function udot=ex6_ode(t,u,nu)
% udot=ex6_ode(t,u)
% Burger's equation, finite differences, uniform mesh, central
% differences
% x in [0,1], t>0
% u(x=0)=1, du/dx(x=1)=0
% nu is diffusion coeff, defaults to 1

% mms $Id: $
% {@(#) Tue Jan 27 15:20:40 2009 }

N=500;
uleft=1;
dx=1/N;
x=(1:N)*dx;
if nargin<3
  nu=1;
end

% error checking
if length(u) ~= N
  error('ex6_ode: length(u) is wrong.');
end

for n=1:N
  if n==1  %left
    udot(n,1)=nu*(u(n+1)-2*u(n)+uleft )/dx^2- ...
	      u(n)*(u(n+1)-uleft )/(2*dx);
  elseif n<N-1  %interior
    udot(n,1)=nu*(u(n+1)-2*u(n)+u(n-1))/dx^2- ...
	      u(n)*(u(n+1)-u(n-1))/(2*dx);
  else %right
    % approximate Neumann b.c.
    uright=u(n);
    udot(n,1)=nu*(uright-2*u(n)+u(n-1))/dx^2- ...
	      u(n)*(uright-u(n-1))/(2*dx);
  end
end