Plots

 Is there a way to make the plot wave move through the domain til x=1?

freq = 1;                                        % Hz
omega = 2*pi*freq;                   % angular speed m/s
c = 10;                                           % m/s
amp = 1;
% Space
dx = 0.001;
xmax = 1;                                    % domain of unit length
lambda = 0.05;                          % size of wave
k = 2*pi/lambda;                      % wavenumber
x = 0:dx:xmax;
Vx = length(x);                         % matrix of propagation in the x direction
u_0 = zeros(size(x));
% defining wave initial conditions 
for i = 1:Vx;
if x(i) < lambda;
    u_0(i) = (1 - cos(k*x(i)))*0.5;
else
    break
end
end
%Time
dt = 0.01;
t = 0:dt:1;
Vt = length(t);

phi = zeros(Vx,Vt);
for n = 1:Vx;
phi(1,i) = u_0(i);
phi(2,i) = u_0(i); 
end
for i = 2:Vt
 for n = 2:Vx-1
    phi(i,n+1) = phi(i,n-1) + (u_0(i)*(dt/dx))*(phi(i+1,n) - phi(i-1,n)/phi(i,n-1));
 end
end

 figure(1)
plot(x,u_0,'.-b');
axis([0 1 0 1])

[Francis Mboya]

preferably using the scheme (phi)

Answer 1

[Laura Proctor]

If you add the following block of code to the end, it will show the wave propagating along the x-axis, but I don't think this is exactly what you envision - particularly since the variable PHI seems to be defined, but not used in the plot. I would imagine that defining a 2-dimensional variable where each column represents the amplitude at a time step and each row gives the amplitude of a specific x-location over time would be useful.

while u_0(end)==0
    u_0 = [ u_0(end-5:end) u_0(1:end-6) ];
    plot(x,u_0,'.-b');
    pause(0.05)
end

[Francis Mboya]

that is the problem i am having. I would like to use phi (leap frog scheme) to propagate along x and make it behave the same way. How do i define that in te plot script, thanks?

[Laura Proctor]

I'm not entirely sure without knowing the equations. It seems like you're trying to perform some numerical analysis, but I'm just not sure of the equations.