unpl(i)=u(i)-dt/dx*v*(u(i)-u(i-1));

%clear workspaces
clear
clc

% define variables
xmin=-10;      % minimum value of x
xmax=10;       % maximum value of x
N=100;         % no. nodes - 1
dt=0.005;      % timestep
t=0;           % time
tmax=10;       % maximum value of time
v = [1 0 0; 0 1 0; 0 0 2]

% discretise the domain
dx= (xmax-xmin)/N;
x = xmin -dx : dx : xmax + dx;

% initial conditions
for x=xmin:dx:xmax
if x<0
    u0=[0 1 1]
else
    u0=[1 1 2]
end
end

u=u0;
unpl=u0;

% loop through time
nsteps= tmax/dt;
for n=1 : nsteps



    % calculate the FOU scheme
    for i = 2 : N+2
        unpl(i)=u(i)-dt/dx*v*(u(i)-u(i-1));
    end

    % update t and u
    t=t+dt;
    u=unpl;


    % plot solution
    plot(x,u,'bo-','markerfacelor','b');
    shg;
    pause(dt);

end