Linear convection coding basics part-1

% Inputs for the linear convection problem

L = 1;
n = 20,40,80,160;
c = 1;
dt = 1e-3;

% Calculations
x = linspace(0,L,n);
dx = x(2)-x(1);
%dx = L/(n-1)

%Define the start and end position for the square wave
% x_start = 0.1
% x_end = 0.3
% n_start = f(x_start)
% n_end = f(x_end)
n_start = 3;
n_stop = 5;

%Initialize arrays and apply boundary conditions
u = 0.1*ones(1,n);
u(n_start:n_stop) = 0.2;

% BC
u(1) = 0.1;
uold = u;
u_initial = u;

nt = 10
% Time loop
for k = 1:nt
    % spaceloop
    % du/dt = -cdu/dx
    % du/dx - FDS,BDS
    for i = 2:n
    u(i) = uold(i) - (c*dt/dx)*(uold(i) - uold(i-1));
    end
    
    % update old velocities
    uold = u;
    
    % plotting the velocities
    plot(x,u_initial,\'r\')
    hold on
    plot(x,u,\'b\')
    axis([0 1 0 0.2])
    pause(0.3)
 end