% Staggered Leapfrog Script Template
clear;close;

% build a cell-centered grid with N=200 and L=1;
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% define the initial displacement and velocity vs. x
y = exp(-(x-L/2).^2*160/L^2)-exp(-(0-L/2).^2*160/L^2);
v = 0*x; % multiplying x by zero makes an array of zeroes
         % of the same length as x

subplot(2,1,1)
plot(x,y) % plot the initial conditions
xlabel('x');ylabel('y(x,0)');title('Initial Displacement')
subplot(2,1,2)
plot(x,vy) % plot the initial conditions
xlabel('x');ylabel('v_y(x,0)');title('Initial Velocity')

pause;

% Set the wave speed;
c=2; % wave speed

% Suggest to the user that a time step no larger than taulim be used
taulim=h/c;
fprintf(' Courant time step limit %g \n',taulim)
tau=input(' Enter the time step - ')

% Get the initial value of yold from the initial y and vy
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% load the ghost point boundary conditions in yold(1) and yold(N+2)
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tfinal=input(' Enter tfinal - ')
skip=input(' Enter # of steps to skip between plots (runs faster) - ')
nsteps=tfinal/tau;

% here is the loop that steps the solution along

figure  % open a new frame for the animation
for n=1:nsteps
   time=n*tau;  % compute the time
   % Use leapfrog and the boundary conditions to load ynew with y at
   % the next time step using y and yold, i.e., ynew(2:N+1)=...
   % Be sure to use colon commands so it will run fast.
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   %update yold and y
   yold=y;y=ynew;

% make plots every skip time steps
   if mod(n,skip)==0
      plot(x,y,'b-')
      xlabel('x');ylabel('y');
% Print a top label with the time included
      topline=sprintf('Staggered Leapfrog Wave: time= %g',time)
      title(topline)
      axis([min(x) max(x) -2 2]);
      pause(.1)
   end
end