pde matlab code for wave equation

this is my code so far, however it seems matlab is not going through my iteration and simply plotting the initial condition. can someone please check to see where i am going wrong?

% setup and  parameters
Nx = 50;  % number of mesh points
dx = 10/Nx; % spactial mesh 
Tend = 1;% solve from t=0..tmax
c = 0.2*ones(Nx-1,1); %  vector  of ones , size Nx-1
dt = 0.95*dx/max(c);% time step
t = 0:dt:Tend;  % time mesh
R = round(Tend/dt); %  number of timesteps
x = linspace(0,10,Nx-1);% create spatial coordinates vector for plots

% set up differentiation matrices 
e = ones(Nx-1,1); % vector of ones of same size x
Dx  =(spdiags([-e e],[-1 1],Nx-1,Nx-1)); % 1st order matrix
Dxx = (spdiags([e -2*e e], [-1 1], Nx-1,Nx-1)); % 2nd order matrix

% initialization and initial conditions,   u = zero at boundaries 
u = exp(-100 * (x-5).^2);
data = u; % store data 

for n = 2:R-1 % iteratre, step in time
    for j= 2:Nx-1
   u(j,n+1) = u(j,n) - 0.5*dt/dx * c.*(Dx*u(j,n)) + 0.5*(dt/dx)^2 * c.^2*(Dxx*u(j,n)) ...
      + 0.125*(dt/dx)^2 * c.*(Dx*c).*(Dx*u(j,n));
    end
end

(plot(x,data,'o - r'));xlabel('x'); ylabel('u'); title('Solution at t=1')

[Torsten]

R=1, so the loop over n is never executed.

[nandine]

R is my time step,and I need my scheme to start at t=0 to t=1. In in increments of dt

[Torsten]

You use for n=2:R-1, thus for n=2:0, thus the loop is never executed.

Answer 1

[Sigurd Askeland]

It seems you are plotting data in stead of u. When you set data = u before the for loop, any subsequent changes to u are not reflected in data. data is a copy of u, and does not point to the same memory address.