advection diffusion solution in matlab in matlab

main.m
% Define parameters
L = 1; % Length of the domain
nx = 100; % Number of spatial points
dx = L/nx;
x = linspace(0, L, nx);

T = 1; % Total time
dt = 0.001; % Time step size
nt = T/dt;

D = 0.1; % Diffusion coefficient
u = 1;   % Velocity

% Initial condition
C = zeros(1,nx);
C(1:round(nx/4)) = 1;

figure;
for t = 1:nt
    C_new = C;
    for i = 2:nx-1
       C_new(i) = C(i) + D*dt*(C(i+1)-2*C(i)+C(i-1))/dx^2 - u*dt*(C(i)-C(i-1))/dx;
    end
    C = C_new;
    
    plot(x, C);
    axis([0 L 0 1.2]);
    title(['Time = ', num2str(t*dt)]);
    drawnow;
end
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