A = (1+2*r)*speye(N) - r*spdiags(ones(N-1,1)*[-1 2 -1], [-1 0 1], N, N);

% Time-stepping loop
for t = 0:dt:t_final
    T(2:end-1) = A\T(2:end-1);
end

% Plot temperature profile
x = linspace(0, L, N+2)';
plot(x, T);
xlabel('Distance (m)');
ylabel('Temperature (C)');
title(['Temperature Profile at t = ', num2str(t_final), ' s']);
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