function wave(N,steps)
%wave(N,steps) solves the wave equation u_t + u_x = 0 
%    with N+1 gridpoints for 0 <= x <= 1
%    to time t = steps*h, h = 1/N (CFL factor = 1)
%    For the ICs, N >= 20 should be an integer multiple of 10
%    Uses upwind method & periodic BCs

h = 1/N;
dt = h; % CFL factor = 1
u = zeros(N+1,1); % set u to be an N+1 dimensional column vector
j = 0:N/10;
u(j+1) = sin(10*j*pi/N); % ICs
x = linspace(0,1,N+1);
for n = 1:steps % timestep loop
    upwind = [u(N+1);u(1:N)]; % with periodic BC
    u = u - dt*(u-upwind)/h; % upwind method
end
plot(x,u,'r-')
xlabel('x','FontSize',16)
ylabel('u','FontSize',16)

end