function [UU, x, t] = waveleap(J)
% WAVELEAP Solve wave equation by staggered leap frog method.
% Example:  
%  >> [UU, x, t] = waveleap(100);
%  >> imagesc(x,t,UU), xlabel x, ylabel t
% ELB 4/25/07

c = 1;  L = 100;  tf = 40;

dx = L / J;  x = 0:dx:L;  
dt = 0.5 * dx;  N = ceil(tf / dt);  dt = tf / N;  t = 0:dt:tf;
nu = c * dt / dx;
UU = zeros(N+1,J+1);

UU(1,:) = exp(- (x-50).^2 /4);
W = - c * (UU(1,2:J+1) - UU(1,1:J)) / dx;
V = zeros(1,J+1);

for n = 1:N
    UU(n+1,:) = UU(n,:) + dt * V;
    W = W - nu * (V(2:J+1) - V(1:J));
    V(2:J) = V(2:J) - nu * (W(2:J) - W(1:J-1));
end