function Y = stringFreeFixed(Y,c,dt,dx)
%Y = stringFreeFixed(Y,c,dt,dx);
% adavnce PDE solution for fixed (right end) & free (left end) string 
% by one time step, using two previous steps
%  Y <=> [N,3] matrix of [y(:,n-2) y(:,n-1) y(:,n)], string displacements 
%  c --> wave speed
% dt --> time step
% dx --> space step (be sure that c <= dx/dt)

% a constant calculated here rather than in loop
r2 = (c*dt/dx)^2;

% loop over space to determine Y(:,1), paying attention to BC
% free end has unique EOM, so it goes outside space loop
Y(1,3) = r2*(Y(2,2) - Y(1,2)) - Y(1,1) + 2*Y(1,2);
for ii = 2:size(Y,1)-1
    Y(ii,3) = r2*(Y(ii+1,2) + Y(ii-1,2) -2*Y(ii,2)) - Y(ii,1) + 2*Y(ii,2);
end

return